diff --git a/changelog_entry.yaml b/changelog_entry.yaml
index e69de29..500a9d3 100644
--- a/changelog_entry.yaml
+++ b/changelog_entry.yaml
@@ -0,0 +1,6 @@
+- bump: minor
+  changes:
+    added:
+    - Benchmarking experiments for wealth imputation paper draft.
+    - MDN model to experiments run in imputing-from-scf-to-cps.ipynb.
+    - Privacy & Terms to microimputation-dashboard.
diff --git a/microimputation-dashboard/app/page.tsx b/microimputation-dashboard/app/page.tsx
index a8bc1b6..8c731ae 100644
--- a/microimputation-dashboard/app/page.tsx
+++ b/microimputation-dashboard/app/page.tsx
@@ -8,12 +8,61 @@ import { parseImputationCSV } from '@/utils/csvParser';
 import { ImputationDataPoint } from '@/types/imputation';
 import { parseDeeplinkParams, GitHubArtifactInfo } from '@/utils/deeplinks';
 
+function PrivacyModal({ isOpen, onClose }: { isOpen: boolean; onClose: () => void }) {
+  if (!isOpen) return null;
+
+  return (
+    <div className="fixed inset-0 bg-black bg-opacity-50 z-50 flex items-center justify-center p-4">
+      <div className="bg-white rounded-lg max-w-lg w-full p-6 shadow-xl">
+        <h2 className="text-xl font-bold text-gray-900 mb-4">Privacy & Terms of Use</h2>
+
+        <div className="space-y-4 text-sm text-gray-700">
+          <div>
+            <h3 className="font-semibold text-gray-900 mb-1">Data Privacy</h3>
+            <p>
+              All data uploaded to this dashboard is processed entirely within your browser.
+              No data is transmitted to or stored on PolicyEngine servers. When you close or
+              refresh this page, all loaded data is cleared from memory.
+            </p>
+          </div>
+
+          <div>
+            <h3 className="font-semibold text-gray-900 mb-1">Disclaimer</h3>
+            <p>
+              This tool is provided &quot;as is&quot; without warranty of any kind, express or implied.
+              PolicyEngine assumes no responsibility for the security, accuracy, or confidentiality
+              of any data you choose to load into this application.
+            </p>
+          </div>
+
+          <div>
+            <h3 className="font-semibold text-gray-900 mb-1">User Responsibility</h3>
+            <p>
+              Users are solely responsible for ensuring they have appropriate rights to use any
+              data loaded into this dashboard and for compliance with applicable data protection
+              regulations.
+            </p>
+          </div>
+        </div>
+
+        <button
+          onClick={onClose}
+          className="mt-6 w-full bg-blue-600 hover:bg-blue-700 text-white font-medium py-2 px-4 rounded-md transition-colors"
+        >
+          Close
+        </button>
+      </div>
+    </div>
+  );
+}
+
 function HomeContent() {
   const [data, setData] = useState<ImputationDataPoint[]>([]);
   const [fileName, setFileName] = useState<string>('');
   const [showDashboard, setShowDashboard] = useState(false);
   const [isLoadingFromDeeplink, setIsLoadingFromDeeplink] = useState(false);
   const [githubArtifactInfo, setGithubArtifactInfo] = useState<GitHubArtifactInfo | null>(null);
+  const [showPrivacyModal, setShowPrivacyModal] = useState(false);
 
   const searchParams = useSearchParams();
   const deeplinkParams = parseDeeplinkParams(searchParams);
@@ -109,10 +158,20 @@ function HomeContent() {
               >
                 PolicyEngine.org
               </a>
+              {' • '}
+              <button
+                onClick={() => setShowPrivacyModal(true)}
+                className="text-blue-600 hover:text-blue-800"
+              >
+                Privacy & Terms
+              </button>
             </p>
           </div>
         </div>
       </footer>
+
+      {/* Privacy Modal */}
+      <PrivacyModal isOpen={showPrivacyModal} onClose={() => setShowPrivacyModal(false)} />
     </main>
   );
 }
diff --git a/microimputation-dashboard/components/BenchmarkLossCharts.tsx b/microimputation-dashboard/components/BenchmarkLossCharts.tsx
index 8cf9e5c..cadee0b 100644
--- a/microimputation-dashboard/components/BenchmarkLossCharts.tsx
+++ b/microimputation-dashboard/components/BenchmarkLossCharts.tsx
@@ -372,7 +372,7 @@ export default function BenchmarkLossCharts({ data }: BenchmarkLossChartsProps)
                   <span className="font-semibold text-gray-900">{bestModel.quantileLoss.toFixed(6)}</span>
                 </div>
                 {bestModel.quantileTrainTestRatio !== undefined && (
-                  <span className={`text-xs ${bestModel.quantileTrainTestRatio > 1.1 ? 'text-amber-600' : 'text-gray-700'}`}>
+                  <span className={`text-xs ${bestModel.quantileTrainTestRatio > 1.1 ? 'text-gray-700' : 'text-gray-900'}`}>
                     Train/test ratio: {bestModel.quantileTrainTestRatio.toFixed(3)}
                   </span>
                 )}
diff --git a/microimputation-dashboard/components/DistributionOverlay.tsx b/microimputation-dashboard/components/DistributionOverlay.tsx
index 6e621b9..0c395e7 100644
--- a/microimputation-dashboard/components/DistributionOverlay.tsx
+++ b/microimputation-dashboard/components/DistributionOverlay.tsx
@@ -11,8 +11,26 @@ import {
   Tooltip,
   Legend,
   ResponsiveContainer,
+  Brush,
 } from 'recharts';
 
+/**
+ * Format a number to scientific notation if it's very large or very small
+ * Returns the original number formatted normally if within reasonable range
+ */
+function formatLargeNumber(value: number, precision: number = 2): string {
+  const absValue = Math.abs(value);
+  // Use scientific notation for values >= 100,000 or <= 0.0001 (but not 0)
+  if (absValue >= 100000 || (absValue > 0 && absValue <= 0.0001)) {
+    return value.toExponential(precision);
+  }
+  // For smaller numbers, use fixed notation
+  if (absValue < 1 && absValue > 0) {
+    return value.toFixed(precision + 2);
+  }
+  return value.toFixed(precision);
+}
+
 interface DistributionOverlayProps {
   data: ImputationDataPoint[];
 }
@@ -72,14 +90,16 @@ export default function DistributionOverlay({
         const info = JSON.parse(d.additional_info);
 
         if (d.metric_name === 'histogram_distribution') {
-          // Numerical variable
+          // Numerical variable - use scientific notation for large values
+          const binStartFormatted = formatLargeNumber(info.bin_start);
+          const binEndFormatted = formatLargeNumber(info.bin_end);
           (distributions[variable].data as BinData[]).push({
             binIndex: info.bin_index,
             binStart: info.bin_start,
             binEnd: info.bin_end,
             donorHeight: info.donor_height,
             receiverHeight: info.receiver_height,
-            binLabel: `${info.bin_start.toFixed(2)}-${info.bin_end.toFixed(2)}`,
+            binLabel: `${binStartFormatted}-${binEndFormatted}`,
           });
           distributions[variable].nSamplesDonor = info.n_samples_donor;
           distributions[variable].nSamplesReceiver = info.n_samples_receiver;
@@ -130,7 +150,7 @@ export default function DistributionOverlay({
 
     return (
       <div>
-        <ResponsiveContainer width="100%" height={400}>
+        <ResponsiveContainer width="100%" height={580}>
           <BarChart
             data={chartData}
             margin={{ top: 20, right: 30, left: 20, bottom: 60 }}
@@ -161,11 +181,19 @@ export default function DistributionOverlay({
             />
             <Tooltip
               formatter={(value: number) => [`${value.toFixed(2)}%`, '']}
-              labelFormatter={(label) => `Bin: ${label}`}
+              labelFormatter={(_label, payload) => {
+                if (payload && payload.length > 0 && payload[0].payload) {
+                  const { binStart, binEnd } = payload[0].payload;
+                  // Show full values with commas in tooltip for readability
+                  const startStr = binStart.toLocaleString(undefined, { maximumFractionDigits: 2 });
+                  const endStr = binEnd.toLocaleString(undefined, { maximumFractionDigits: 2 });
+                  return `Bin: ${startStr} - ${endStr}`;
+                }
+                return `Bin: ${_label}`;
+              }}
               contentStyle={{ color: '#000000' }}
               labelStyle={{ color: '#000000' }}
             />
-            <Legend wrapperStyle={{ color: '#000000', paddingTop: '10px' }} />
             <Bar
               dataKey="Donor"
               fill="#3b82f6"
@@ -178,10 +206,21 @@ export default function DistributionOverlay({
               fillOpacity={0.7}
               name={`Receiver (n=${dist.nSamplesReceiver})`}
             />
+            <Brush
+              dataKey="name"
+              height={30}
+              stroke="#8884d8"
+              fill="#f3f4f6"
+              tickFormatter={() => ''}
+            />
+            <Legend
+              verticalAlign="bottom"
+              wrapperStyle={{ color: '#000000', paddingTop: '45px' }}
+            />
           </BarChart>
         </ResponsiveContainer>
         <p className="text-xs text-gray-600 mt-2 text-center">
-          Histogram with {(dist.data as BinData[]).length} bins. Each bin shows the percentage of values falling within that range.
+          Histogram with {(dist.data as BinData[]).length} bins. Drag the handles below to zoom into a specific range.
           Overlapping bars indicate similar distributions.
         </p>
       </div>
diff --git a/microimputation-dashboard/components/ImputationResults.tsx b/microimputation-dashboard/components/ImputationResults.tsx
index 57f5387..6f1f177 100644
--- a/microimputation-dashboard/components/ImputationResults.tsx
+++ b/microimputation-dashboard/components/ImputationResults.tsx
@@ -14,6 +14,8 @@ interface DistributionMetric {
   method: string;
   metricName: string;
   value: number;
+  normalizedValue?: number;  // Wasserstein distance as percentage of variable range
+  variableRange?: number;    // Range of the variable for context
 }
 
 export default function ImputationResults({ data }: ImputationResultsProps) {
@@ -22,6 +24,34 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
     return data.filter(d => d.type === 'distribution_distance');
   }, [data]);
 
+  // Extract variable ranges from distribution_bins data
+  const variableRanges = useMemo(() => {
+    const ranges: Record<string, { min: number; max: number }> = {};
+    const distributionBins = data.filter(d => d.type === 'distribution_bins' && d.metric_name === 'histogram_distribution');
+
+    distributionBins.forEach(d => {
+      try {
+        const info = JSON.parse(d.additional_info);
+        const variable = d.variable;
+
+        if (!ranges[variable]) {
+          ranges[variable] = { min: Infinity, max: -Infinity };
+        }
+
+        if (info.bin_start !== undefined) {
+          ranges[variable].min = Math.min(ranges[variable].min, info.bin_start);
+        }
+        if (info.bin_end !== undefined) {
+          ranges[variable].max = Math.max(ranges[variable].max, info.bin_end);
+        }
+      } catch (e) {
+        // Ignore parsing errors
+      }
+    });
+
+    return ranges;
+  }, [data]);
+
   // Group by metric type
   const { wassersteinData, klDivergenceData } = useMemo(() => {
     const wasserstein: DistributionMetric[] = [];
@@ -36,21 +66,28 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
       };
 
       if (d.metric_name === 'wasserstein_distance') {
+        // Calculate normalized value as percentage of variable range
+        const range = variableRanges[d.variable];
+        if (range && range.max > range.min) {
+          const variableRange = range.max - range.min;
+          metric.variableRange = variableRange;
+          metric.normalizedValue = (metric.value / variableRange) * 100;
+        }
         wasserstein.push(metric);
       } else if (d.metric_name === 'kl_divergence') {
         klDiv.push(metric);
       }
     });
 
-    // Sort by value (ascending - lower is better)
-    wasserstein.sort((a, b) => a.value - b.value);
+    // Sort by normalized value if available, otherwise by raw value (ascending - lower is better)
+    wasserstein.sort((a, b) => (a.normalizedValue ?? a.value) - (b.normalizedValue ?? b.value));
     klDiv.sort((a, b) => a.value - b.value);
 
     return {
       wassersteinData: wasserstein,
       klDivergenceData: klDiv
     };
-  }, [distributionData]);
+  }, [distributionData, variableRanges]);
 
   const hasWasserstein = wassersteinData.length > 0;
   const hasKLDivergence = klDivergenceData.length > 0;
@@ -59,13 +96,17 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
     return null;
   }
 
-  // Color function based on value quality (lower is better)
-  const getWassersteinColor = (value: number): string => {
-    if (value < 0.01) return '#16a34a'; // Dark green - excellent
-    if (value < 0.05) return '#22c55e'; // Green - good
-    if (value < 0.1) return '#eab308'; // Yellow - moderate
-    if (value < 0.2) return '#f97316'; // Orange - fair
-    return '#ef4444'; // Red - poor
+  // Color function based on normalized value (percentage of range) - lower is better
+  const getWassersteinColor = (normalizedValue: number | undefined, rawValue: number): string => {
+    // Use normalized value if available, otherwise fall back to raw thresholds
+    const value = normalizedValue ?? (rawValue * 100);  // Assume raw is already a fraction if no range
+
+    // Thresholds as percentage of variable range
+    if (value < 1) return '#16a34a';   // Dark green - excellent (<1% of range)
+    if (value < 3) return '#22c55e';   // Green - good (<3% of range)
+    if (value < 5) return '#eab308';   // Yellow - moderate (<5% of range)
+    if (value < 10) return '#f97316';  // Orange - fair (<10% of range)
+    return '#ef4444';                   // Red - poor (>=10% of range)
   };
 
   const getKLColor = (value: number): string => {
@@ -112,9 +153,9 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
               greater differences between imputed and true distributions.
             </p>
             <p className="text-sm text-gray-700">
-              <strong>Interpretation:</strong> Values closer to 0 are better. Generally, values below
-              0.05 indicate good imputation quality, while values above 0.2 suggest significant
-              distributional differences.
+              <strong>Interpretation:</strong> Since Wasserstein distance is scale-dependent, quality is assessed
+              relative to each variable&apos;s range. A distance of &lt;1% of the variable range is excellent,
+              &lt;3% is good, &lt;5% is moderate, &lt;10% is fair, and &ge;10% suggests poor distributional match.
             </p>
           </div>
 
@@ -130,14 +171,21 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
                 <XAxis type="number" tick={{ fill: '#000000' }} />
                 <YAxis type="category" dataKey="variable" width={90} tick={{ fill: '#000000' }} />
                 <Tooltip
-                  formatter={(value: number) => [value.toFixed(6), 'Wasserstein Distance']}
+                  formatter={(value: number, _name: string, props: { payload?: DistributionMetric }) => {
+                    const normalizedValue = props.payload?.normalizedValue;
+                    const distanceStr = value.toFixed(6);
+                    const pctStr = normalizedValue !== undefined ? ` (${normalizedValue.toFixed(2)}% of range)` : '';
+                    return [`${distanceStr}${pctStr}`, 'Wasserstein Distance'];
+                  }}
+                  contentStyle={{ color: '#000000' }}
+                  labelStyle={{ color: '#000000' }}
                 />
                 <Legend wrapperStyle={{ color: '#000000' }} />
                 <Bar dataKey="value" name="Wasserstein Distance">
                   {wassersteinData.map((entry, index) => (
                     <Cell
                       key={`cell-${index}`}
-                      fill={getWassersteinColor(entry.value)}
+                      fill={getWassersteinColor(entry.normalizedValue, entry.value)}
                     />
                   ))}
                 </Bar>
@@ -156,6 +204,9 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
                   <th className="px-4 py-3 text-left text-xs font-medium text-gray-500 uppercase tracking-wider">
                     Wasserstein Distance
                   </th>
+                  <th className="px-4 py-3 text-left text-xs font-medium text-gray-500 uppercase tracking-wider">
+                    % of Range
+                  </th>
                   <th className="px-4 py-3 text-left text-xs font-medium text-gray-500 uppercase tracking-wider">
                     Quality Assessment
                   </th>
@@ -166,16 +217,19 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
                   let assessment = '';
                   let assessmentColor = '';
 
-                  if (item.value < 0.01) {
+                  // Use normalized value (percentage of range) for assessment
+                  const normalizedValue = item.normalizedValue ?? (item.value * 100);
+
+                  if (normalizedValue < 1) {
                     assessment = 'Excellent';
                     assessmentColor = 'text-green-700 font-semibold';
-                  } else if (item.value < 0.05) {
+                  } else if (normalizedValue < 3) {
                     assessment = 'Good';
                     assessmentColor = 'text-green-600';
-                  } else if (item.value < 0.1) {
+                  } else if (normalizedValue < 5) {
                     assessment = 'Moderate';
                     assessmentColor = 'text-yellow-600';
-                  } else if (item.value < 0.2) {
+                  } else if (normalizedValue < 10) {
                     assessment = 'Fair';
                     assessmentColor = 'text-orange-600';
                   } else {
@@ -191,6 +245,9 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
                       <td className="px-4 py-3 whitespace-nowrap text-sm text-gray-700">
                         {item.value.toFixed(6)}
                       </td>
+                      <td className="px-4 py-3 whitespace-nowrap text-sm text-gray-700">
+                        {item.normalizedValue !== undefined ? `${item.normalizedValue.toFixed(2)}%` : 'N/A'}
+                      </td>
                       <td className={`px-4 py-3 whitespace-nowrap text-sm ${assessmentColor}`}>
                         {assessment}
                       </td>
@@ -243,6 +300,8 @@ export default function ImputationResults({ data }: ImputationResultsProps) {
                 <YAxis type="category" dataKey="variable" width={90} tick={{ fill: '#000000' }} />
                 <Tooltip
                   formatter={(value: number) => [value.toFixed(6), 'KL-Divergence']}
+                  contentStyle={{ color: '#000000' }}
+                  labelStyle={{ color: '#000000' }}
                 />
                 <Legend wrapperStyle={{ color: '#000000' }} />
                 <Bar dataKey="value" name="KL-Divergence">
diff --git a/microimputation-dashboard/components/PredictorCorrelationMatrix.tsx b/microimputation-dashboard/components/PredictorCorrelationMatrix.tsx
index 6a47799..fac3918 100644
--- a/microimputation-dashboard/components/PredictorCorrelationMatrix.tsx
+++ b/microimputation-dashboard/components/PredictorCorrelationMatrix.tsx
@@ -179,7 +179,7 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
     return '#f3f4f6'; // Nearly white
   };
 
-  const cellSize = 80; // Size of each cell in pixels
+  const cellSize = 100; // Size of each cell in pixels
 
   return (
     <div className="bg-white p-6 rounded-lg shadow">
@@ -219,7 +219,7 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
       </div>
 
       {/* Correlation Matrix */}
-      <div className="overflow-x-auto overflow-y-hidden">
+      <div className="overflow-auto max-h-[600px]">
         <div className="inline-block">
           <div style={{ display: 'grid', gridTemplateColumns: `${cellSize}px repeat(${predictors.length}, ${cellSize}px)`, border: '1px solid #e5e7eb' }}>
             {/* Top-left empty cell */}
@@ -235,13 +235,18 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
                   borderRight: idx < predictors.length - 1 ? '1px solid #e5e7eb' : 'none',
                   borderBottom: '1px solid #e5e7eb'
                 }}
-                className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900 text-sm"
+                className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900"
+                title={pred}
               >
                 <div
                   style={{
                     transform: 'rotate(-45deg)',
                     transformOrigin: 'center',
                     whiteSpace: 'nowrap',
+                    overflow: 'hidden',
+                    textOverflow: 'ellipsis',
+                    maxWidth: cellSize * 1.2,
+                    fontSize: '11px',
                   }}
                 >
                   {pred}
@@ -261,9 +266,21 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
                     borderRight: '1px solid #e5e7eb',
                     borderBottom: rowIdx < predictors.length - 1 ? '1px solid #e5e7eb' : 'none'
                   }}
-                  className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900 text-sm"
+                  className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900"
+                  title={pred1}
                 >
-                  {pred1}
+                  <div
+                    style={{
+                      overflow: 'hidden',
+                      textOverflow: 'ellipsis',
+                      whiteSpace: 'nowrap',
+                      maxWidth: cellSize - 8,
+                      fontSize: '11px',
+                      padding: '0 4px',
+                    }}
+                  >
+                    {pred1}
+                  </div>
                 </div>
 
                 {/* Correlation cells */}
@@ -343,7 +360,7 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
             </p>
 
             {/* MI Matrix */}
-            <div className="overflow-x-auto overflow-y-hidden mb-4">
+            <div className="overflow-auto max-h-[600px] mb-4">
               <div className="inline-block">
                 <div style={{ display: 'grid', gridTemplateColumns: `${cellSize}px repeat(${targetsList.length}, ${cellSize}px)`, border: '1px solid #e5e7eb' }}>
                   {/* Top-left empty cell */}
@@ -359,13 +376,18 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
                         borderRight: idx < targetsList.length - 1 ? '1px solid #e5e7eb' : 'none',
                         borderBottom: '1px solid #e5e7eb'
                       }}
-                      className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900 text-sm"
+                      className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900"
+                      title={target}
                     >
                       <div
                         style={{
                           transform: 'rotate(-45deg)',
                           transformOrigin: 'center',
                           whiteSpace: 'nowrap',
+                          overflow: 'hidden',
+                          textOverflow: 'ellipsis',
+                          maxWidth: cellSize * 1.2,
+                          fontSize: '11px',
                         }}
                       >
                         {target}
@@ -385,9 +407,21 @@ export default function PredictorCorrelationMatrix({ data }: PredictorCorrelatio
                           borderRight: '1px solid #e5e7eb',
                           borderBottom: rowIdx < predictorsList.length - 1 ? '1px solid #e5e7eb' : 'none'
                         }}
-                        className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900 text-sm"
+                        className="bg-gray-100 flex items-center justify-center font-semibold text-gray-900"
+                        title={predictor}
                       >
-                        {predictor}
+                        <div
+                          style={{
+                            overflow: 'hidden',
+                            textOverflow: 'ellipsis',
+                            whiteSpace: 'nowrap',
+                            maxWidth: cellSize - 8,
+                            fontSize: '11px',
+                            padding: '0 4px',
+                          }}
+                        >
+                          {predictor}
+                        </div>
                       </div>
 
                       {/* MI cells */}
diff --git a/microimputation-dashboard/components/PredictorOrderingRobustness.tsx b/microimputation-dashboard/components/PredictorOrderingRobustness.tsx
index fea48da..2d13c9b 100644
--- a/microimputation-dashboard/components/PredictorOrderingRobustness.tsx
+++ b/microimputation-dashboard/components/PredictorOrderingRobustness.tsx
@@ -309,6 +309,8 @@ export default function PredictorOrderingRobustness({ data }: PredictorOrderingR
                     }
                     return [value.toFixed(6), 'Loss Increase'];
                   }}
+                  contentStyle={{ color: '#000000' }}
+                  labelStyle={{ color: '#000000' }}
                 />
                 <Legend wrapperStyle={{ color: '#000000' }} />
                 <Bar dataKey="relativeImpact" name="Relative Impact (%)">
diff --git a/microimputation-dashboard/components/VisualizationDashboard.tsx b/microimputation-dashboard/components/VisualizationDashboard.tsx
index 6904329..f5a5513 100644
--- a/microimputation-dashboard/components/VisualizationDashboard.tsx
+++ b/microimputation-dashboard/components/VisualizationDashboard.tsx
@@ -500,7 +500,7 @@ export default function VisualizationDashboard({
             {dataAnalysis.bestModel ? (
               <div className="space-y-2">
                 <div className="flex items-center gap-2">
-                  <span className="text-lg font-bold text-blue-700">
+                  <span className="text-base font-bold text-blue-700">
                     {dataAnalysis.bestModel}
                   </span>
                   {dataAnalysis.allMethods.length === 1 && (
diff --git a/microimputation-dashboard/utils/colors.ts b/microimputation-dashboard/utils/colors.ts
index 9e7e870..cf92a16 100644
--- a/microimputation-dashboard/utils/colors.ts
+++ b/microimputation-dashboard/utils/colors.ts
@@ -1,16 +1,17 @@
 // Consistent color mapping for imputation methods across all charts
 // Using Plotly color palette for consistency with Python visualizations
 
-export const METHOD_COLORS: Record<string, string> = {
-  QRF: '#636EFA',           // Plotly blue
-  OLS: '#EF553B',           // Plotly red
-  QuantReg: '#00CC96',      // Plotly teal
-  Matching: '#AB63FA',      // Plotly purple
-  // Add more methods as needed
-};
+// Primary colors to use in order of appearance for the first 5 models
+export const PRIMARY_COLORS = [
+  '#636EFA', // Plotly blue
+  '#EF553B', // Plotly red
+  '#00CC96', // Plotly teal
+  '#AB63FA', // Plotly purple
+  '#FFA15A', // Plotly orange
+];
 
+// Additional fallback colors for when there are more than 5 models
 export const FALLBACK_COLORS = [
-  '#FFA15A', // Plotly orange
   '#19D3F3', // Plotly cyan
   '#FF6692', // Plotly pink
   '#B6E880', // Plotly lime
@@ -19,11 +20,13 @@ export const FALLBACK_COLORS = [
 ];
 
 /**
- * Get color for a method, using predefined colors or fallback palette
+ * Get color for a method based on its index in the order of appearance.
+ * First 5 models use PRIMARY_COLORS, additional models use FALLBACK_COLORS.
  */
-export function getMethodColor(method: string, index: number = 0): string {
-  if (method in METHOD_COLORS) {
-    return METHOD_COLORS[method];
+export function getMethodColor(_method: string, index: number = 0): string {
+  if (index < PRIMARY_COLORS.length) {
+    return PRIMARY_COLORS[index];
   }
-  return FALLBACK_COLORS[index % FALLBACK_COLORS.length];
+  const fallbackIndex = index - PRIMARY_COLORS.length;
+  return FALLBACK_COLORS[fallbackIndex % FALLBACK_COLORS.length];
 }
diff --git a/microimpute/comparisons/autoimpute.py b/microimpute/comparisons/autoimpute.py
index e5ca952..41b370a 100644
--- a/microimpute/comparisons/autoimpute.py
+++ b/microimpute/comparisons/autoimpute.py
@@ -294,7 +294,6 @@ def _generate_imputations_for_all_models(
     weight_col: Optional[str],
     imputation_q: float,
     train_size: float,
-    tune_hyperparameters: bool,
     hyperparams: Optional[Dict[str, Any]],
     log_level: str,
     preprocessing: Optional[Dict[str, str]] = None,
@@ -344,7 +343,7 @@ def _generate_imputations_for_all_models(
 
         # Get model-specific hyperparameters if available
         model_hyperparams = None
-        if tune_hyperparameters and hyperparams and model_name in hyperparams:
+        if hyperparams and model_name in hyperparams:
             model_hyperparams = hyperparams[model_name]
 
         # Fit and predict
@@ -601,6 +600,16 @@ def autoimpute(
         ):
             model_hyperparams = best_hyperparams[best_method]
 
+        # Merge with original hyperparameters (e.g., force_retrain for MDN)
+        # Tuned params take precedence over original params
+        if hyperparameters and best_method in hyperparameters:
+            original_params = hyperparameters[best_method]
+            if model_hyperparams:
+                # Tuned params override original params
+                model_hyperparams = {**original_params, **model_hyperparams}
+            else:
+                model_hyperparams = original_params
+
         # Fit and predict with best model
         best_fitted_model, imputations = fit_and_predict_model(
             chosen_model,
@@ -646,6 +655,19 @@ def autoimpute(
 
         # Step 5: Generate imputations for all models if requested
         if impute_all:
+            # Merge original hyperparameters with tuned ones
+            # Tuned params take precedence over original params
+            merged_hyperparams = {}
+            if hyperparameters:
+                for model_name, params in hyperparameters.items():
+                    merged_hyperparams[model_name] = params.copy()
+            if best_hyperparams:
+                for model_name, params in best_hyperparams.items():
+                    if model_name in merged_hyperparams:
+                        merged_hyperparams[model_name].update(params)
+                    else:
+                        merged_hyperparams[model_name] = params
+
             other_imputations, other_models = (
                 _generate_imputations_for_all_models(
                     model_classes,
@@ -657,8 +679,7 @@ def autoimpute(
                     weight_col,
                     imputation_q,
                     train_size,
-                    tune_hyperparameters,
-                    best_hyperparams,
+                    merged_hyperparams if merged_hyperparams else None,
                     log_level,
                     preprocessing=preprocessing,
                 )
diff --git a/microimpute/evaluations/cross_validation.py b/microimpute/evaluations/cross_validation.py
index cbf6e9e..371ca1d 100644
--- a/microimpute/evaluations/cross_validation.py
+++ b/microimpute/evaluations/cross_validation.py
@@ -153,17 +153,17 @@ def _fit_model_for_fold(
                 return None, None
 
     # Handle model-specific hyperparameters
-    if model_hyperparams and model_name in model_hyperparams:
+    if model_hyperparams:
         try:
             log.info(
-                f"Fitting {model_name} with hyperparameters: {model_hyperparams[model_name]}"
+                f"Fitting {model_name} with hyperparameters: {model_hyperparams}"
             )
             fitted_model = model.fit(
                 X_train=train_data,
                 predictors=predictors,
                 imputed_variables=imputed_variables,
                 weight_col=weight_col,
-                **model_hyperparams[model_name],
+                **model_hyperparams,
             )
         except ValueError as e:
             # Check if it's due to categorical incompatibility
diff --git a/microimpute/models/mdn.py b/microimpute/models/mdn.py
index 72001ee..7558e7f 100644
--- a/microimpute/models/mdn.py
+++ b/microimpute/models/mdn.py
@@ -3,6 +3,7 @@
 import hashlib
 import logging
 import os
+import shutil
 from pathlib import Path
 from typing import Any, Dict, List, Optional, Tuple, Union
 
@@ -35,6 +36,13 @@
     # Suppress pytorch_tabular warnings
     import warnings
 
+    # Suppress all FutureWarnings from pytorch_tabular
+    warnings.filterwarnings(
+        "ignore",
+        category=FutureWarning,
+        module="pytorch_tabular.*",
+    )
+
     warnings.filterwarnings(
         "ignore",
         message=".*does not have many workers.*",
@@ -46,13 +54,6 @@
         module="torch.utils.data.dataloader",
     )
 
-    warnings.filterwarnings(
-        "ignore",
-        message=".*Setting an item of incompatible dtype is deprecated.*",
-        category=FutureWarning,
-        module="pytorch_tabular.tabular_datamodule",
-    )
-
     warnings.filterwarnings(
         "ignore",
         message=".*training batches.*smaller than the logging interval.*",
@@ -205,29 +206,36 @@ def fit(
         self,
         X: pd.DataFrame,
         y: pd.Series,
+        categorical_cols: Optional[List[str]] = None,
     ) -> None:
         """Fit the MDN model.
 
         Args:
             X: Feature DataFrame (predictors are already dummy-encoded).
             y: Target Series.
+            categorical_cols: Optional list of column names that are dummy-encoded
+                categorical variables. These will be passed to PyTorch Tabular
+                as categorical columns for embedding.
         """
         _suppress_pytorch_logging()
         self.output_column = y.name
+        categorical_cols = categorical_cols or []
 
         # Combine X and y for PyTorch Tabular
         train_data = X.copy()
         train_data[y.name] = y
 
-        # All predictors are continuous (categorical predictors were
-        # dummy-encoded during preprocessing in the base Imputer class)
-        continuous_cols = X.columns.tolist()
+        # Separate continuous and categorical columns
+        # Categorical columns get embeddings, continuous columns are passed as-is
+        continuous_cols = [
+            col for col in X.columns.tolist() if col not in categorical_cols
+        ]
 
         # Configure data
         data_config = DataConfig(
             target=[y.name],
             continuous_cols=continuous_cols,
-            categorical_cols=[],
+            categorical_cols=categorical_cols,
         )
 
         # Configure trainer
@@ -375,6 +383,7 @@ def fit(
         y: pd.Series,
         var_type: str,
         categories: Optional[List] = None,
+        categorical_cols: Optional[List[str]] = None,
     ) -> None:
         """Fit the neural classifier.
 
@@ -383,10 +392,14 @@ def fit(
             y: Target Series (original categorical/boolean column).
             var_type: Type of variable ("boolean" or "categorical").
             categories: List of categories for categorical variables.
+            categorical_cols: Optional list of column names that are dummy-encoded
+                categorical variables. These will be passed to PyTorch Tabular
+                as categorical columns for embedding.
         """
         _suppress_pytorch_logging()
         self.output_column = y.name
         self.var_type = var_type
+        categorical_cols = categorical_cols or []
 
         if var_type == "boolean":
             y_encoded = y.astype(int)
@@ -407,15 +420,17 @@ def fit(
         train_data = X.copy()
         train_data[y.name] = y_encoded.astype(int)
 
-        # All predictors are continuous (categorical predictors were
-        # dummy-encoded during preprocessing in the base Imputer class)
-        continuous_cols = X.columns.tolist()
+        # Separate continuous and categorical columns
+        # Categorical columns get embeddings, continuous columns are passed as-is
+        continuous_cols = [
+            col for col in X.columns.tolist() if col not in categorical_cols
+        ]
 
         # Configure data
         data_config = DataConfig(
             target=[y.name],
             continuous_cols=continuous_cols,
-            categorical_cols=[],
+            categorical_cols=categorical_cols,
         )
 
         # Configure trainer
@@ -920,9 +935,22 @@ def _fit(
 
             self.models = {}
 
+            # If force_retrain is True, delete existing cached models
+            if self.force_retrain and Path(self.model_dir).exists():
+                shutil.rmtree(self.model_dir)
+                self.logger.info(
+                    f"Deleted cached models directory: {self.model_dir}"
+                )
+
             # Ensure model directory exists
             Path(self.model_dir).mkdir(parents=True, exist_ok=True)
 
+            # Extract categorical columns from dummy_processor
+            categorical_cols = []
+            if hasattr(self, "dummy_processor") and self.dummy_processor:
+                for dummy_cols in self.dummy_processor.dummy_mapping.values():
+                    categorical_cols.extend(dummy_cols)
+
             for variable in imputed_variables:
                 # Handle constant targets (no caching needed)
                 if variable in (constant_targets or {}):
@@ -991,6 +1019,7 @@ def _fit(
                         categories=categorical_targets[variable].get(
                             "categories"
                         ),
+                        categorical_cols=categorical_cols,
                     )
                     self.logger.info(
                         f"Neural classifier fitted for categorical variable "
@@ -1013,13 +1042,13 @@ def _fit(
                         use_batch_norm=self.use_batch_norm,
                         learning_rate=self.learning_rate,
                         max_epochs=self.max_epochs,
-                        early_stopping_patience=self.early_stopping_patience,
                         batch_size=self.batch_size,
                     )
                     model.fit(
                         X_train[predictors],
                         Y,
                         var_type="boolean",
+                        categorical_cols=categorical_cols,
                     )
                     self.logger.info(
                         f"Neural classifier fitted for boolean variable "
@@ -1044,12 +1073,12 @@ def _fit(
                         n_samples=self.n_samples,
                         learning_rate=self.learning_rate,
                         max_epochs=self.max_epochs,
-                        early_stopping_patience=self.early_stopping_patience,
                         batch_size=self.batch_size,
                     )
                     model.fit(
                         X_train[predictors],
                         Y,
+                        categorical_cols=categorical_cols,
                     )
                     self.logger.info(
                         f"MDN fitted for numeric variable {variable}"
@@ -1156,7 +1185,6 @@ def objective(trial: optuna.Trial) -> float:
                         n_samples=self.n_samples,
                         learning_rate=learning_rate,
                         max_epochs=40,  # Reduced for tuning
-                        early_stopping_patience=self.early_stopping_patience,
                         batch_size=self.batch_size,
                     )
                     model.fit(X_train_fold[predictors], y_train)
@@ -1293,7 +1321,6 @@ def objective(trial: optuna.Trial) -> float:
                         use_batch_norm=self.use_batch_norm,
                         learning_rate=learning_rate,
                         max_epochs=40,  # Reduced for tuning
-                        early_stopping_patience=self.early_stopping_patience,
                         batch_size=self.batch_size,
                     )
                     model.fit(
diff --git a/microimpute/utils/dashboard_formatter.py b/microimpute/utils/dashboard_formatter.py
index 613f461..c8847d4 100644
--- a/microimpute/utils/dashboard_formatter.py
+++ b/microimpute/utils/dashboard_formatter.py
@@ -304,7 +304,7 @@ def format_csv(
 
     autoimpute_result : Dict, optional
         Result from autoimpute containing cv_results with benchmark losses.
-        Expected structure: {'cv_results': {method: {'quantile_loss': {...}, 'log_loss': {...}}}}
+        Expected structure: {method: {'quantile_loss': {...}, 'log_loss': {...}}}
 
     comparison_metrics_df : pd.DataFrame, optional
         DataFrame from compare_metrics() with columns:
@@ -358,60 +358,68 @@ def format_csv(
     rows = []
 
     # 1. Process autoimpute benchmark losses from cv_results
-    if autoimpute_result and "cv_results" in autoimpute_result:
-        for method, cv_result in autoimpute_result["cv_results"].items():
-            # Append "_best_method" if this is the best method
-            method_label = (
-                f"{method}_best_method"
-                if method == best_method_name
-                else method
-            )
+    if autoimpute_result and isinstance(autoimpute_result, dict):
+        first_value = next(iter(autoimpute_result.values()), None)
+        if isinstance(first_value, dict) and (
+            "quantile_loss" in first_value or "log_loss" in first_value
+        ):
+            for method, cv_result in autoimpute_result.items():
+                # Append "_best_method" if this is the best method
+                method_label = (
+                    f"{method}_best_method"
+                    if method == best_method_name
+                    else method
+                )
 
-            for metric_type in ["quantile_loss", "log_loss"]:
-                if metric_type in cv_result:
-                    data = cv_result[metric_type]
-                    results_df = data.get("results")
-                    variables = data.get("variables", [])
-
-                    if results_df is not None:
-                        # Add individual quantile results
-                        for split in ["train", "test"]:
-                            if split in results_df.index:
-                                for quantile in results_df.columns:
-                                    # Add mean_all row for this quantile
-                                    rows.append(
-                                        {
-                                            "type": "benchmark_loss",
-                                            "method": method_label,
-                                            "variable": f"{metric_type}_mean_all",
-                                            "quantile": float(quantile),
-                                            "metric_name": metric_type,
-                                            "metric_value": results_df.loc[
-                                                split, quantile
-                                            ],
-                                            "split": split,
-                                            "additional_info": json.dumps(
-                                                {"n_variables": len(variables)}
-                                            ),
-                                        }
-                                    )
-
-                        # Add mean across all quantiles
-                        if "mean_train" in data:
-                            rows.append(
-                                {
-                                    "type": "benchmark_loss",
-                                    "method": method_label,
-                                    "variable": f"{metric_type}_mean_all",
-                                    "quantile": "mean",
-                                    "metric_name": metric_type,
-                                    "metric_value": data["mean_train"],
-                                    "split": "train",
-                                    "additional_info": json.dumps(
-                                        {"n_variables": len(variables)}
-                                    ),
-                                }
-                            )
+                for metric_type in ["quantile_loss", "log_loss"]:
+                    if metric_type in cv_result:
+                        data = cv_result[metric_type]
+                        results_df = data.get("results")
+                        variables = data.get("variables", [])
+
+                        if results_df is not None:
+                            # Add individual quantile results
+                            for split in ["train", "test"]:
+                                if split in results_df.index:
+                                    for quantile in results_df.columns:
+                                        # Add mean_all row for this quantile
+                                        rows.append(
+                                            {
+                                                "type": "benchmark_loss",
+                                                "method": method_label,
+                                                "variable": f"{metric_type}_mean_all",
+                                                "quantile": float(quantile),
+                                                "metric_name": metric_type,
+                                                "metric_value": results_df.loc[
+                                                    split, quantile
+                                                ],
+                                                "split": split,
+                                                "additional_info": json.dumps(
+                                                    {
+                                                        "n_variables": len(
+                                                            variables
+                                                        )
+                                                    }
+                                                ),
+                                            }
+                                        )
+
+                            # Add mean across all quantiles
+                            if "mean_train" in data:
+                                rows.append(
+                                    {
+                                        "type": "benchmark_loss",
+                                        "method": method_label,
+                                        "variable": f"{metric_type}_mean_all",
+                                        "quantile": "mean",
+                                        "metric_name": metric_type,
+                                        "metric_value": data["mean_train"],
+                                        "split": "train",
+                                        "additional_info": json.dumps(
+                                            {"n_variables": len(variables)}
+                                        ),
+                                    }
+                                )
 
                         if "mean_test" in data:
                             rows.append(
diff --git a/paper/.gitignore b/paper/.gitignore
new file mode 100644
index 0000000..86b65ed
--- /dev/null
+++ b/paper/.gitignore
@@ -0,0 +1,32 @@
+## Core latex/pdflatex auxiliary files:
+*.aux
+*.lof
+*.log
+*.lot
+*.fls
+*.out
+*.toc
+*.fmt
+*.fot
+*.cb
+*.cb2
+.*.lb
+
+## Generated if empty string is given at "Please type another file name for output:"
+.pdf
+
+## Bibliography auxiliary files (bibtex/biblatex/biber):
+*.bbl
+*.bcf
+*.blg
+*-blx.aux
+*-blx.bib
+*.run.xml
+
+## Build tool auxiliary files:
+*.fdb_latexmk
+*.synctex
+*.synctex(busy)
+*.synctex.gz
+*.synctex.gz(busy)
+*.pdfsync
\ No newline at end of file
diff --git a/paper/bibliography/references.bib b/paper/bibliography/references.bib
new file mode 100644
index 0000000..d59c202
--- /dev/null
+++ b/paper/bibliography/references.bib
@@ -0,0 +1,482 @@
+@techreport{advani2020capital,
+  title={Capital Gains and {UK} Inequality},
+  author={Advani, Arun and Summers, Andy},
+  year={2020},
+  month={May},
+  institution={University of Warwick, Department of Economics},
+  number={1260},
+  series={Warwick Economics Research Papers}
+}
+
+@article{advani2023measuring,
+  title={Measuring top income shares in the {UK}},
+  author={Advani, Arun and Summers, Andy and Tarrant, Hannah},
+  journal={Journal of the Royal Statistical Society Series A: Statistics in Society},
+  volume={186},
+  number={2},
+  pages={241--265},
+  year={2023},
+  publisher={Oxford University Press},
+  doi={10.1093/jrsssa/qnac008}
+}
+
+@article{alaa2024deep,
+  title     = {Deep learning for missing data imputation: A comprehensive review and new perspectives},
+  author    = {Alaa, Ahmed M. and Van Breugel, Boris and Sontag, David and van der Schaar, Mihaela},
+  journal   = {Foundations and Trends in Machine Learning},
+  volume    = {17},
+  number    = {2},
+  pages     = {139--301},
+  year      = {2024}
+}
+
+@article{andridge2010review,
+  title     = {A review of hot deck imputation for survey non-response},
+  author    = {Andridge, Rebecca R. and Little, Roderick J. A.},
+  journal   = {International Statistical Review},
+  volume    = {78},
+  number    = {1},
+  pages     = {40--64},
+  year      = {2010}
+}
+
+@misc{anil_regression,
+  title     = {Regression imputation - Deterministic \& stochastic},
+  author    = {Anil},
+  publisher = {RPubs},
+  note      = {Retrieved May 23, 2025},
+  url       = {https://www.rpubs.com/anilpmm/regression_det_stoc}
+}
+
+@techreport{barcelo2006imputation,
+  title       = {Imputation of household wealth components in the Spanish survey of household finances},
+  author      = {Barceló, Cristina},
+  institution = {Banco de España},
+  number      = {0629},
+  series      = {Documentos de Trabajo},
+  year        = {2006}
+}
+
+@techreport{barcelo2008impact,
+  title       = {The impact of alternative imputation methods on the measurement of income and wealth: Evidence from the Spanish survey of household finances},
+  author      = {Barceló, Cristina},
+  institution = {Banco de España},
+  number      = {0829},
+  series      = {Documento de Trabajo},
+  year        = {2008}
+}
+
+@article{beretta2016nearest,
+  title     = {Nearest neighbor imputation algorithms: A critical evaluation},
+  author    = {Beretta, Lorenzo and Santaniello, Alessandro},
+  journal   = {BMC Medical Informatics and Decision Making},
+  volume    = {16},
+  number    = {Suppl 3},
+  pages     = {Article 74},
+  year      = {2016}
+}
+
+@article{breiman2001random,
+  title     = {Random forests},
+  author    = {Breiman, Leo},
+  journal   = {Machine Learning},
+  volume    = {45},
+  number    = {1},
+  pages     = {5--32},
+  year      = {2001}
+}
+
+@techreport{bruch2023imputation,
+  title       = {Imputation of missing values in survey data: An overview},
+  author      = {Bruch, Christian},
+  institution = {GESIS - Leibniz Institute for the Social Sciences},
+  series      = {GESIS Survey Guidelines},
+  year        = {2023}
+}
+
+@techreport{bryant2023general,
+  title       = {General description booklet for the 2015 public use tax file demographic file},
+  author      = {Bryant, Victoria},
+  institution = {Statistics of Income Division, Internal Revenue Service},
+  type        = {Technical documentation},
+  year        = {2023},
+  url         = {https://drive.google.com/file/d/1WoTU70GEjYMO0KHsHvTTH0NwCc-kN5cE/view}
+}
+
+@article{crawford2016distribution,
+  title     = {The distribution of household wealth in the UK},
+  author    = {Crawford, Rowena and Innes, David and O'Dea, Cormac},
+  journal   = {Fiscal Studies},
+  volume    = {37},
+  number    = {1},
+  pages     = {35--54},
+  year      = {2016}
+}
+
+@article{chen2000nearest,
+  title     = {Nearest neighbor imputation for survey data},
+  author    = {Chen, Jie and Shao, Jun},
+  journal   = {Journal of Official Statistics},
+  volume    = {16},
+  number    = {2},
+  pages     = {113--131},
+  year      = {2000}
+}
+
+@inproceedings{chen2007confidentiality,
+  title     = {Confidentiality protection by data synthesis using quantile regression and hot deck imputation},
+  author    = {Chen, Qizhi and Yu, Keming},
+  booktitle = {Proceedings of the Survey Research Methods Section},
+  publisher = {American Statistical Association},
+  year      = {2007}
+}
+
+@article{chen2020imputation,
+  title     = {Imputation for skewed data using a cube-root transformation},
+  author    = {Chen, Shu and Haziza, David and Léger, Christian},
+  journal   = {Journal of Survey Statistics and Methodology},
+  volume    = {8},
+  number    = {3},
+  pages     = {545--567},
+  year      = {2020}
+}
+
+@article{chu2018accounting,
+  title     = {Accounting for missing data in clinical research},
+  author    = {Chu, Katherine and Ashfaq, Ajar and Newgard, Craig D.},
+  journal   = {JAMA Surgery},
+  volume    = {153},
+  number    = {6},
+  pages     = {584--585},
+  year      = {2018}
+}
+
+@incollection{dempster1983introduction,
+  title     = {Introduction},
+  author    = {Dempster, Arthur P. and Rubin, Donald B.},
+  booktitle = {Incomplete data in sample surveys: Vol. 2. Theory and bibliographies},
+  editor    = {Madow, William G. and Olkin, Ingram and Rubin, Donald B.},
+  pages     = {3--10},
+  publisher = {Academic Press},
+  year      = {1983}
+}
+
+@article{dorazio2021statistical,
+  title     = {Statistical matching and imputation of survey data with R},
+  author    = {D'Orazio, Marcello and Di Zio, Marco and Scanu, Mauro},
+  journal   = {Journal of Statistical Software},
+  volume    = {98},
+  number    = {1},
+  pages     = {1--35},
+  year      = {2021}
+}
+
+@misc{dwp2023frs,
+  title={Family Resources Survey: Financial Year 2021 to 2022},
+  author={{Department for Work and Pensions}},
+  year={2023},
+  month={July},
+  publisher={GOV.UK},
+  url={https://www.gov.uk/government/statistics/family-resources-survey-financial-year-2021-to-2022/}
+}
+
+@misc{editage2023introduction,
+  title     = {An introduction to multiple imputation by chained equations for biomedical researchers},
+  author    = {{Editage Insights}},
+  publisher = {Editage},
+  year      = {2023},
+  month     = {December},
+  day       = {22},
+  url       = {https://www.editage.com/insights/an-introduction-to-multiple-imputation-by-chained-equations-for-biomedical-researchers}
+}
+
+@article{graham2009missing,
+  title     = {Missing data analysis: Making it work in the real world},
+  author    = {Graham, John W.},
+  journal   = {Annual Review of Psychology},
+  volume    = {60},
+  pages     = {549--576},
+  year      = {2009}
+}
+
+@misc{ghenis2018quantile,
+  title   = {Quantile Regression: From Linear Models to Trees to Deep Learning},
+  author  = {Ghenis, Max},
+  year    = {2018},
+  howpublished = {Towards Data Science},
+  note    = {Medium blog post},
+  url     = {https://medium.com/data-science/quantile-regression-from-linear-models-to-trees-to-deep-learning-af3738b527c3}
+}
+
+@book{hao2007quantile,
+  title     = {Quantile regression},
+  author    = {Hao, Lingxin and Naiman, Daniel Q.},
+  publisher = {Sage Publications},
+  year      = {2007}
+}
+
+@incollection{haziza2009imputation,
+  title     = {Imputation and inference in the presence of missing data},
+  author    = {Haziza, David},
+  booktitle = {Handbook of statistics, Vol. 29A: Sample surveys: Design, methods and applications},
+  editor    = {Pfeffermann, Danny and Rao, C. R.},
+  pages     = {215--246},
+  publisher = {Elsevier},
+  year      = {2009}
+}
+
+@misc{ifs2025new,
+  title     = {New data suggest dramatic decline in living standards, but it may just be the quality of the data that has declined},
+  author    = {{Institute for Fiscal Studies}},
+  year      = {2025},
+  month     = {March},
+  day       = {31},
+  url       = {https://ifs.org.uk/articles/new-data-suggest-dramatic-decline-living-standards-it-may-just-be-quality-data-has}
+}
+
+@article{jadhav2021survey,
+  title     = {A survey on missing data in machine learning},
+  author    = {Jadhav, Amar and Pramod, Dhanya and Ramanathan, Krishnan},
+  journal   = {Journal of Big Data},
+  volume    = {8},
+  number    = {1},
+  pages     = {140},
+  year      = {2021}
+}
+
+@techreport{kennickell1998multiple,
+  title={Multiple Imputation in the Survey of Consumer Finances},
+  author={Kennickell, Arthur B.},
+  year={1998},
+  month={September},
+  institution={Board of Governors of the Federal Reserve System},
+  note={Prepared for the August 1998 Joint Statistical Meetings, Dallas, TX}
+}
+
+@inproceedings{kleinke2023robust,
+  title     = {Robust multiple imputation based on quantile forests},
+  author    = {Kleinke, Kristian and Fritsch, Markus},
+  booktitle = {GESIS Workshop on Longitudinal Data Analysis},
+  year      = {2023}
+}
+
+@article{kleinke2020multiple,
+  title     = {Multiple imputation of incomplete zero-inflated count data},
+  author    = {Kleinke, Kristian and Reinecke, Jost},
+  journal   = {Statistica Neerlandica},
+  volume    = {74},
+  number    = {4},
+  pages     = {515--539},
+  year      = {2020}
+}
+
+@book{koenker2005quantile,
+  title     = {Quantile regression},
+  author    = {Koenker, Roger},
+  publisher = {Cambridge University Press},
+  year      = {2005}
+}
+
+@article{koenker1978regression,
+  title     = {Regression quantiles},
+  author    = {Koenker, Roger and Bassett, Gilbert J.},
+  journal   = {Econometrica},
+  volume    = {46},
+  number    = {1},
+  pages     = {33--50},
+  year      = {1978}
+}
+
+@article{little1988missing,
+  title     = {Missing-data adjustments in large surveys},
+  author    = {Little, Roderick J. A.},
+  journal   = {Journal of Business \& Economic Statistics},
+  volume    = {6},
+  number    = {3},
+  pages     = {287--296},
+  year      = {1988}
+}
+
+@book{little2002statistical,
+  title     = {Statistical analysis with missing data},
+  author    = {Little, Roderick J. A. and Rubin, Donald B.},
+  edition   = {2nd},
+  publisher = {John Wiley \& Sons},
+  year      = {2002}
+}
+
+@inproceedings{lun2019multiple,
+  title     = {Multiple imputation for skewed multivariate data: A marriage of the MI and COPULA procedures},
+  author    = {Lun, Zhixin and Khattree, Ravindra},
+  booktitle = {Proceedings of the SAS Global Forum 2019 Conference},
+  publisher = {SAS Institute Inc.},
+  number    = {Paper 3605-2019},
+  year      = {2019},
+  url       = {https://support.sas.com/resources/papers/proceedings19/3605-2019.pdf}
+}
+
+@article{meinshausen2006quantile,
+  title     = {Quantile regression forests},
+  author    = {Meinshausen, Nicolai and Ridgeway, Greg},
+  journal   = {Journal of Machine Learning Research},
+  volume    = {7},
+  number    = {Jun},
+  pages     = {983--999},
+  year      = {2006}
+}
+
+@article{myers2011goodbye,
+  title     = {Goodbye, listwise deletion: Presenting hot deck imputation as an easy and effective tool for handling missing data},
+  author    = {Myers, Terri A.},
+  journal   = {Communication Methods and Measures},
+  volume    = {5},
+  number    = {4},
+  pages     = {297--310},
+  year      = {2011}
+}
+
+@techreport{nces2021methods,
+  title       = {2020–21 NTPS methods and procedures},
+  author      = {{National Center for Education Statistics}},
+  institution = {U.S. Department of Education},
+  year        = {2021}
+}
+
+@misc{ons2019using,
+  title     = {Using tax data to better capture top earners in household income inequality statistics},
+  author    = {{Office for National Statistics}},
+  year      = {2019},
+  month     = {February},
+  day       = {26},
+  url       = {https://www.ons.gov.uk/peoplepopulationandcommunity/personalandhouseholdfinances/incomeandwealth/articles/usingtaxdatatobettercapturetopearnersinhouseholdincomeinequalitystatistics/2019-02-26}
+}
+
+@techreport{ota2012revenue,
+  title       = {Revenue estimating models at the U.S. Treasury Department},
+  author      = {{Office of Tax Analysis}},
+  institution = {U.S. Department of the Treasury},
+  number      = {Technical Paper 12},
+  year        = {2012}
+}
+
+@misc{parker_missing,
+  title  = {Missing data and quantile regression [Lecture notes]},
+  author = {Parker, D.},
+  school = {Reed College},
+  note   = {Retrieved May 23, 2025},
+  url    = {https://www.reed.edu/economics/parker/312/online_slides/312_4-29.pdf}
+}
+
+@misc{policyengine2025microimpute,
+  title  = {Microimpute documentation},
+  author = {{PolicyEngine}},
+  year   = {2025},
+  note   = {Retrieved from},
+  url    = {https://policyengine.github.io/microimpute/}
+}
+
+@book{rubin1987multiple,
+  title     = {Multiple imputation for nonresponse in surveys},
+  author    = {Rubin, Donald B.},
+  publisher = {John Wiley \& Sons},
+  year      = {1987}
+}
+
+@article{siddique2008multiple,
+  title     = {Multiple imputation using chained equations: What is it and how does it work?},
+  author    = {Siddique, Juned and Belin, Thomas R.},
+  journal   = {American Journal of Public Health},
+  volume    = {98},
+  number    = {4},
+  pages     = {644--659},
+  year      = {2008}
+}
+
+@article{stuart2009multiple,
+  title     = {Multiple imputation with large data sets: A case study of the Children's Mental Health Initiative},
+  author    = {Stuart, Elizabeth A. and Azur, Melissa and Frangakis, Constantine and Leaf, Philip},
+  journal   = {American Journal of Epidemiology},
+  volume    = {169},
+  number    = {9},
+  pages     = {1133--1139},
+  year      = {2009}
+}
+
+@article{tang2017random,
+  title     = {Random forest missing data algorithms},
+  author    = {Tang, Fei and Ishwaran, Hemant},
+  journal   = {Statistical Analysis and Data Mining: The ASA Data Science Journal},
+  volume    = {10},
+  number    = {6},
+  pages     = {363--377},
+  year      = {2017}
+}
+
+@misc{uscensus_data,
+  title  = {Data editing and imputation},
+  author = {{U.S. Census Bureau}},
+  series = {Survey of Income and Program Participation},
+  note   = {Retrieved May 23, 2025},
+  url    = {https://www.census.gov/programs-surveys/sipp/methodology/data-editing-and-imputation.html}
+}
+
+@article{vanbuuren2011mice,
+  title     = {mice: Multivariate Imputation by Chained Equations in R},
+  author    = {Van Buuren, Stef and Groothuis-Oudshoorn, Karin},
+  journal   = {Journal of Statistical Software},
+  volume    = {45},
+  number    = {3},
+  pages     = {1--67},
+  year      = {2011}
+}
+
+@techreport{vonhippel2007should,
+  title       = {Should a normal imputation model be modified to impute skewed variables?},
+  author      = {Von Hippel, Paul T.},
+  institution = {LBJ School of Public Affairs, University of Texas at Austin},
+  year        = {2007}
+}
+
+@article{wei2014multiple,
+  title     = {Multiple imputation in quantile regression},
+  author    = {Wei, Ying and Ma, Yang and Carroll, Raymond J.},
+  journal   = {Biometrics},
+  volume    = {70},
+  number    = {1},
+  pages     = {196--205},
+  year      = {2014}
+}
+
+@techreport{woodruff2023survey,
+  title       = {Surveying the (loss) landscape: using machine learning to improve household survey accuracy},
+  author      = {Woodruff, Nikhil},
+  institution = {University of Durham},
+  year        = {2023},
+  month       = {April},
+  note        = {Demonstrates superiority of machine learning approaches over traditional methods for survey enhancement through comprehensive benchmarking},
+  url         = {https://github.com/policyengine/survey-enhance/blob/main/docs/paper/project_paper.pdf}
+}
+
+@techreport{woodruff2024enhancing,
+  title     = {Enhancing survey microdata with administrative records: A novel approach to microsimulation dataset construction},
+  author    = {Woodruff, Nikhil and Ghenis, Max},
+  publisher = {PolicyEngine},
+  year      = {2024}
+}
+
+@article{zhao2023quantile,
+  title     = {Quantile regression for electronic medical records analysis with nonignorable missing responses},
+  author    = {Zhao, Qian Y. and Ma, Shuangge and Wang, Lan},
+  journal   = {Biometrics},
+  volume    = {79},
+  number    = {3},
+  pages     = {2036--2048},
+  year      = {2023}
+}
+
+@misc{zillow2024quantile,
+  title  = {quantile-forest: Scikit-learn compatible quantile regression forests},
+  author = {{Zillow Group}},
+  year   = {2024},
+  url    = {https://zillow.github.io/quantile-forest/}
+}
diff --git a/paper/figures/imputation_comparison_by_income_decile.png b/paper/figures/imputation_comparison_by_income_decile.png
new file mode 100644
index 0000000..d3eb1a6
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diff --git a/paper/figures/imputation_distributions_method_comparison.png b/paper/figures/imputation_distributions_method_comparison.png
new file mode 100644
index 0000000..45f20aa
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diff --git a/paper/figures/quantile_loss_comparison.png b/paper/figures/quantile_loss_comparison.png
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diff --git a/paper/imputing-from-scf-to-cps.ipynb b/paper/imputing-from-scf-to-cps.ipynb
index 9491b78..fc2a827 100644
--- a/paper/imputing-from-scf-to-cps.ipynb
+++ b/paper/imputing-from-scf-to-cps.ipynb
@@ -19,16 +19,7 @@
    "execution_count": 1,
    "id": "1c672d6a",
    "metadata": {},
-   "outputs": [
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "Error importing in API mode: ImportError(\"dlopen(/Users/movil1/envs/pe3.13/lib/python3.13/site-packages/_rinterface_cffi_api.abi3.so, 0x0002): Library not loaded: /Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.dylib\\n  Referenced from: <21BE8260-F4D5-3597-9DD0-6953BC4DDF3D> /Users/movil1/envs/pe3.13/lib/python3.13/site-packages/_rinterface_cffi_api.abi3.so\\n  Reason: tried: '/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.dylib' (no such file), '/System/Volumes/Preboot/Cryptexes/OS/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.dylib' (no such file), '/Library/Frameworks/R.framework/Versions/4.5-arm64/Resources/lib/libRblas.dylib' (no such file)\")\n",
-      "Trying to import in ABI mode.\n"
-     ]
-    }
-   ],
+   "outputs": [],
    "source": [
     "import io\n",
     "import logging\n",
@@ -77,7 +68,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "100%|██████████| 1/1 [00:01<00:00,  1.85s/it]\n"
+      "100%|██████████| 1/1 [00:00<00:00,  1.47it/s]\n"
      ]
     }
    ],
@@ -317,7 +308,7 @@
      "name": "stderr",
      "output_type": "stream",
      "text": [
-      "/var/folders/yg/xdp70k_n4qj9ph1_0lm435c00000gp/T/ipykernel_19823/1719285347.py:136: SettingWithCopyWarning: \n",
+      "/var/folders/yg/xdp70k_n4qj9ph1_0lm435c00000gp/T/ipykernel_22131/1719285347.py:136: SettingWithCopyWarning: \n",
       "A value is trying to be set on a copy of a slice from a DataFrame.\n",
       "Try using .loc[row_indexer,col_indexer] = value instead\n",
       "\n",
@@ -509,7 +500,7 @@
           "color": "#1f77b4"
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+         "nbinsx": 200,
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@@ -23496,713563 +23487,267671 @@
           "color": "#ff7f0e"
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          "name": "SCF Weighted (through sampling)",
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+         "nbinsx": 200,
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           4,
-          6,
-          8,
-          10
-         ],
-         "title": {
-          "text": "Net Worth (log10 scale)"
-         }
-        },
-        "yaxis": {
-         "title": {
-          "text": "Percentage"
-         }
-        }
-       }
-      }
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "weights_col = scf_data[\"wgt\"].values\n",
-    "weights_normalized = weights_col / weights_col.sum()\n",
-    "scf_data_weighted = scf_data.sample(\n",
-    "    n=len(scf_data),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "\n",
-    "# Create a combined plot comparing weighted and unweighted SCF distributions\n",
-    "def safe_log10(x):\n",
-    "    \"\"\"Apply log10 to absolute values, preserving sign.\"\"\"\n",
-    "    sign = np.sign(x)\n",
-    "    log_x = np.log10(np.maximum(np.abs(x), 1e-10))\n",
-    "    return sign * log_x\n",
-    "\n",
-    "\n",
-    "# Apply safe log transformation to both datasets\n",
-    "scf_log = safe_log10(scf_data[\"networth\"])\n",
-    "scf_weighted_log = safe_log10(scf_data_weighted[\"networth\"])\n",
-    "\n",
-    "# Create the figure\n",
-    "fig = go.Figure()\n",
-    "\n",
-    "# Add unweighted SCF histogram\n",
-    "fig.add_trace(\n",
-    "    go.Histogram(\n",
-    "        x=scf_log,\n",
-    "        nbinsx=150,\n",
-    "        opacity=0.7,\n",
-    "        name=\"SCF Unweighted\",\n",
-    "        marker_color=\"#1f77b4\",\n",
-    "        histnorm=\"percent\",  # Normalize to percentages for better comparison\n",
-    "    )\n",
-    ")\n",
-    "\n",
-    "# Add weighted SCF histogram\n",
-    "fig.add_trace(\n",
-    "    go.Histogram(\n",
-    "        x=scf_weighted_log,\n",
-    "        nbinsx=150,\n",
-    "        opacity=0.7,\n",
-    "        name=\"SCF Weighted (through sampling)\",\n",
-    "        marker_color=\"#ff7f0e\",\n",
-    "        histnorm=\"percent\",  # Normalize to percentages for better comparison\n",
-    "    )\n",
-    ")\n",
-    "\n",
-    "# Calculate statistics for both distributions\n",
-    "unweighted_median = np.median(scf_log)\n",
-    "weighted_median = np.median(scf_weighted_log)\n",
-    "unweighted_mean = np.mean(scf_log)\n",
-    "weighted_mean = np.mean(scf_weighted_log)\n",
-    "\n",
-    "# Add median lines\n",
-    "fig.add_trace(\n",
-    "    go.Scatter(\n",
-    "        x=[unweighted_median, unweighted_median],\n",
-    "        y=[0, 8],\n",
-    "        mode=\"lines\",\n",
-    "        line=dict(color=\"#1f77b4\", width=2, dash=\"dash\"),\n",
-    "        name=f\"Unweighted Median: ${10**unweighted_median:,.0f}\",\n",
-    "    )\n",
-    ")\n",
-    "\n",
-    "fig.add_trace(\n",
-    "    go.Scatter(\n",
-    "        x=[weighted_median, weighted_median],\n",
-    "        y=[0, 8],\n",
-    "        mode=\"lines\",\n",
-    "        line=dict(color=\"#ff7f0e\", width=2, dash=\"dash\"),\n",
-    "        name=f\"Weighted Median: ${10**weighted_median:,.0f}\",\n",
-    "    )\n",
-    ")\n",
-    "\n",
-    "# Update layout\n",
-    "fig.update_layout(\n",
-    "    title=\"SCF Net Worth Distribution: Weighted vs Unweighted (Log Scale)\",\n",
-    "    xaxis_title=\"Net Worth (log10 scale)\",\n",
-    "    yaxis_title=\"Percentage\",\n",
-    "    height=600,\n",
-    "    width=900,\n",
-    "    barmode=\"overlay\",\n",
-    "    bargap=0.1,\n",
-    "    paper_bgcolor=\"#F0F0F0\",\n",
-    "    plot_bgcolor=\"#F0F0F0\",\n",
-    "    legend=dict(\n",
-    "        x=0.01,\n",
-    "        y=0.99,\n",
-    "        bgcolor=\"rgba(255,255,255,0.8)\",\n",
-    "        bordercolor=\"rgba(0,0,0,0.3)\",\n",
-    "        borderwidth=1,\n",
-    "        orientation=\"v\",\n",
-    "        xanchor=\"left\",\n",
-    "        yanchor=\"top\",\n",
-    "    ),\n",
-    ")\n",
-    "\n",
-    "# Custom tick formatting for x-axis\n",
-    "tick_values = [-6, -4, -2, 0, 2, 4, 6, 8, 10]\n",
-    "tick_labels = []\n",
-    "for x in tick_values:\n",
-    "    if x >= 0:\n",
-    "        tick_labels.append(f\"${10**x:,.0f}\")\n",
-    "    else:\n",
-    "        tick_labels.append(f\"-${10**abs(x):,.0f}\")\n",
-    "\n",
-    "fig.update_xaxes(tickvals=tick_values, ticktext=tick_labels)\n",
-    "\n",
-    "# Add annotations with statistics\n",
-    "fig.add_annotation(\n",
-    "    x=0.98,\n",
-    "    y=0.95,\n",
-    "    xref=\"paper\",\n",
-    "    yref=\"paper\",\n",
-    "    text=(\n",
-    "        f\"<b>Unweighted:</b><br>\"\n",
-    "        f\"Median: ${10**unweighted_median:,.0f}<br>\"\n",
-    "        f\"Mean: ${10**unweighted_mean:,.0f}<br><br>\"\n",
-    "        f\"<b>Weighted:</b><br>\"\n",
-    "        f\"Median: ${10**weighted_median:,.0f}<br>\"\n",
-    "        f\"Mean: ${10**weighted_mean:,.0f}\"\n",
-    "    ),\n",
-    "    showarrow=False,\n",
-    "    bgcolor=\"rgba(255,255,255,0.9)\",\n",
-    "    bordercolor=\"rgba(0,0,0,0.3)\",\n",
-    "    borderwidth=1,\n",
-    "    font=dict(size=11),\n",
-    "    xanchor=\"right\",\n",
-    "    yanchor=\"top\",\n",
-    ")\n",
-    "\n",
-    "fig.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "f9c19660",
-   "metadata": {},
-   "source": [
-    "## Running wealth imputation with autoimpute\n",
-    "\n",
-    "After harmonizing the two datasets, the `autoimpute` function from `microimpute` can be used to transfer wealth information from the SCF to the CPS. This powerful function streamlines the imputation process by automating hyperparameter tuning, method selection, validation, and application.\n",
-    "\n",
-    "Behind the scenes, `autoimpute` evaluates multiple statistical approaches, including Quantile Random Forest, Ordinary Least Squares, Quantile Regression, and Statistical Matching. It performs cross-validation to determine which method most accurately captures the relationship between the predictor variables and wealth measures in the SCF data. The function then applies the best-performing method to generate synthetic wealth values for CPS households.\n",
-    "\n",
-    "By enabling hyperparameter tuning, the function can optimize each method's parameters, further improving imputation accuracy. This automated approach saves considerable time and effort compared to manually testing different imputation strategies, while ensuring the selection of the most appropriate method for this specific imputation task."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 7,
-   "id": "c7a96f83",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "0519dc84d4d14bea9fd5e120d1978669",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Evaluating models:   0%|          | 0/4 [00:00<?, ?it/s]"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "name": "stderr",
-     "output_type": "stream",
-     "text": [
-      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
-      "[Parallel(n_jobs=-1)]: Done   2 out of   5 | elapsed:   20.9s remaining:   31.4s\n",
-      "[Parallel(n_jobs=-1)]: Done   3 out of   5 | elapsed:   21.1s remaining:   14.1s\n",
-      "[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:   21.2s finished\n",
-      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
-      "[Parallel(n_jobs=-1)]: Done   2 out of   5 | elapsed:    0.5s remaining:    0.7s\n",
-      "[Parallel(n_jobs=-1)]: Done   3 out of   5 | elapsed:    0.5s remaining:    0.3s\n",
-      "[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    0.5s finished\n",
-      "[Parallel(n_jobs=-1)]: Using backend LokyBackend with 8 concurrent workers.\n",
-      "[Parallel(n_jobs=-1)]: Done   2 out of   5 | elapsed:    5.0s remaining:    7.5s\n",
-      "[Parallel(n_jobs=-1)]: Done   3 out of   5 | elapsed:    5.0s remaining:    3.4s\n",
-      "[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    5.5s finished\n",
-      "[Parallel(n_jobs=1)]: Done   1 tasks      | elapsed:   51.1s\n",
-      "[Parallel(n_jobs=1)]: Done   4 tasks      | elapsed:  3.3min\n",
-      "[Parallel(n_jobs=1)]: Done   5 out of   5 | elapsed:  4.2min finished\n"
-     ]
-    }
-   ],
-   "source": [
-    "warnings.filterwarnings(\"ignore\")\n",
-    "\n",
-    "# Run the autoimpute process\n",
-    "autoimpute_results = autoimpute(\n",
-    "    donor_data=scf_data,\n",
-    "    receiver_data=cps_data,\n",
-    "    predictors=predictors,\n",
-    "    imputed_variables=imputed_variables,\n",
-    "    weight_col=weights[0],\n",
-    "    tune_hyperparameters=False,  # enable automated hyperparameter tuning\n",
-    "    normalize_data=True,  # normalization\n",
-    "    impute_all=True,\n",
-    ")\n",
-    "\n",
-    "logger.info(\n",
-    "    f\"Shape of receiver data before imputation: {cps_data.shape} \\nShape of receiver data after imputation: {autoimpute_results.receiver_data.shape}\"\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "32c2c1ad",
-   "metadata": {},
-   "source": [
-    "## Comparing method performance\n",
-    "\n",
-    "The method comparison plot below shows how different imputation methods performed across various quantiles. Lower quantile loss values indicate better performance. "
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 8,
-   "id": "38693461",
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-        }
-       }
-      }
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from microimpute.visualizations.comparison_plots import method_comparison_results\n",
-    "\n",
-    "comparison_viz = method_comparison_results(\n",
-    "    data=autoimpute_results.cv_results,\n",
-    "    metric_name=\"quantile loss\",\n",
-    "    data_format=\"wide\",\n",
-    ")\n",
-    "fig = comparison_viz.plot(\n",
-    "    title=\"Autoimpute method comparison\",\n",
-    "    show_mean=True,\n",
-    ")\n",
-    "fig.show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "7e92e41c",
-   "metadata": {},
-   "source": [
-    "## Evaluating predictors' influence on the imputation results\n",
-    "\n",
-    "To understand the relationship between the variables we have selected as predictors and the imputation results obtained, we can assess correlation between predictors, and the sensitivity that our results demonstrate to a different number or sequence of predictors used."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "8ee36de3",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from microimpute.evaluations.predictor_analysis import compute_predictor_correlations\n",
-    "\n",
-    "correlations = compute_predictor_correlations(scf_data, predictors, imputed_variables)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 18,
-   "id": "7a6a13b6",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>is_female</th>\n",
-       "      <th>age</th>\n",
-       "      <th>race</th>\n",
-       "      <th>employment_income</th>\n",
-       "      <th>interest_dividend_income</th>\n",
-       "      <th>pension_income</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>is_female</th>\n",
-       "      <td>1.000000</td>\n",
-       "      <td>-0.018881</td>\n",
-       "      <td>0.057994</td>\n",
-       "      <td>-0.085917</td>\n",
-       "      <td>-0.037146</td>\n",
-       "      <td>-0.055694</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>age</th>\n",
-       "      <td>-0.018881</td>\n",
-       "      <td>1.000000</td>\n",
-       "      <td>-0.204776</td>\n",
-       "      <td>0.018204</td>\n",
-       "      <td>0.093807</td>\n",
-       "      <td>0.283672</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>race</th>\n",
-       "      <td>0.057994</td>\n",
-       "      <td>-0.204776</td>\n",
-       "      <td>1.000000</td>\n",
-       "      <td>-0.046325</td>\n",
-       "      <td>-0.036117</td>\n",
-       "      <td>-0.111804</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>employment_income</th>\n",
-       "      <td>-0.085917</td>\n",
-       "      <td>0.018204</td>\n",
-       "      <td>-0.046325</td>\n",
-       "      <td>1.000000</td>\n",
-       "      <td>0.056797</td>\n",
-       "      <td>0.040700</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>interest_dividend_income</th>\n",
-       "      <td>-0.037146</td>\n",
-       "      <td>0.093807</td>\n",
-       "      <td>-0.036117</td>\n",
-       "      <td>0.056797</td>\n",
-       "      <td>1.000000</td>\n",
-       "      <td>0.121772</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>pension_income</th>\n",
-       "      <td>-0.055694</td>\n",
-       "      <td>0.283672</td>\n",
-       "      <td>-0.111804</td>\n",
-       "      <td>0.040700</td>\n",
-       "      <td>0.121772</td>\n",
-       "      <td>1.000000</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "                          is_female       age      race  employment_income  \\\n",
-       "is_female                  1.000000 -0.018881  0.057994          -0.085917   \n",
-       "age                       -0.018881  1.000000 -0.204776           0.018204   \n",
-       "race                       0.057994 -0.204776  1.000000          -0.046325   \n",
-       "employment_income         -0.085917  0.018204 -0.046325           1.000000   \n",
-       "interest_dividend_income  -0.037146  0.093807 -0.036117           0.056797   \n",
-       "pension_income            -0.055694  0.283672 -0.111804           0.040700   \n",
-       "\n",
-       "                          interest_dividend_income  pension_income  \n",
-       "is_female                                -0.037146       -0.055694  \n",
-       "age                                       0.093807        0.283672  \n",
-       "race                                     -0.036117       -0.111804  \n",
-       "employment_income                         0.056797        0.040700  \n",
-       "interest_dividend_income                  1.000000        0.121772  \n",
-       "pension_income                            0.121772        1.000000  "
-      ]
-     },
-     "execution_count": 18,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "correlations[\"pearson\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 10,
-   "id": "e5de4cfe",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>networth</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>is_female</th>\n",
-       "      <td>0.014095</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>age</th>\n",
-       "      <td>0.119553</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>race</th>\n",
-       "      <td>0.027996</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>employment_income</th>\n",
-       "      <td>0.121915</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>interest_dividend_income</th>\n",
-       "      <td>0.085286</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>pension_income</th>\n",
-       "      <td>0.059902</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "                          networth\n",
-       "is_female                 0.014095\n",
-       "age                       0.119553\n",
-       "race                      0.027996\n",
-       "employment_income         0.121915\n",
-       "interest_dividend_income  0.085286\n",
-       "pension_income            0.059902"
-      ]
-     },
-     "execution_count": 10,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "correlations[\"predictor_target_mi\"]"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 11,
-   "id": "cbbe4764",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "3104428a4ff4437a98f6f64c1ed04f04",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Leave-one-out analysis:   0%|          | 0/6 [00:00<?, ?it/s]"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    },
-    {
-     "data": {
-      "application/vnd.jupyter.widget-view+json": {
-       "model_id": "6b4f2c3c10c84c079582ca905a824774",
-       "version_major": 2,
-       "version_minor": 0
-      },
-      "text/plain": [
-       "Progressive inclusion:   0%|          | 0/6 [00:00<?, ?it/s]"
-      ]
-     },
-     "metadata": {},
-     "output_type": "display_data"
-    }
-   ],
-   "source": [
-    "from microimpute.evaluations.predictor_analysis import progressive_predictor_inclusion, leave_one_out_analysis\n",
-    "from microimpute.models import QRF\n",
-    "\n",
-    "leave_one_out_results = leave_one_out_analysis(\n",
-    "    scf_data,\n",
-    "    predictors,\n",
-    "    imputed_variables,\n",
-    "    QRF\n",
-    ")\n",
-    "\n",
-    "predictor_inclusion_results = progressive_predictor_inclusion(\n",
-    "    scf_data,\n",
-    "    predictors,\n",
-    "    imputed_variables,\n",
-    "    QRF\n",
-    ")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 12,
-   "id": "6fc4dbd3",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/html": [
-       "<div>\n",
-       "<style scoped>\n",
-       "    .dataframe tbody tr th:only-of-type {\n",
-       "        vertical-align: middle;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe tbody tr th {\n",
-       "        vertical-align: top;\n",
-       "    }\n",
-       "\n",
-       "    .dataframe thead th {\n",
-       "        text-align: right;\n",
-       "    }\n",
-       "</style>\n",
-       "<table border=\"1\" class=\"dataframe\">\n",
-       "  <thead>\n",
-       "    <tr style=\"text-align: right;\">\n",
-       "      <th></th>\n",
-       "      <th>predictor_removed</th>\n",
-       "      <th>avg_quantile_loss</th>\n",
-       "      <th>avg_log_loss</th>\n",
-       "      <th>loss_increase</th>\n",
-       "      <th>relative_impact</th>\n",
-       "      <th>baseline_quantile_loss</th>\n",
-       "      <th>baseline_log_loss</th>\n",
-       "    </tr>\n",
-       "  </thead>\n",
-       "  <tbody>\n",
-       "    <tr>\n",
-       "      <th>4</th>\n",
-       "      <td>interest_dividend_income</td>\n",
-       "      <td>3.413499e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>1.865978e+06</td>\n",
-       "      <td>120.578572</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>3</th>\n",
-       "      <td>employment_income</td>\n",
-       "      <td>2.073023e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>5.255021e+05</td>\n",
-       "      <td>33.957678</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>1</th>\n",
-       "      <td>age</td>\n",
-       "      <td>2.051171e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>5.036499e+05</td>\n",
-       "      <td>32.545597</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>5</th>\n",
-       "      <td>pension_income</td>\n",
-       "      <td>1.724660e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>1.771395e+05</td>\n",
-       "      <td>11.446667</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>2</th>\n",
-       "      <td>race</td>\n",
-       "      <td>1.586420e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>3.889930e+04</td>\n",
-       "      <td>2.513653</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "    <tr>\n",
-       "      <th>0</th>\n",
-       "      <td>is_female</td>\n",
-       "      <td>1.579172e+06</td>\n",
-       "      <td>0</td>\n",
-       "      <td>3.165105e+04</td>\n",
-       "      <td>2.045275</td>\n",
-       "      <td>1.547521e+06</td>\n",
-       "      <td>0</td>\n",
-       "    </tr>\n",
-       "  </tbody>\n",
-       "</table>\n",
-       "</div>"
-      ],
-      "text/plain": [
-       "          predictor_removed  avg_quantile_loss  avg_log_loss  loss_increase  \\\n",
-       "4  interest_dividend_income       3.413499e+06             0   1.865978e+06   \n",
-       "3         employment_income       2.073023e+06             0   5.255021e+05   \n",
-       "1                       age       2.051171e+06             0   5.036499e+05   \n",
-       "5            pension_income       1.724660e+06             0   1.771395e+05   \n",
-       "2                      race       1.586420e+06             0   3.889930e+04   \n",
-       "0                 is_female       1.579172e+06             0   3.165105e+04   \n",
-       "\n",
-       "   relative_impact  baseline_quantile_loss  baseline_log_loss  \n",
-       "4       120.578572            1.547521e+06                  0  \n",
-       "3        33.957678            1.547521e+06                  0  \n",
-       "1        32.545597            1.547521e+06                  0  \n",
-       "5        11.446667            1.547521e+06                  0  \n",
-       "2         2.513653            1.547521e+06                  0  \n",
-       "0         2.045275            1.547521e+06                  0  "
-      ]
-     },
-     "execution_count": 12,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
-   "source": [
-    "leave_one_out_results"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 13,
-   "id": "3581c6a8",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Inclusion order: ['interest_dividend_income', 'age', 'employment_income', 'pension_income', 'race', 'is_female']\n",
-      "Predictor: interest_dividend_income \n",
-      "Loss reduction: inf\n",
-      "Predictor: age \n",
-      "Loss reduction: 2060406.080826412\n",
-      "Predictor: employment_income \n",
-      "Loss reduction: 805506.5277186302\n",
-      "Predictor: pension_income \n",
-      "Loss reduction: 179712.68249378656\n",
-      "Predictor: race \n",
-      "Loss reduction: 32655.528693717206\n",
-      "Predictor: is_female \n",
-      "Loss reduction: 29449.27407725784\n"
-     ]
-    }
-   ],
-   "source": [
-    "print(f\"Inclusion order: {predictor_inclusion_results['inclusion_order']}\")\n",
-    "for element in predictor_inclusion_results[\"predictor_impacts\"]:\n",
-    "    print(f\"Predictor: {element['predictor']} \\nLoss reduction: {element['loss_reduction']}\")"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "62ef14a3",
-   "metadata": {},
-   "source": [
-    "## Evaluating wealth imputations\n",
-    "\n",
-    "To assess the imputation results, a comparison of the distribution of wealth in the original SCF data with the imputed values in the CPS allows examining how well the imputation preserves important characteristics of the wealth distribution, such as its shape, central tendency, and dispersion.\n",
-    "\n",
-    "Wealth distributions are typically highly skewed, with a long right tail representing a small number of households with very high net worth. A successful imputation should preserve this characteristic skewness while maintaining realistic values across the entire distribution. Examining both the raw distributions and log-transformed versions of wealth values can better capture important information for evaluation."
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 14,
-   "id": "db073e13",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Model: best_method, distribution similarity: \n",
-      "   Variable                Metric      Distance\n",
-      "0  networth  wasserstein_distance  1.589601e+07\n",
-      "Model: OLS, distribution similarity: \n",
-      "   Variable                Metric      Distance\n",
-      "0  networth  wasserstein_distance  7.211268e+07\n",
-      "Model: QuantReg, distribution similarity: \n",
-      "   Variable                Metric      Distance\n",
-      "0  networth  wasserstein_distance  5.352203e+07\n",
-      "Model: Matching, distribution similarity: \n",
-      "   Variable                Metric      Distance\n",
-      "0  networth  wasserstein_distance  1.440218e+07\n"
-     ]
-    }
-   ],
-   "source": [
-    "from microimpute.comparisons.metrics import compare_distributions\n",
-    "\n",
-    "for model, imputations in autoimpute_results.imputations.items():\n",
-    "    print(f\"Model: {model}, distribution similarity: \\n{compare_distributions(\n",
-    "    donor_data=pd.DataFrame(scf_data[\"networth\"]),\n",
-    "    receiver_data=pd.DataFrame(imputations[\"networth\"]),\n",
-    "    imputed_variables=imputed_variables,\n",
-    ")}\")"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 15,
-   "id": "ca8d5faf",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "def plot_log_transformed_distributions(\n",
-    "    scf_data: pd.DataFrame,\n",
-    "    imputed_data: pd.DataFrame,\n",
-    "    title: Optional[str] = None,\n",
-    ") -> go.Figure:\n",
-    "    \"\"\"Plot the log-transformed distribution of net worth in SCF and imputed CPS data.\"\"\"\n",
-    "\n",
-    "    palette = px.colors.qualitative.Plotly\n",
-    "    scf_color = \"#1f77b4\"  # palette[0]\n",
-    "    cps_color = \"#9467bd\"  # palette[1]\n",
-    "    scf_median_color = scf_color\n",
-    "    cps_median_color = cps_color\n",
-    "    scf_mean_color = scf_color\n",
-    "    cps_mean_color = cps_color\n",
-    "\n",
-    "    def safe_log(x):\n",
-    "        sign = np.sign(x)\n",
-    "        log_x = np.log10(np.maximum(np.abs(x), 1e-10))\n",
-    "        return sign * log_x\n",
-    "\n",
-    "    scf_log = safe_log(scf_data[\"networth\"])\n",
-    "    cps_log = safe_log(imputed_data[\"networth\"])\n",
-    "\n",
-    "    scf_log_median, cps_log_median = np.median(scf_log), np.median(cps_log)\n",
-    "    scf_log_mean, cps_log_mean = np.mean(scf_log), np.mean(cps_log)\n",
-    "\n",
-    "    fig = go.Figure()\n",
-    "\n",
-    "    # histograms\n",
-    "    fig.add_trace(\n",
-    "        go.Histogram(\n",
-    "            x=scf_log,\n",
-    "            nbinsx=150,\n",
-    "            opacity=0.7,\n",
-    "            name=\"SCF (weighted) log net worth\",\n",
-    "            marker_color=scf_color,\n",
-    "        )\n",
-    "    )\n",
-    "    fig.add_trace(\n",
-    "        go.Histogram(\n",
-    "            x=cps_log,\n",
-    "            nbinsx=150,\n",
-    "            opacity=0.7,\n",
-    "            name=\"CPS imputed log net worth\",\n",
-    "            marker_color=cps_color,\n",
-    "        )\n",
-    "    )\n",
-    "\n",
-    "    # medians (dashed)\n",
-    "    fig.add_trace(\n",
-    "        go.Scatter(\n",
-    "            x=[scf_log_median, scf_log_median],\n",
-    "            y=[0, 20],\n",
-    "            mode=\"lines\",\n",
-    "            line=dict(color=scf_median_color, width=2, dash=\"dash\"),\n",
-    "            name=f\"SCF median: ${10**scf_log_median:,.0f}\",\n",
-    "        )\n",
-    "    )\n",
-    "    fig.add_trace(\n",
-    "        go.Scatter(\n",
-    "            x=[cps_log_median, cps_log_median],\n",
-    "            y=[0, 20],\n",
-    "            mode=\"lines\",\n",
-    "            line=dict(color=cps_median_color, width=2, dash=\"dash\"),\n",
-    "            name=f\"CPS median: ${10**cps_log_median:,.0f}\",\n",
-    "        )\n",
-    "    )\n",
-    "\n",
-    "    # means (dotted)\n",
-    "    fig.add_trace(\n",
-    "        go.Scatter(\n",
-    "            x=[scf_log_mean, scf_log_mean],\n",
-    "            y=[0, 20],\n",
-    "            mode=\"lines\",\n",
-    "            line=dict(color=scf_mean_color, width=2, dash=\"dot\"),\n",
-    "            name=f\"SCF mean: ${10**scf_log_mean:,.0f}\",\n",
-    "        )\n",
-    "    )\n",
-    "    fig.add_trace(\n",
-    "        go.Scatter(\n",
-    "            x=[cps_log_mean, cps_log_mean],\n",
-    "            y=[0, 20],\n",
-    "            mode=\"lines\",\n",
-    "            line=dict(color=cps_mean_color, width=2, dash=\"dot\"),\n",
-    "            name=f\"CPS mean: ${10**cps_log_mean:,.0f}\",\n",
-    "        )\n",
-    "    )\n",
-    "\n",
-    "    # layout\n",
-    "    fig.update_layout(\n",
-    "        title=(\n",
-    "            title\n",
-    "            if title\n",
-    "            else \"Log-transformed net worth distribution comparison\"\n",
-    "        ),\n",
-    "        xaxis_title=\"Net worth\",\n",
-    "        yaxis_title=\"Frequency\",\n",
-    "        height=PLOT_CONFIG[\"height\"],\n",
-    "        width=PLOT_CONFIG[\"width\"],\n",
-    "        barmode=\"overlay\",\n",
-    "        bargap=0.1,\n",
-    "        paper_bgcolor=\"#F0F0F0\",\n",
-    "        plot_bgcolor=\"#F0F0F0\",\n",
-    "        legend=dict(\n",
-    "            x=0.01,\n",
-    "            y=0.99,\n",
-    "            bgcolor=\"rgba(255,255,255,0.8)\",\n",
-    "            bordercolor=\"rgba(0,0,0,0.3)\",\n",
-    "            borderwidth=1,\n",
-    "            orientation=\"v\",\n",
-    "            xanchor=\"left\",\n",
-    "            yanchor=\"top\",\n",
-    "        ),\n",
-    "    )\n",
-    "\n",
-    "    # custom ticks\n",
-    "    tick_values = [-6, -4, -2, 0, 2, 4, 6, 8]\n",
-    "    tick_labels = [\n",
-    "        \"$\" + format(10**x if x >= 0 else -(10 ** abs(x)), \",.0f\")\n",
-    "        for x in tick_values\n",
-    "    ]\n",
-    "    fig.update_xaxes(\n",
-    "        showgrid=False,\n",
-    "        zeroline=False,\n",
-    "        tickvals=tick_values,\n",
-    "        ticktext=tick_labels,\n",
-    "    )\n",
-    "    fig.update_yaxes(showgrid=False, zeroline=False)\n",
-    "\n",
-    "    return fig"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 16,
-   "id": "7f501fd2",
-   "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "application/vnd.plotly.v1+json": {
-       "config": {
-        "plotlyServerURL": "https://plot.ly"
-       },
-       "data": [
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-         "marker": {
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-         "name": "SCF (weighted) log net worth",
-         "nbinsx": 150,
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-         "type": "histogram",
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-         "text": "Log-transformed net worth distribution comparison"
-        },
-        "width": 750,
-        "xaxis": {
-         "showgrid": false,
-         "ticktext": [
-          "$-1,000,000",
-          "$-10,000",
-          "$-100",
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-          "$10,000",
-          "$1,000,000",
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-          "text": "Net worth"
-         },
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-          "text": "Frequency"
-         },
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-     "metadata": {},
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-   ],
-   "source": [
-    "weights_col = cps_data[\"household_weight\"].values\n",
-    "weights_normalized = weights_col / weights_col.sum()\n",
-    "imputed_data_weighted = autoimpute_results.receiver_data.sample(\n",
-    "    n=len(autoimpute_results.receiver_data),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "plot_log_transformed_distributions(scf_data_weighted, autoimpute_results.receiver_data).show()"
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "4ab616c4",
-   "metadata": {},
-   "source": [
-    "The logarithmic transformation provides a clearer view of the wealth distribution across its entire range. By logarithmically scaling the data, the extreme values are compressed while expanding the visibility of differences in the lower and middle portions of the distribution.\n",
-    "\n",
-    "This transformation is particularly valuable for wealth data, where values can span many orders of magnitude. The plot above, shows how closely the imputed CPS wealth distribution matches the original SCF distribution in terms of shape and central tendency. The vertical lines marking the mean and median values help gauge how these statistical properties have been preserved through the imputation process."
-   ]
-  },
-  {
-   "cell_type": "markdown",
-   "id": "d287a7aa",
-   "metadata": {},
-   "source": [
-    "## Imputing wealth with the models separately"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": 17,
-   "id": "d0194bd2",
-   "metadata": {},
-   "outputs": [
-    {
-     "ename": "ValueError",
-     "evalue": "not enough values to unpack (expected 3, got 2)",
-     "output_type": "error",
-     "traceback": [
-      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
-      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
-      "Cell \u001b[0;32mIn[17], line 4\u001b[0m\n\u001b[1;32m      1\u001b[0m donor_data \u001b[38;5;241m=\u001b[39m scf_data[predictors \u001b[38;5;241m+\u001b[39m imputed_variables \u001b[38;5;241m+\u001b[39m weights]\n\u001b[1;32m      2\u001b[0m receiver_data \u001b[38;5;241m=\u001b[39m cps_data[predictors \u001b[38;5;241m+\u001b[39m household_weights]\n\u001b[0;32m----> 4\u001b[0m donor_data, dummy_info, normalizing_params \u001b[38;5;241m=\u001b[39m preprocess_data(\n\u001b[1;32m      5\u001b[0m     donor_data[predictors \u001b[38;5;241m+\u001b[39m imputed_variables], normalize\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, full_data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m      6\u001b[0m )\n\u001b[1;32m      7\u001b[0m donor_data[weights[\u001b[38;5;241m0\u001b[39m]] \u001b[38;5;241m=\u001b[39m scf_data[weights[\u001b[38;5;241m0\u001b[39m]]\n\u001b[1;32m      8\u001b[0m receiver_data, dummy_info_cps, _ \u001b[38;5;241m=\u001b[39m preprocess_data(\n\u001b[1;32m      9\u001b[0m     receiver_data[predictors], normalize\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m, full_data\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m     10\u001b[0m )\n",
-      "\u001b[0;31mValueError\u001b[0m: not enough values to unpack (expected 3, got 2)"
-     ]
-    }
-   ],
-   "source": [
-    "donor_data = scf_data[predictors + imputed_variables + weights]\n",
-    "receiver_data = cps_data[predictors + household_weights]\n",
-    "\n",
-    "donor_data, dummy_info, normalizing_params = preprocess_data(\n",
-    "    donor_data[predictors + imputed_variables], normalize=True, full_data=True\n",
-    ")\n",
-    "donor_data[weights[0]] = scf_data[weights[0]]\n",
-    "receiver_data, dummy_info_cps, _ = preprocess_data(\n",
-    "    receiver_data[predictors], normalize=True, full_data=True\n",
-    ")\n",
-    "receiver_data[\"household_weight\"] = cps_data[\"household_weight\"]\n",
-    "receiver_data[\"household_net_income\"] = cps_data[\"household_net_income\"]\n",
-    "\n",
-    "mean = pd.Series({col: p[\"mean\"] for col, p in normalizing_params.items()})\n",
-    "std = pd.Series({col: p[\"std\"] for col, p in normalizing_params.items()})\n",
-    "\n",
-    "for col, dummy_cols in dummy_info[\"column_mapping\"].items():\n",
-    "    if col in predictors:\n",
-    "        predictors.remove(col)\n",
-    "        predictors.extend(dummy_cols)\n",
-    "    elif col in imputed_variables:\n",
-    "        imputed_variables.remove(col)\n",
-    "        imputed_variables.extend(dummy_cols)"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "3f889c3d",
-   "metadata": {},
-   "outputs": [],
-   "source": [
-    "from microimpute.models import *\n",
-    "\n",
-    "\n",
-    "def impute_scf_to_cps(\n",
-    "    model: Type[Imputer],\n",
-    "    donor_data: pd.DataFrame,\n",
-    "    receiver_data: pd.DataFrame,\n",
-    "    cps_data: pd.DataFrame,\n",
-    "    predictors: List[str],\n",
-    "    imputed_variables: List[str],\n",
-    "    weights: List[str],\n",
-    ") -> pd.DataFrame:\n",
-    "    \"\"\"Impute SCF data into CPS data using the specified model.\"\"\"\n",
-    "    model = model()\n",
-    "    logger.info(\"Created model\")\n",
-    "    fitted_model = model.fit(\n",
-    "        X_train=donor_data,\n",
-    "        predictors=predictors,\n",
-    "        imputed_variables=imputed_variables,\n",
-    "        weight_col=weights[0],\n",
-    "    )\n",
-    "    logger.info(\"Fitted model\")\n",
-    "    imputations = fitted_model.predict(X_test=receiver_data)\n",
-    "    logger.info(\"Generated imputations\")\n",
-    "\n",
-    "    cps_imputed = cps_data.copy()\n",
-    "    logger.info(\"Copied original receiver data\")\n",
-    "    cps_imputed[\"networth\"] = imputations[0.5][\"networth\"]\n",
-    "    logger.info(\"Added imputed networth to receiver data\")\n",
-    "\n",
-    "    return cps_imputed"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "e1df07ee",
-   "metadata": {},
-   "outputs": [
-    {
-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Created model\n",
-      "Fitted model\n",
-      "Generated imputations\n",
-      "Copied original receiver data\n",
-      "Added imputed networth to receiver data\n"
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-    "quantreg_cps_imputed = impute_scf_to_cps(\n",
-    "    model=QuantReg,\n",
-    "    donor_data=donor_data,\n",
-    "    receiver_data=receiver_data,\n",
-    "    cps_data=cps_data,\n",
-    "    predictors=predictors,\n",
-    "    imputed_variables=imputed_variables,\n",
-    "    weights=weights,\n",
-    ")\n",
-    "\n",
-    "quantreg_cps_imputed[\"networth\"] = quantreg_cps_imputed[\"networth\"].mul(\n",
-    "    std[\"networth\"]\n",
-    ")\n",
-    "quantreg_cps_imputed[\"networth\"] = quantreg_cps_imputed[\"networth\"].add(\n",
-    "    mean[\"networth\"]\n",
-    ")\n",
-    "\n",
-    "weights_col = receiver_data[\"household_weight\"].values\n",
-    "weights_normalized = weights_col / weights_col.sum()\n",
-    "quantreg_cps_imputed_weighted = quantreg_cps_imputed.sample(\n",
-    "    n=len(quantreg_cps_imputed),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "\n",
-    "plot_log_transformed_distributions(\n",
-    "    scf_data,\n",
-    "    quantreg_cps_imputed_weighted,\n",
-    "    \"Log-transformed net worth distribution comparison for QuantReg model\",\n",
-    ").show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "2cc63a51",
-   "metadata": {},
-   "outputs": [
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-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Created model\n",
-      "Fitted model\n",
-      "Generated imputations\n",
-      "Copied original receiver data\n",
-      "Added imputed networth to receiver data\n"
-     ]
-    },
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-         "text": "Log-transformed net worth distribution comparison for OLS model"
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-          "text": "Frequency"
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-   "source": [
-    "ols_cps_imputed = impute_scf_to_cps(\n",
-    "    model=OLS,\n",
-    "    donor_data=donor_data,\n",
-    "    receiver_data=receiver_data,\n",
-    "    cps_data=cps_data,\n",
-    "    predictors=predictors,\n",
-    "    imputed_variables=imputed_variables,\n",
-    "    weights=weights,\n",
-    ")\n",
-    "\n",
-    "ols_cps_imputed[\"networth\"] = ols_cps_imputed[\"networth\"].mul(std[\"networth\"])\n",
-    "ols_cps_imputed[\"networth\"] = ols_cps_imputed[\"networth\"].add(mean[\"networth\"])\n",
-    "\n",
-    "ols_cps_imputed_weighted = ols_cps_imputed.sample(\n",
-    "    n=len(ols_cps_imputed),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "plot_log_transformed_distributions(\n",
-    "    scf_data,\n",
-    "    ols_cps_imputed_weighted,\n",
-    "    \"Log-transformed net worth distribution comparison for OLS model\",\n",
-    ").show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "df3e3a1e",
-   "metadata": {},
-   "outputs": [
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-     "output_type": "stream",
-     "text": [
-      "Created model\n",
-      "Fitted model\n",
-      "Generated imputations\n",
-      "Copied original receiver data\n",
-      "Added imputed networth to receiver data\n"
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-    },
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-    "matching_cps_imputed = impute_scf_to_cps(\n",
-    "    model=Matching,\n",
-    "    donor_data=donor_data,\n",
-    "    receiver_data=receiver_data,\n",
-    "    cps_data=cps_data,\n",
-    "    predictors=predictors,\n",
-    "    imputed_variables=imputed_variables,\n",
-    "    weights=weights,\n",
-    ")\n",
-    "\n",
-    "matching_cps_imputed[\"networth\"] = matching_cps_imputed[\"networth\"].mul(\n",
-    "    std[\"networth\"]\n",
-    ")\n",
-    "matching_cps_imputed[\"networth\"] = matching_cps_imputed[\"networth\"].add(\n",
-    "    mean[\"networth\"]\n",
-    ")\n",
-    "\n",
-    "matching_cps_imputed_weighted = matching_cps_imputed.sample(\n",
-    "    n=len(matching_cps_imputed),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "plot_log_transformed_distributions(\n",
-    "    scf_data,\n",
-    "    matching_cps_imputed_weighted,\n",
-    "    \"Log-transformed net worth distribution comparison for Matching model\",\n",
-    ").show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "22617850",
-   "metadata": {},
-   "outputs": [
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-     "name": "stdout",
-     "output_type": "stream",
-     "text": [
-      "Created model\n",
-      "Fitted model\n",
-      "Generated imputations\n",
-      "Copied original receiver data\n",
-      "Added imputed networth to receiver data\n"
-     ]
-    },
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-         "text": "Log-transformed net worth distribution comparison for QRF model"
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-        "width": 750,
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-          "$-1,000,000",
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-          "text": "Frequency"
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-   "source": [
-    "from microimpute.models.qrf import QRF\n",
-    "\n",
-    "qrf_model = QRF()\n",
-    "logger.info(\"Created model\")\n",
-    "fitted_model, best_params = qrf_model.fit(\n",
-    "    X_train=donor_data,\n",
-    "    predictors=predictors,\n",
-    "    imputed_variables=imputed_variables,\n",
-    "    weight_col=weights[0],\n",
-    "    tune_hyperparameters=True,\n",
-    ")\n",
-    "logger.info(\"Fitted model\")\n",
-    "imputations = fitted_model.predict(X_test=receiver_data)\n",
-    "logger.info(\"Generated imputations\")\n",
-    "\n",
-    "qrf_cps_imputed = cps_data.copy()\n",
-    "logger.info(\"Copied original receiver data\")\n",
-    "qrf_cps_imputed[\"networth\"] = imputations[0.5][\"networth\"]\n",
-    "logger.info(\"Added imputed networth to receiver data\")\n",
-    "\n",
-    "qrf_cps_imputed[\"networth\"] = qrf_cps_imputed[\"networth\"].mul(std[\"networth\"])\n",
-    "qrf_cps_imputed[\"networth\"] = qrf_cps_imputed[\"networth\"].add(mean[\"networth\"])\n",
-    "\n",
-    "qrf_cps_imputed_weighted = qrf_cps_imputed.sample(\n",
-    "    n=len(qrf_cps_imputed),\n",
-    "    replace=True,\n",
-    "    weights=weights_normalized,\n",
-    ").reset_index(drop=True)\n",
-    "\n",
-    "plot_log_transformed_distributions(\n",
-    "    scf_data_weighted,\n",
-    "    qrf_cps_imputed_weighted,\n",
-    "    \"Log-transformed net worth distribution comparison for QRF model\",\n",
-    ").show()"
-   ]
-  },
-  {
-   "cell_type": "code",
-   "execution_count": null,
-   "id": "9c2888c7",
-   "metadata": {},
-   "outputs": [
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+            "showbackground": true,
+            "ticks": "",
+            "zerolinecolor": "white"
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+           "yaxis": {
+            "backgroundcolor": "#E5ECF6",
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+            "zerolinecolor": "white"
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+           "zaxis": {
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+            "ticks": "",
+            "zerolinecolor": "white"
+           }
+          },
+          "shapedefaults": {
+           "line": {
+            "color": "#2a3f5f"
+           }
+          },
+          "ternary": {
+           "aaxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "baxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "bgcolor": "#E5ECF6",
+           "caxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           }
+          },
+          "title": {
+           "x": 0.05
+          },
+          "xaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
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+           "automargin": true,
+           "gridcolor": "white",
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+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          }
+         }
+        },
+        "title": {
+         "text": "SCF Net Worth Distribution: Weighted vs Unweighted (Log Scale)"
+        },
+        "width": 900,
+        "xaxis": {
+         "ticktext": [
+          "-$1,000,000",
+          "-$10,000",
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+          4,
+          6,
+          8,
+          10
+         ],
+         "title": {
+          "text": "Net Worth (log10 scale)"
+         }
+        },
+        "yaxis": {
+         "title": {
+          "text": "Percentage"
+         }
+        }
+       }
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "weights_col = scf_data[\"wgt\"].values\n",
+    "weights_normalized = weights_col / weights_col.sum()\n",
+    "scf_data_weighted = scf_data.sample(\n",
+    "    n=len(scf_data),\n",
+    "    replace=True,\n",
+    "    weights=weights_normalized,\n",
+    ").reset_index(drop=True)\n",
+    "\n",
+    "\n",
+    "# Create a combined plot comparing weighted and unweighted SCF distributions\n",
+    "def safe_log10(x):\n",
+    "    \"\"\"Apply log10 to absolute values, preserving sign.\"\"\"\n",
+    "    sign = np.sign(x)\n",
+    "    log_x = np.log10(np.maximum(np.abs(x), 1e-10))\n",
+    "    return sign * log_x\n",
+    "\n",
+    "\n",
+    "# Apply safe log transformation to both datasets\n",
+    "scf_log = safe_log10(scf_data[\"networth\"])\n",
+    "scf_weighted_log = safe_log10(scf_data_weighted[\"networth\"])\n",
+    "\n",
+    "# Create the figure\n",
+    "fig = go.Figure()\n",
+    "\n",
+    "# Add unweighted SCF histogram\n",
+    "fig.add_trace(\n",
+    "    go.Histogram(\n",
+    "        x=scf_log,\n",
+    "        nbinsx=200,\n",
+    "        opacity=0.7,\n",
+    "        name=\"SCF Unweighted\",\n",
+    "        marker_color=\"#1f77b4\",\n",
+    "        histnorm=\"percent\",  # Normalize to percentages for better comparison\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "# Add weighted SCF histogram\n",
+    "fig.add_trace(\n",
+    "    go.Histogram(\n",
+    "        x=scf_weighted_log,\n",
+    "        nbinsx=200,\n",
+    "        opacity=0.7,\n",
+    "        name=\"SCF Weighted (through sampling)\",\n",
+    "        marker_color=\"#ff7f0e\",\n",
+    "        histnorm=\"percent\",\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "# Calculate statistics for both distributions\n",
+    "unweighted_median = np.median(scf_log)\n",
+    "weighted_median = np.median(scf_weighted_log)\n",
+    "unweighted_mean = np.mean(scf_log)\n",
+    "weighted_mean = np.mean(scf_weighted_log)\n",
+    "\n",
+    "# Add median lines\n",
+    "fig.add_trace(\n",
+    "    go.Scatter(\n",
+    "        x=[unweighted_median, unweighted_median],\n",
+    "        y=[0, 8],\n",
+    "        mode=\"lines\",\n",
+    "        line=dict(color=\"#1f77b4\", width=2, dash=\"dash\"),\n",
+    "        name=f\"Unweighted Median: ${10**unweighted_median:,.0f}\",\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "fig.add_trace(\n",
+    "    go.Scatter(\n",
+    "        x=[weighted_median, weighted_median],\n",
+    "        y=[0, 8],\n",
+    "        mode=\"lines\",\n",
+    "        line=dict(color=\"#ff7f0e\", width=2, dash=\"dash\"),\n",
+    "        name=f\"Weighted Median: ${10**weighted_median:,.0f}\",\n",
+    "    )\n",
+    ")\n",
+    "\n",
+    "# Update layout\n",
+    "fig.update_layout(\n",
+    "    title=\"SCF Net Worth Distribution: Weighted vs Unweighted (Log Scale)\",\n",
+    "    xaxis_title=\"Net Worth (log10 scale)\",\n",
+    "    yaxis_title=\"Percentage\",\n",
+    "    height=600,\n",
+    "    width=900,\n",
+    "    barmode=\"overlay\",\n",
+    "    bargap=0.1,\n",
+    "    paper_bgcolor=\"#F0F0F0\",\n",
+    "    plot_bgcolor=\"#F0F0F0\",\n",
+    "    legend=dict(\n",
+    "        x=0.01,\n",
+    "        y=0.99,\n",
+    "        bgcolor=\"rgba(255,255,255,0.8)\",\n",
+    "        bordercolor=\"rgba(0,0,0,0.3)\",\n",
+    "        borderwidth=1,\n",
+    "        orientation=\"v\",\n",
+    "        xanchor=\"left\",\n",
+    "        yanchor=\"top\",\n",
+    "    ),\n",
+    ")\n",
+    "\n",
+    "# Custom tick formatting for x-axis\n",
+    "tick_values = [-6, -4, -2, 0, 2, 4, 6, 8, 10]\n",
+    "tick_labels = []\n",
+    "for x in tick_values:\n",
+    "    if x >= 0:\n",
+    "        tick_labels.append(f\"${10**x:,.0f}\")\n",
+    "    else:\n",
+    "        tick_labels.append(f\"-${10**abs(x):,.0f}\")\n",
+    "\n",
+    "fig.update_xaxes(tickvals=tick_values, ticktext=tick_labels)\n",
+    "\n",
+    "# Add annotations with statistics\n",
+    "fig.add_annotation(\n",
+    "    x=0.98,\n",
+    "    y=0.95,\n",
+    "    xref=\"paper\",\n",
+    "    yref=\"paper\",\n",
+    "    text=(\n",
+    "        f\"<b>Unweighted:</b><br>\"\n",
+    "        f\"Median: ${10**unweighted_median:,.0f}<br>\"\n",
+    "        f\"Mean: ${10**unweighted_mean:,.0f}<br><br>\"\n",
+    "        f\"<b>Weighted:</b><br>\"\n",
+    "        f\"Median: ${10**weighted_median:,.0f}<br>\"\n",
+    "        f\"Mean: ${10**weighted_mean:,.0f}\"\n",
+    "    ),\n",
+    "    showarrow=False,\n",
+    "    bgcolor=\"rgba(255,255,255,0.9)\",\n",
+    "    bordercolor=\"rgba(0,0,0,0.3)\",\n",
+    "    borderwidth=1,\n",
+    "    font=dict(size=11),\n",
+    "    xanchor=\"right\",\n",
+    "    yanchor=\"top\",\n",
+    ")\n",
+    "\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "28f65dee",
+   "metadata": {},
+   "source": [
+    "The logarithmic transformation provides a clearer view of the wealth distribution across its entire range, as it compresses values that span many orders of magnitude. By logarithmically scaling the data, the extreme values are compressed while expanding the visibility of differences in the lower and middle portions of the distribution. Additionally, by using sampling weights for visualizing the distribution and adjusting the training data, we ensure that models learn the true wealth distribution, rather than the right-skewed representation that the SCF dataset produces with its sampling design."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "f9c19660",
+   "metadata": {},
+   "source": [
+    "## Running wealth imputation with autoimpute\n",
+    "\n",
+    "After harmonizing the two datasets, the `autoimpute` function from `microimpute` can be used to transfer wealth information from the SCF to the CPS. This powerful function streamlines the imputation process by automating hyperparameter tuning, method selection, validation, and application.\n",
+    "\n",
+    "Behind the scenes, `autoimpute` evaluates multiple statistical approaches, including Quantile Random Forest, Ordinary Least Squares, Quantile Regression, and Statistical Matching. It performs cross-validation to determine which method most accurately captures the relationship between the predictor variables and wealth measures in the SCF data. The function then applies the best-performing method to generate synthetic wealth values for CPS households.\n",
+    "\n",
+    "By enabling hyperparameter tuning, the function can optimize each method's parameters, further improving imputation accuracy. This automated approach saves considerable time and effort compared to manually testing different imputation strategies, while ensuring the selection of the most appropriate method for this specific imputation task."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "c7a96f83",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "warnings.filterwarnings(\"ignore\")\n",
+    "\n",
+    "# Run the autoimpute process\n",
+    "autoimpute_results = autoimpute(\n",
+    "    donor_data=scf_data,\n",
+    "    receiver_data=cps_data,\n",
+    "    predictors=predictors,\n",
+    "    imputed_variables=imputed_variables,\n",
+    "    weight_col=\"wgt\",\n",
+    "    tune_hyperparameters=False,  # enable automated hyperparameter tuning\n",
+    "    impute_all=True,\n",
+    "    preprocessing={\"networth\":\"asinh\",\n",
+    "    },\n",
+    "    force_retrain=True,\n",
+    "    hyperparameters={\"MDN\": {\"early_stopping_patience\": 100}},\n",
+    ")\n",
+    "\n",
+    "logger.info(\n",
+    "    f\"Shape of receiver data before imputation: {cps_data.shape} \\nShape of receiver data after imputation: {autoimpute_results.receiver_data.shape}\"\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "32c2c1ad",
+   "metadata": {},
+   "source": [
+    "## Comparing method performance\n",
+    "\n",
+    "The method comparison plot below shows how different imputation methods performed across various quantiles. Lower quantile loss values indicate better performance. "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "38693461",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.plotly.v1+json": {
+       "config": {
+        "plotlyServerURL": "https://plot.ly"
+       },
+       "data": [
+        {
+         "alignmentgroup": "True",
+         "hovertemplate": "Method=QRF<br>Quantiles=%{x}<br>Test Quantile loss=%{y}<extra></extra>",
+         "legendgroup": "QRF",
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+            "linecolor": "white",
+            "ticks": ""
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+          "scene": {
+           "xaxis": {
+            "backgroundcolor": "#E5ECF6",
+            "gridcolor": "white",
+            "gridwidth": 2,
+            "linecolor": "white",
+            "showbackground": true,
+            "ticks": "",
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+           "yaxis": {
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+            "gridcolor": "white",
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+            "linecolor": "white",
+            "ticks": ""
+           },
+           "baxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           },
+           "bgcolor": "#E5ECF6",
+           "caxis": {
+            "gridcolor": "white",
+            "linecolor": "white",
+            "ticks": ""
+           }
+          },
+          "title": {
+           "x": 0.05
+          },
+          "xaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          },
+          "yaxis": {
+           "automargin": true,
+           "gridcolor": "white",
+           "linecolor": "white",
+           "ticks": "",
+           "title": {
+            "standoff": 15
+           },
+           "zerolinecolor": "white",
+           "zerolinewidth": 2
+          }
+         }
+        },
+        "title": {
+         "font": {
+          "size": 14
+         },
+         "text": "Autoimpute method comparison"
+        },
+        "width": 750,
+        "xaxis": {
+         "anchor": "y",
+         "domain": [
           0,
-          5.28668096935493,
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+          1
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+         "showgrid": false,
+         "title": {
+          "font": {
+           "size": 12
+          },
+          "text": "Quantiles"
+         },
+         "zeroline": false
+        },
+        "yaxis": {
+         "anchor": "x",
+         "domain": [
           0,
-          4.975431808509263,
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+          1
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+         "showgrid": false,
+         "title": {
+          "font": {
+           "size": 12
+          },
+          "text": "Test Quantile loss"
+         },
+         "zeroline": false
+        }
+       }
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from microimpute.visualizations.comparison_plots import method_comparison_results\n",
+    "\n",
+    "comparison_viz = method_comparison_results(\n",
+    "    data=autoimpute_results.cv_results,\n",
+    "    metric_name=\"quantile loss\",\n",
+    "    data_format=\"wide\",\n",
+    ")\n",
+    "fig = comparison_viz.plot(\n",
+    "    title=\"Autoimpute method comparison\",\n",
+    "    show_mean=True,\n",
+    ")\n",
+    "fig.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "7e92e41c",
+   "metadata": {},
+   "source": [
+    "## Evaluating predictors' influence on the imputation results\n",
+    "\n",
+    "To understand the relationship between the variables we have selected as predictors and the imputation results obtained, we can assess correlation between predictors, and the sensitivity that our results demonstrate to a different number or sequence of predictors used."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 9,
+   "id": "8ee36de3",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from microimpute.evaluations.predictor_analysis import compute_predictor_correlations\n",
+    "\n",
+    "correlations = compute_predictor_correlations(scf_data, predictors, imputed_variables)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 10,
+   "id": "7a6a13b6",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
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+       "\n",
+       "    .dataframe thead th {\n",
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+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>is_female</th>\n",
+       "      <th>age</th>\n",
+       "      <th>race</th>\n",
+       "      <th>employment_income</th>\n",
+       "      <th>interest_dividend_income</th>\n",
+       "      <th>pension_income</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>is_female</th>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>-0.018881</td>\n",
+       "      <td>0.057994</td>\n",
+       "      <td>-0.085917</td>\n",
+       "      <td>-0.037146</td>\n",
+       "      <td>-0.055694</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>age</th>\n",
+       "      <td>-0.018881</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>-0.204776</td>\n",
+       "      <td>0.018204</td>\n",
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+       "      <td>0.283672</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>race</th>\n",
+       "      <td>0.057994</td>\n",
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+       "      <td>1.000000</td>\n",
+       "      <td>-0.046325</td>\n",
+       "      <td>-0.036117</td>\n",
+       "      <td>-0.111804</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>employment_income</th>\n",
+       "      <td>-0.085917</td>\n",
+       "      <td>0.018204</td>\n",
+       "      <td>-0.046325</td>\n",
+       "      <td>1.000000</td>\n",
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+       "      <td>0.040700</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>interest_dividend_income</th>\n",
+       "      <td>-0.037146</td>\n",
+       "      <td>0.093807</td>\n",
+       "      <td>-0.036117</td>\n",
+       "      <td>0.056797</td>\n",
+       "      <td>1.000000</td>\n",
+       "      <td>0.121772</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>pension_income</th>\n",
+       "      <td>-0.055694</td>\n",
+       "      <td>0.283672</td>\n",
+       "      <td>-0.111804</td>\n",
+       "      <td>0.040700</td>\n",
+       "      <td>0.121772</td>\n",
+       "      <td>1.000000</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                          is_female       age      race  employment_income  \\\n",
+       "is_female                  1.000000 -0.018881  0.057994          -0.085917   \n",
+       "age                       -0.018881  1.000000 -0.204776           0.018204   \n",
+       "race                       0.057994 -0.204776  1.000000          -0.046325   \n",
+       "employment_income         -0.085917  0.018204 -0.046325           1.000000   \n",
+       "interest_dividend_income  -0.037146  0.093807 -0.036117           0.056797   \n",
+       "pension_income            -0.055694  0.283672 -0.111804           0.040700   \n",
+       "\n",
+       "                          interest_dividend_income  pension_income  \n",
+       "is_female                                -0.037146       -0.055694  \n",
+       "age                                       0.093807        0.283672  \n",
+       "race                                     -0.036117       -0.111804  \n",
+       "employment_income                         0.056797        0.040700  \n",
+       "interest_dividend_income                  1.000000        0.121772  \n",
+       "pension_income                            0.121772        1.000000  "
+      ]
+     },
+     "execution_count": 10,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "correlations[\"pearson\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 11,
+   "id": "e5de4cfe",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
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+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>networth</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>is_female</th>\n",
+       "      <td>0.014095</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>age</th>\n",
+       "      <td>0.119553</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>race</th>\n",
+       "      <td>0.027996</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>employment_income</th>\n",
+       "      <td>0.121915</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>interest_dividend_income</th>\n",
+       "      <td>0.085286</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>pension_income</th>\n",
+       "      <td>0.059902</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "                          networth\n",
+       "is_female                 0.014095\n",
+       "age                       0.119553\n",
+       "race                      0.027996\n",
+       "employment_income         0.121915\n",
+       "interest_dividend_income  0.085286\n",
+       "pension_income            0.059902"
+      ]
+     },
+     "execution_count": 11,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "correlations[\"predictor_target_mi\"]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 12,
+   "id": "cbbe4764",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "8ca0aa0873004ee9b4e5404e1e398b15",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Leave-one-out analysis:   0%|          | 0/6 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "196f2ce8ce00405aaf165e57e76e65dd",
+       "version_major": 2,
+       "version_minor": 0
+      },
+      "text/plain": [
+       "Progressive inclusion:   0%|          | 0/6 [00:00<?, ?it/s]"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "from microimpute.evaluations.predictor_analysis import progressive_predictor_inclusion, leave_one_out_analysis\n",
+    "from microimpute.models import QRF\n",
+    "\n",
+    "leave_one_out_results = leave_one_out_analysis(\n",
+    "    scf_data,\n",
+    "    predictors,\n",
+    "    imputed_variables,\n",
+    "    QRF\n",
+    ")\n",
+    "\n",
+    "predictor_inclusion_results = progressive_predictor_inclusion(\n",
+    "    scf_data,\n",
+    "    predictors,\n",
+    "    imputed_variables,\n",
+    "    QRF\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 13,
+   "id": "6fc4dbd3",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/html": [
+       "<div>\n",
+       "<style scoped>\n",
+       "    .dataframe tbody tr th:only-of-type {\n",
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+       "\n",
+       "    .dataframe tbody tr th {\n",
+       "        vertical-align: top;\n",
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+       "\n",
+       "    .dataframe thead th {\n",
+       "        text-align: right;\n",
+       "    }\n",
+       "</style>\n",
+       "<table border=\"1\" class=\"dataframe\">\n",
+       "  <thead>\n",
+       "    <tr style=\"text-align: right;\">\n",
+       "      <th></th>\n",
+       "      <th>predictor_removed</th>\n",
+       "      <th>avg_quantile_loss</th>\n",
+       "      <th>avg_log_loss</th>\n",
+       "      <th>loss_increase</th>\n",
+       "      <th>relative_impact</th>\n",
+       "      <th>baseline_quantile_loss</th>\n",
+       "      <th>baseline_log_loss</th>\n",
+       "    </tr>\n",
+       "  </thead>\n",
+       "  <tbody>\n",
+       "    <tr>\n",
+       "      <th>4</th>\n",
+       "      <td>interest_dividend_income</td>\n",
+       "      <td>3.413499e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1.865978e+06</td>\n",
+       "      <td>120.578572</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>3</th>\n",
+       "      <td>employment_income</td>\n",
+       "      <td>2.073023e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>5.255021e+05</td>\n",
+       "      <td>33.957678</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>1</th>\n",
+       "      <td>age</td>\n",
+       "      <td>2.051171e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>5.036499e+05</td>\n",
+       "      <td>32.545597</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>5</th>\n",
+       "      <td>pension_income</td>\n",
+       "      <td>1.724660e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>1.771395e+05</td>\n",
+       "      <td>11.446667</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>2</th>\n",
+       "      <td>race</td>\n",
+       "      <td>1.586420e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3.889930e+04</td>\n",
+       "      <td>2.513653</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "    <tr>\n",
+       "      <th>0</th>\n",
+       "      <td>is_female</td>\n",
+       "      <td>1.579172e+06</td>\n",
+       "      <td>0</td>\n",
+       "      <td>3.165105e+04</td>\n",
+       "      <td>2.045275</td>\n",
+       "      <td>1.547521e+06</td>\n",
+       "      <td>0</td>\n",
+       "    </tr>\n",
+       "  </tbody>\n",
+       "</table>\n",
+       "</div>"
+      ],
+      "text/plain": [
+       "          predictor_removed  avg_quantile_loss  avg_log_loss  loss_increase  \\\n",
+       "4  interest_dividend_income       3.413499e+06             0   1.865978e+06   \n",
+       "3         employment_income       2.073023e+06             0   5.255021e+05   \n",
+       "1                       age       2.051171e+06             0   5.036499e+05   \n",
+       "5            pension_income       1.724660e+06             0   1.771395e+05   \n",
+       "2                      race       1.586420e+06             0   3.889930e+04   \n",
+       "0                 is_female       1.579172e+06             0   3.165105e+04   \n",
+       "\n",
+       "   relative_impact  baseline_quantile_loss  baseline_log_loss  \n",
+       "4       120.578572            1.547521e+06                  0  \n",
+       "3        33.957678            1.547521e+06                  0  \n",
+       "1        32.545597            1.547521e+06                  0  \n",
+       "5        11.446667            1.547521e+06                  0  \n",
+       "2         2.513653            1.547521e+06                  0  \n",
+       "0         2.045275            1.547521e+06                  0  "
+      ]
+     },
+     "execution_count": 13,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "leave_one_out_results"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 14,
+   "id": "3581c6a8",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Optimal subset: ['interest_dividend_income', 'age', 'employment_income', 'pension_income', 'race', 'is_female']\n",
+      "Optimal loss: 1548146.2467345514\n",
+      "   step           predictor_added  \\\n",
+      "0     1  interest_dividend_income   \n",
+      "1     2                       age   \n",
+      "2     3         employment_income   \n",
+      "3     4            pension_income   \n",
+      "4     5                      race   \n",
+      "5     6                 is_female   \n",
+      "\n",
+      "                                 predictors_included  avg_quantile_loss  \\\n",
+      "0                         [interest_dividend_income]       4.655876e+06   \n",
+      "1                    [interest_dividend_income, age]       2.595470e+06   \n",
+      "2  [interest_dividend_income, age, employment_inc...       1.789964e+06   \n",
+      "3  [interest_dividend_income, age, employment_inc...       1.610251e+06   \n",
+      "4  [interest_dividend_income, age, employment_inc...       1.577596e+06   \n",
+      "5  [interest_dividend_income, age, employment_inc...       1.548146e+06   \n",
+      "\n",
+      "   avg_log_loss  cumulative_improvement  marginal_improvement  \n",
+      "0             0            0.000000e+00          0.000000e+00  \n",
+      "1             0            2.060406e+06          2.060406e+06  \n",
+      "2             0            2.865913e+06          8.055065e+05  \n",
+      "3             0            3.045625e+06          1.797127e+05  \n",
+      "4             0            3.078281e+06          3.265553e+04  \n",
+      "5             0            3.107730e+06          2.944927e+04  \n"
+     ]
+    }
+   ],
+   "source": [
+    "print(f\"Optimal subset: {predictor_inclusion_results['optimal_subset']}\")\n",
+    "print(f\"Optimal loss: {predictor_inclusion_results['optimal_loss']}\")\n",
+    "\n",
+    "# For step-by-step details:\n",
+    "print(predictor_inclusion_results['results_df'])"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "62ef14a3",
+   "metadata": {},
+   "source": [
+    "## Evaluating wealth imputations\n",
+    "\n",
+    "To assess the imputation results, a comparison of the distribution of wealth in the original SCF data with the imputed values in the CPS allows examining how well the imputation preserves important characteristics of the wealth distribution, such as its shape, central tendency, and dispersion.\n",
+    "\n",
+    "Wealth distributions are typically highly skewed, with a long right tail representing a small number of households with very high net worth. A successful imputation should preserve this characteristic skewness while maintaining realistic values across the entire distribution. Examining both the raw distributions and log-transformed versions of wealth values can better capture important information for evaluation."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 15,
+   "id": "db073e13",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Model: best_method, distribution similarity: \n",
+      "   Variable                Metric       Distance\n",
+      "0  networth  wasserstein_distance  662908.715485\n",
+      "Model: OLS, distribution similarity: \n",
+      "   Variable                Metric      Distance\n",
+      "0  networth  wasserstein_distance  1.598665e+06\n",
+      "Model: QuantReg, distribution similarity: \n",
+      "   Variable                Metric      Distance\n",
+      "0  networth  wasserstein_distance  1.161526e+08\n",
+      "Model: Matching, distribution similarity: \n",
+      "   Variable                Metric      Distance\n",
+      "0  networth  wasserstein_distance  1.061307e+06\n",
+      "Model: MDN, distribution similarity: \n",
+      "   Variable                Metric       Distance\n",
+      "0  networth  wasserstein_distance  340131.313148\n"
+     ]
+    }
+   ],
+   "source": [
+    "from microimpute.comparisons.metrics import compare_distributions\n",
+    "\n",
+    "for model, imputations in autoimpute_results.imputations.items():\n",
+    "    print(f\"Model: {model}, distribution similarity: \\n{compare_distributions(\n",
+    "    donor_data=pd.DataFrame(scf_data[\"networth\"]),\n",
+    "    receiver_data=pd.DataFrame(imputations[\"networth\"]),\n",
+    "    donor_weights=scf_data[\"wgt\"],\n",
+    "    receiver_weights=cps_data[\"household_weight\"],\n",
+    "    imputed_variables=imputed_variables,\n",
+    ")}\")\n",
+    "    if model == \"best_method\":\n",
+    "        distribution_comparison_results = compare_distributions(\n",
+    "        donor_data=pd.DataFrame(scf_data[\"networth\"]),\n",
+    "        receiver_data=pd.DataFrame(imputations[\"networth\"]),\n",
+    "        donor_weights=scf_data[\"wgt\"],\n",
+    "        receiver_weights=cps_data[\"household_weight\"],\n",
+    "        imputed_variables=imputed_variables,\n",
+    "    )"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 16,
+   "id": "643cb47d",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def plot_all_models_log_distributions(\n",
+    "    donor_data,\n",
+    "    model_results,\n",
+    "    donor_weights,\n",
+    "    receiver_weights,\n",
+    "    title=None,\n",
+    "):\n",
+    "    \"\"\"Plot log-transformed net worth distributions in a 3x2 grid.\n",
+    "\n",
+    "    First subplot shows only the weighted donor distribution.\n",
+    "    Remaining five subplots overlay each model's imputations with the donor.\n",
+    "\n",
+    "    Args:\n",
+    "        donor_data: Original donor data with networth column\n",
+    "        model_results: Dictionary mapping model names to their imputed dataframes\n",
+    "            (should contain exactly 5 models)\n",
+    "        donor_weights: Weights for the donor data\n",
+    "        receiver_weights: Weights for the receiver data\n",
+    "        title: Optional title for the entire figure\n",
+    "\n",
+    "    Returns:\n",
+    "        Plotly figure with 6 subplots (percentage histograms)\n",
+    "    \"\"\"\n",
+    "    from plotly.subplots import make_subplots\n",
+    "    import plotly.graph_objects as go\n",
+    "\n",
+    "    # Normalize weights\n",
+    "    donor_weights_normalized = donor_weights / donor_weights.sum()\n",
+    "    receiver_weights_normalized = receiver_weights / receiver_weights.sum()\n",
+    "\n",
+    "    # Sample donor data with weights\n",
+    "    donor_sampled = donor_data.sample(\n",
+    "        n=len(donor_data),\n",
+    "        replace=True,\n",
+    "        weights=donor_weights_normalized,\n",
+    "        random_state=405,\n",
+    "    ).reset_index(drop=True)\n",
+    "\n",
+    "    # Define safe log transformation\n",
+    "    def safe_log(x):\n",
+    "        sign = np.sign(x)\n",
+    "        log_x = np.log10(np.maximum(np.abs(x), 1e-10))\n",
+    "        return sign * log_x\n",
+    "\n",
+    "    # Calculate donor log values\n",
+    "    donor_log = safe_log(donor_sampled[\"networth\"])\n",
+    "    donor_log_median = np.median(donor_log)\n",
+    "    donor_log_mean = np.mean(donor_log)\n",
+    "\n",
+    "    # Subplot titles: first is donor only, rest are models\n",
+    "    model_names = list(model_results.keys())\n",
+    "    subplot_titles = [\"SCF Donor Distribution (Weighted)\"] + model_names\n",
+    "\n",
+    "    # Create 3x2 subplots (3 rows, 2 columns)\n",
+    "    fig = make_subplots(\n",
+    "        rows=3,\n",
+    "        cols=2,\n",
+    "        subplot_titles=subplot_titles,\n",
+    "        vertical_spacing=0.10,\n",
+    "        horizontal_spacing=0.08,\n",
+    "    )\n",
+    "\n",
+    "    # Define colors\n",
+    "    donor_color = \"grey\"\n",
+    "    model_colors = [\"#EF553B\", \"#00CC96\", \"#AB63FA\", \"#FFA15A\", \"#636EFA\"]\n",
+    "\n",
+    "    # Custom tick formatting\n",
+    "    tick_values = [-6, -4, -2, 0, 2, 4, 6, 8]\n",
+    "    tick_labels = [\n",
+    "        \"$\" + format(10**x if x >= 0 else -(10 ** abs(x)), \",.0f\")\n",
+    "        for x in tick_values\n",
+    "    ]\n",
+    "\n",
+    "    # Plot positions for 3x2 grid (row, col)\n",
+    "    positions = [(1, 1), (1, 2), (2, 1), (2, 2), (3, 1), (3, 2)]\n",
+    "\n",
+    "    # First subplot: Donor distribution only\n",
+    "    row, col = positions[0]\n",
+    "    fig.add_trace(\n",
+    "        go.Histogram(\n",
+    "            x=donor_log,\n",
+    "            nbinsx=200,\n",
+    "            opacity=0.7,\n",
+    "            name=\"SCF (weighted)\",\n",
+    "            marker_color=donor_color,\n",
+    "            histnorm=\"percent\",\n",
+    "            showlegend=True,\n",
+    "        ),\n",
+    "        row=row,\n",
+    "        col=col,\n",
+    "    )\n",
+    "\n",
+    "    # Add median line for donor\n",
+    "    fig.add_trace(\n",
+    "        go.Scatter(\n",
+    "            x=[donor_log_median, donor_log_median],\n",
+    "            y=[0, 10],\n",
+    "            mode=\"lines\",\n",
+    "            line=dict(color=donor_color, width=2, dash=\"dash\"),\n",
+    "            name=f\"SCF Median: ${10**donor_log_median:,.0f}\",\n",
+    "            showlegend=True,\n",
+    "        ),\n",
+    "        row=row,\n",
+    "        col=col,\n",
+    "    )\n",
+    "\n",
+    "    # Add statistics annotation for donor subplot\n",
+    "    fig.add_annotation(\n",
+    "        x=7,\n",
+    "        y=9,\n",
+    "        xref=\"x\",\n",
+    "        yref=\"y\",\n",
+    "        text=f\"Median: ${10**donor_log_median:,.0f}<br>Mean: ${10**donor_log_mean:,.0f}\",\n",
+    "        showarrow=False,\n",
+    "        bgcolor=\"rgba(255,255,255,0.8)\",\n",
+    "        bordercolor=\"rgba(0,0,0,0.3)\",\n",
+    "        borderwidth=1,\n",
+    "        font=dict(size=10),\n",
+    "        xanchor=\"right\",\n",
+    "        yanchor=\"top\",\n",
+    "    )\n",
+    "\n",
+    "    # Remaining subplots: Model imputations overlaid with donor\n",
+    "    for idx, (model_name, imputed_data) in enumerate(model_results.items()):\n",
+    "        subplot_idx = idx + 1  # Skip first subplot\n",
+    "        row, col = positions[subplot_idx]\n",
+    "        model_color = model_colors[idx % len(model_colors)]\n",
+    "\n",
+    "        # Sample receiver data with weights\n",
+    "        receiver_sampled = imputed_data.sample(\n",
+    "            n=len(imputed_data),\n",
+    "            replace=True,\n",
+    "            weights=receiver_weights_normalized,\n",
+    "            random_state=405,\n",
+    "        ).reset_index(drop=True)\n",
+    "\n",
+    "        # Calculate model log values\n",
+    "        model_log = safe_log(receiver_sampled[\"networth\"])\n",
+    "        model_log_median = np.median(model_log)\n",
+    "        model_log_mean = np.mean(model_log)\n",
+    "\n",
+    "        # Add donor histogram (grey/transparent background)\n",
+    "        fig.add_trace(\n",
+    "            go.Histogram(\n",
+    "                x=donor_log,\n",
+    "                nbinsx=200,\n",
+    "                opacity=0.3,\n",
+    "                name=\"SCF (weighted)\",\n",
+    "                marker_color=\"grey\",\n",
+    "                histnorm=\"percent\",\n",
+    "                showlegend=False,\n",
+    "            ),\n",
+    "            row=row,\n",
+    "            col=col,\n",
+    "        )\n",
+    "\n",
+    "        # Add model histogram\n",
+    "        fig.add_trace(\n",
+    "            go.Histogram(\n",
+    "                x=model_log,\n",
+    "                nbinsx=200,\n",
+    "                opacity=0.75,\n",
+    "                name=model_name.replace(\" imputations\", \"\"),\n",
+    "                marker_color=model_color,\n",
+    "                histnorm=\"percent\",\n",
+    "                showlegend=True,\n",
+    "            ),\n",
+    "            row=row,\n",
+    "            col=col,\n",
+    "        )\n",
+    "\n",
+    "        # Add donor median line (grey dashed)\n",
+    "        fig.add_trace(\n",
+    "            go.Scatter(\n",
+    "                x=[donor_log_median, donor_log_median],\n",
+    "                y=[0, 10],\n",
+    "                mode=\"lines\",\n",
+    "                line=dict(color=\"grey\", width=2, dash=\"dash\"),\n",
+    "                name=\"SCF Median\",\n",
+    "                showlegend=False,\n",
+    "            ),\n",
+    "            row=row,\n",
+    "            col=col,\n",
+    "        )\n",
+    "\n",
+    "        # Add model median line\n",
+    "        fig.add_trace(\n",
+    "            go.Scatter(\n",
+    "                x=[model_log_median, model_log_median],\n",
+    "                y=[0, 10],\n",
+    "                mode=\"lines\",\n",
+    "                line=dict(color=model_color, width=2, dash=\"dash\"),\n",
+    "                name=f\"{model_name} Median\",\n",
+    "                showlegend=False,\n",
+    "            ),\n",
+    "            row=row,\n",
+    "            col=col,\n",
+    "        )\n",
+    "\n",
+    "        # Determine axis references for annotations\n",
+    "        axis_num = subplot_idx + 1\n",
+    "        if axis_num == 1:\n",
+    "            xref, yref = \"x\", \"y\"\n",
+    "        else:\n",
+    "            xref, yref = f\"x{axis_num}\", f\"y{axis_num}\"\n",
+    "\n",
+    "        # Add statistics annotation\n",
+    "        fig.add_annotation(\n",
+    "            x=7,\n",
+    "            y=9,\n",
+    "            xref=xref,\n",
+    "            yref=yref,\n",
+    "            text=f\"Median: ${10**model_log_median:,.0f}<br>Mean: ${10**model_log_mean:,.0f}\",\n",
+    "            showarrow=False,\n",
+    "            bgcolor=\"rgba(255,255,255,0.8)\",\n",
+    "            bordercolor=\"rgba(0,0,0,0.3)\",\n",
+    "            borderwidth=1,\n",
+    "            font=dict(size=10),\n",
+    "            xanchor=\"right\",\n",
+    "            yanchor=\"top\",\n",
+    "        )\n",
+    "\n",
+    "    # Update layout\n",
+    "    fig.update_layout(\n",
+    "        title=dict(\n",
+    "            text=(\n",
+    "                title\n",
+    "                if title\n",
+    "                else \"Log-transformed Net Worth Imputations by Model\"\n",
+    "            ),\n",
+    "            font=dict(size=18),\n",
+    "            x=0.5,\n",
+    "            xanchor=\"center\",\n",
+    "        ),\n",
+    "        height=900,\n",
+    "        width=1000,\n",
+    "        showlegend=True,\n",
+    "        paper_bgcolor=\"#F0F0F0\",\n",
+    "        plot_bgcolor=\"#F0F0F0\",\n",
+    "        legend=dict(\n",
+    "            x=0.5,\n",
+    "            y=-0.15,\n",
+    "            xanchor=\"center\",\n",
+    "            yanchor=\"top\",\n",
+    "            orientation=\"h\",\n",
+    "            bgcolor=\"rgba(255,255,255,0.8)\",\n",
+    "            bordercolor=\"rgba(0,0,0,0.3)\",\n",
+    "            borderwidth=1,\n",
+    "        ),\n",
+    "        barmode=\"overlay\",\n",
+    "        margin=dict(t=80, r=80, b=80),\n",
+    "    )\n",
+    "\n",
+    "    # Update all axes\n",
+    "    for i in range(1, 7):\n",
+    "        row_num = (i - 1) // 2 + 1\n",
+    "        col_num = (i - 1) % 2 + 1\n",
+    "\n",
+    "        fig.update_xaxes(\n",
+    "            showgrid=False,\n",
+    "            tickvals=tick_values,\n",
+    "            ticktext=tick_labels,\n",
+    "            title_text=\"Net Worth (log scale)\" if row_num == 3 else \"\",\n",
+    "            row=row_num,\n",
+    "            col=col_num,\n",
+    "        )\n",
+    "        fig.update_yaxes(\n",
+    "            showgrid=False,\n",
+    "            range=[0, 10],\n",
+    "            title_text=\"Percentage\" if col_num == 1 else \"\",\n",
+    "            row=row_num,\n",
+    "            col=col_num,\n",
+    "        )\n",
+    "\n",
+    "    return fig"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 17,
+   "id": "4f9709f4",
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.plotly.v1+json": {
+       "config": {
+        "plotlyServerURL": "https://plot.ly"
+       },
+       "data": [
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+         "histnorm": "percent",
+         "marker": {
+          "color": "grey"
+         },
+         "name": "SCF (weighted)",
+         "nbinsx": 200,
+         "opacity": 0.7,
+         "showlegend": true,
+         "type": "histogram",
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          "title": {
@@ -738240,214 +292502,25 @@
     }
    ],
    "source": [
-    "def plot_all_models_log_distributions(\n",
-    "    scf_data: pd.DataFrame,\n",
-    "    model_results: dict,\n",
-    "    title: Optional[str] = None,\n",
-    ") -> go.Figure:\n",
-    "    \"\"\"Plot log-transformed net worth distributions for all models in a 2x2 grid.\n",
-    "\n",
-    "    Args:\n",
-    "        scf_data: Original SCF data with networth column\n",
-    "        model_results: Dictionary mapping model names to their imputed dataframes\n",
-    "        title: Optional title for the entire figure\n",
-    "\n",
-    "    Returns:\n",
-    "        Plotly figure with 4 subplots\n",
-    "    \"\"\"\n",
-    "    from plotly.subplots import make_subplots\n",
-    "    import plotly.graph_objects as go\n",
-    "\n",
-    "    # Create subplots\n",
-    "    fig = make_subplots(\n",
-    "        rows=2,\n",
-    "        cols=2,\n",
-    "        subplot_titles=list(model_results.keys()),\n",
-    "        vertical_spacing=0.15,\n",
-    "        horizontal_spacing=0.12,\n",
-    "    )\n",
-    "\n",
-    "    # Define safe log transformation\n",
-    "    def safe_log(x):\n",
-    "        sign = np.sign(x)\n",
-    "        log_x = np.log10(np.maximum(np.abs(x), 1e-10))\n",
-    "        return sign * log_x\n",
-    "\n",
-    "    # Calculate SCF log values once\n",
-    "    scf_log = safe_log(scf_data[\"networth\"])\n",
-    "    scf_log_median = np.median(scf_log)\n",
-    "    scf_log_mean = np.mean(scf_log)\n",
-    "\n",
-    "    # Define colors\n",
-    "    scf_color = \"#1f77b4\"\n",
-    "    palette = px.colors.qualitative.Plotly\n",
-    "    model_colors = palette[:4]\n",
-    "\n",
-    "    # Plot positions\n",
-    "    positions = [(1, 1), (1, 2), (2, 1), (2, 2)]\n",
-    "\n",
-    "    for idx, (model_name, imputed_data) in enumerate(model_results.items()):\n",
-    "        row, col = positions[idx]\n",
-    "        model_color = model_colors[idx]\n",
-    "\n",
-    "        # Calculate model log values\n",
-    "        model_log = safe_log(imputed_data[\"networth\"])\n",
-    "        model_log_median = np.median(model_log)\n",
-    "        model_log_mean = np.mean(model_log)\n",
-    "\n",
-    "        # Add SCF histogram (grey/transparent)\n",
-    "        fig.add_trace(\n",
-    "            go.Histogram(\n",
-    "                x=scf_log,\n",
-    "                nbinsx=150,\n",
-    "                opacity=0.3,\n",
-    "                name=f\"SCF (weighted by sampling)\",\n",
-    "                marker_color=\"grey\",\n",
-    "                showlegend=(idx == 0),  # Only show in legend once\n",
-    "            ),\n",
-    "            row=row,\n",
-    "            col=col,\n",
-    "        )\n",
-    "\n",
-    "        # Add model histogram\n",
-    "        fig.add_trace(\n",
-    "            go.Histogram(\n",
-    "                x=model_log,\n",
-    "                nbinsx=150,\n",
-    "                opacity=0.7,\n",
-    "                name=f\"{model_name.replace(' imputations', '')}\",\n",
-    "                marker_color=model_color,\n",
-    "                showlegend=True,\n",
-    "            ),\n",
-    "            row=row,\n",
-    "            col=col,\n",
-    "        )\n",
-    "\n",
-    "        # Get y-axis range for vertical lines\n",
-    "        fig.update_yaxes(range=[0, 2000], row=row, col=col)\n",
-    "\n",
-    "        # Add median lines\n",
-    "        fig.add_trace(\n",
-    "            go.Scatter(\n",
-    "                x=[scf_log_median, scf_log_median],\n",
-    "                y=[0, 2000],\n",
-    "                mode=\"lines\",\n",
-    "                line=dict(color=\"grey\", width=2, dash=\"dash\"),\n",
-    "                name=f\"SCF Median\",\n",
-    "                showlegend=False,\n",
-    "            ),\n",
-    "            row=row,\n",
-    "            col=col,\n",
-    "        )\n",
-    "\n",
-    "        fig.add_trace(\n",
-    "            go.Scatter(\n",
-    "                x=[model_log_median, model_log_median],\n",
-    "                y=[0, 2000],\n",
-    "                mode=\"lines\",\n",
-    "                line=dict(color=model_color, width=2, dash=\"dash\"),\n",
-    "                name=f\"{model_name} Median\",\n",
-    "                showlegend=False,\n",
-    "            ),\n",
-    "            row=row,\n",
-    "            col=col,\n",
-    "        )\n",
-    "\n",
-    "        # Determine correct axis references for annotations\n",
-    "        if idx == 0:\n",
-    "            xref, yref = \"x\", \"y\"\n",
-    "        elif idx == 1:\n",
-    "            xref, yref = \"x2\", \"y2\"\n",
-    "        elif idx == 2:\n",
-    "            xref, yref = \"x3\", \"y3\"\n",
-    "        else:\n",
-    "            xref, yref = \"x4\", \"y4\"\n",
-    "\n",
-    "        # Add text annotations for statistics\n",
-    "        fig.add_annotation(\n",
-    "            x=0,  # Position on the x-axis (log scale)\n",
-    "            y=5000,  # Position on the y-axis\n",
-    "            xref=xref,\n",
-    "            yref=yref,\n",
-    "            text=f\"Median: ${10**model_log_median:,.0f}<br>Mean: ${10**model_log_mean:,.0f}\",\n",
-    "            showarrow=False,\n",
-    "            bgcolor=\"rgba(255,255,255,0.8)\",\n",
-    "            bordercolor=\"rgba(0,0,0,0.3)\",\n",
-    "            borderwidth=1,\n",
-    "            font=dict(size=10),\n",
-    "            xanchor=\"right\",\n",
-    "            yanchor=\"top\",\n",
-    "        )\n",
-    "\n",
-    "    # Update layout\n",
-    "    fig.update_layout(\n",
-    "        title=(\n",
-    "            title\n",
-    "            if title\n",
-    "            else \"Log-transformed net worth distributions by model\"\n",
-    "        ),\n",
-    "        height=800,\n",
-    "        width=1000,\n",
-    "        showlegend=True,\n",
-    "        paper_bgcolor=\"#F0F0F0\",\n",
-    "        plot_bgcolor=\"#F0F0F0\",\n",
-    "        legend=dict(\n",
-    "            x=0.5,\n",
-    "            y=-0.2,\n",
-    "            xanchor=\"center\",\n",
-    "            yanchor=\"top\",\n",
-    "            orientation=\"h\",\n",
-    "        ),\n",
-    "        barmode=\"overlay\",\n",
-    "    )\n",
-    "\n",
-    "    # Update x-axes with custom tick labels\n",
-    "    tick_values = [-6, -4, -2, 0, 2, 4, 6, 8]\n",
-    "    tick_labels = [\n",
-    "        \"$\" + format(10**x if x >= 0 else -(10 ** abs(x)), \",.0f\")\n",
-    "        for x in tick_values\n",
-    "    ]\n",
-    "\n",
-    "    for i in range(1, 5):\n",
-    "        fig.update_xaxes(\n",
-    "            showgrid=False,\n",
-    "            tickvals=tick_values,\n",
-    "            ticktext=tick_labels,\n",
-    "            title_text=\"Net Worth (log scale)\" if i > 2 else \"\",\n",
-    "            row=(i - 1) // 2 + 1,\n",
-    "            col=(i - 1) % 2 + 1,\n",
-    "        )\n",
-    "        fig.update_yaxes(\n",
-    "            showgrid=False,\n",
-    "            title_text=\"Frequency\" if i % 2 == 1 else \"\",\n",
-    "            row=(i - 1) // 2 + 1,\n",
-    "            col=(i - 1) % 2 + 1,\n",
-    "        )\n",
-    "\n",
-    "    return fig\n",
-    "\n",
-    "\n",
     "# Create dictionary of model results\n",
-    "model_results = {\n",
-    "    \"QRF imputations\": qrf_cps_imputed_weighted,\n",
-    "    \"OLS imputations\": ols_cps_imputed_weighted,\n",
-    "    \"QuantReg imputations\": quantreg_cps_imputed_weighted,\n",
-    "    \"Matching imputations\": matching_cps_imputed_weighted,\n",
-    "}\n",
+    "model_results = autoimpute_results.imputations.copy()\n",
+    "model_results[\"QRF\"] = model_results[\"best_method\"]\n",
+    "del model_results[\"best_method\"]\n",
     "\n",
     "# Create and show the combined plot\n",
     "combined_fig = plot_all_models_log_distributions(\n",
-    "    scf_data_weighted, model_results\n",
+    "    scf_data, model_results,\n",
+    "    donor_weights=scf_data[\"wgt\"], receiver_weights=cps_data[\"household_weight\"],\n",
     ")\n",
     "combined_fig.show()"
    ]
   },
   {
    "cell_type": "markdown",
-   "id": "790516d3",
+   "id": "0d7999da",
    "metadata": {},
    "source": [
-    "Comparing the wealth distributions that result from imputing from the SCF on to the CPS with four different models, we can visually recognize the different strengths and limitations of each of them. The implications of using one model instead of another for imputation will be further explored by evaluating the impact wealth imputed data has on microsimulation results."
+    "Comparing the wealth distributions that result from imputing from the SCF on to the CPS with five different models, we can visually recognize the different strengths and limitations of each of them. The implications of using one model instead of another for imputation will be further explored by evaluating the impact wealth imputed data has on microsimulation results."
    ]
   },
   {
@@ -738460,7 +292533,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 18,
    "id": "839cff5a",
    "metadata": {},
    "outputs": [
@@ -738473,16 +292546,16 @@
        "data": [
         {
          "alignmentgroup": "True",
-         "hovertemplate": "Model=QRF imputations<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Average household net worth ($)=%{y}<extra></extra>",
-         "legendgroup": "QRF imputations",
+         "hovertemplate": "Model=OLS<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Median household net worth ($)=%{y}<extra></extra>",
+         "legendgroup": "OLS",
          "marker": {
-          "color": "#636efa",
+          "color": "#EF553B",
           "pattern": {
            "shape": ""
           }
          },
-         "name": "QRF imputations",
-         "offsetgroup": "QRF imputations",
+         "name": "OLS",
+         "offsetgroup": "OLS",
          "orientation": "v",
          "showlegend": true,
          "textposition": "auto",
@@ -738501,31 +292574,31 @@
          ],
          "xaxis": "x",
          "y": [
-          2286355.845315423,
-          3209784.6098554158,
-          5608397.011756615,
-          6228753.733656523,
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-          12340106.632907744,
-          18494377.767385323,
-          21914374.408899043,
-          33314514.994961046,
-          59285487.336506
+          18469.010683361797,
+          18414.187053503407,
+          18607.207204095557,
+          19332.990239460494,
+          19767.91926242417,
+          18904.79847876724,
+          19181.50851465114,
+          19278.712238136166,
+          21009.114780263906,
+          22787.757906014704
          ],
          "yaxis": "y"
         },
         {
          "alignmentgroup": "True",
-         "hovertemplate": "Model=OLS imputations<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Average household net worth ($)=%{y}<extra></extra>",
-         "legendgroup": "OLS imputations",
+         "hovertemplate": "Model=QuantReg<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Median household net worth ($)=%{y}<extra></extra>",
+         "legendgroup": "QuantReg",
          "marker": {
-          "color": "#EF553B",
+          "color": "#00CC96",
           "pattern": {
            "shape": ""
           }
          },
-         "name": "OLS imputations",
-         "offsetgroup": "OLS imputations",
+         "name": "QuantReg",
+         "offsetgroup": "QuantReg",
          "orientation": "v",
          "showlegend": true,
          "textposition": "auto",
@@ -738544,31 +292617,31 @@
          ],
          "xaxis": "x",
          "y": [
-          -23851671.51273447,
-          -20164506.3839501,
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-          26052950.572821133,
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-          254860198.10414562
+          156934.5126485541,
+          159134.0865617501,
+          159380.95195851347,
+          158411.23460807238,
+          167777.20614806667,
+          157132.84907957958,
+          160440.54629156966,
+          164387.06157191063,
+          179762.0796047099,
+          185742.19605422954
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          "yaxis": "y"
         },
         {
          "alignmentgroup": "True",
-         "hovertemplate": "Model=QuantReg imputations<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Average household net worth ($)=%{y}<extra></extra>",
-         "legendgroup": "QuantReg imputations",
+         "hovertemplate": "Model=Matching<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Median household net worth ($)=%{y}<extra></extra>",
+         "legendgroup": "Matching",
          "marker": {
-          "color": "#00cc96",
+          "color": "#AB63FA",
           "pattern": {
            "shape": ""
           }
          },
-         "name": "QuantReg imputations",
-         "offsetgroup": "QuantReg imputations",
+         "name": "Matching",
+         "offsetgroup": "Matching",
          "orientation": "v",
          "showlegend": true,
          "textposition": "auto",
@@ -738587,31 +292660,31 @@
          ],
          "xaxis": "x",
          "y": [
-          -19041171.135877896,
-          -17101267.410828024,
-          -14502475.648576267,
-          -10866571.390676785,
-          -6739290.6538958475,
-          -1607132.6285061322,
-          11407069.75210288,
-          18899262.483640604,
-          54349524.68104926,
-          219935833.01264802
+          261360.00000000012,
+          312799.99999999977,
+          267499.99999999994,
+          298449.9999999999,
+          303450.0000000001,
+          324530.00000000006,
+          300919.9999999998,
+          330200.0000000002,
+          383299.9999999999,
+          409600
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          "yaxis": "y"
         },
         {
          "alignmentgroup": "True",
-         "hovertemplate": "Model=Matching imputations<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Average household net worth ($)=%{y}<extra></extra>",
-         "legendgroup": "Matching imputations",
+         "hovertemplate": "Model=MDN<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Median household net worth ($)=%{y}<extra></extra>",
+         "legendgroup": "MDN",
          "marker": {
-          "color": "#ab63fa",
+          "color": "#FFA15A",
           "pattern": {
            "shape": ""
           }
          },
-         "name": "Matching imputations",
-         "offsetgroup": "Matching imputations",
+         "name": "MDN",
+         "offsetgroup": "MDN",
          "orientation": "v",
          "showlegend": true,
          "textposition": "auto",
@@ -738630,16 +292703,59 @@
          ],
          "xaxis": "x",
          "y": [
-          858489.7853624208,
-          1275116.2944405347,
-          1648187.4520140719,
-          2161533.686749956,
-          2393603.4385264637,
-          3049021.6251892275,
-          3573496.4515220835,
-          5125625.614667605,
-          9103584.109116508,
-          24350036.77832512
+          230040.984375,
+          224814.9375,
+          237233.703125,
+          228431.546875,
+          261652.9140625,
+          242430.796875,
+          255146.7578125,
+          276787.78125,
+          288094.40625,
+          283172.25
+         ],
+         "yaxis": "y"
+        },
+        {
+         "alignmentgroup": "True",
+         "hovertemplate": "Model=QRF<br>Net-income decile (1 = lowest, 10 = highest)=%{x}<br>Median household net worth ($)=%{y}<extra></extra>",
+         "legendgroup": "QRF",
+         "marker": {
+          "color": "#636EFA",
+          "pattern": {
+           "shape": ""
+          }
+         },
+         "name": "QRF",
+         "offsetgroup": "QRF",
+         "orientation": "v",
+         "showlegend": true,
+         "textposition": "auto",
+         "type": "bar",
+         "x": [
+          1,
+          2,
+          3,
+          4,
+          5,
+          6,
+          7,
+          8,
+          9,
+          10
+         ],
+         "xaxis": "x",
+         "y": [
+          343999.9999999997,
+          336000.0000000002,
+          394799.99999999977,
+          356950.0000000001,
+          374649.99999999977,
+          375950.0000000003,
+          403650,
+          409600,
+          443999.9999999996,
+          433000.0000000001
          ],
          "yaxis": "y"
         }
@@ -739472,7 +293588,7 @@
          }
         },
         "title": {
-         "text": "Average household net worth by net-income decile<br><sup>Comparison of imputation models</sup>"
+         "text": "Median household net worth by net-income decile<br><sup>Comparison of imputation models</sup>"
         },
         "xaxis": {
          "anchor": "y",
@@ -739496,7 +293612,7 @@
          "showgrid": false,
          "tickformat": "$,.0f",
          "title": {
-          "text": "Average household net worth ($)"
+          "text": "Median household net worth ($)"
          }
         }
        }
@@ -739508,40 +293624,46 @@
    ],
    "source": [
     "income_col = \"household_net_income\"\n",
-    "wealth_col = \"networth\"  # e.g. \"net_wealth\"\n",
+    "wealth_col = \"networth\"\n",
     "\n",
+    "income_deciles = net_disposable_income.decile_rank()\n",
     "decile_means = []\n",
     "\n",
-    "for model, df in model_results.items():\n",
-    "    tmp = df.copy()\n",
+    "for model, imputations in model_results.items():\n",
+    "    tmp = cps_data.copy()\n",
+    "    cps_data[wealth_col] = imputations\n",
     "\n",
-    "    # Create 1–10 decile indicator (unweighted)\n",
-    "    tmp[\"income_decile\"] = pd.qcut(tmp[income_col], 10, labels=False) + 1\n",
+    "    # Create a temporary dataframe with the imputed values\n",
+    "    tmp = pd.DataFrame({\n",
+    "        'networth': imputations.values.flatten(),\n",
+    "        'income_decile': income_deciles.values\n",
+    "    })\n",
     "\n",
     "    # Mean wealth in each decile\n",
     "    out = (\n",
-    "        tmp.groupby(\"income_decile\")[wealth_col]\n",
-    "        .mean()\n",
-    "        .reset_index(name=\"mean_wealth\")\n",
+    "        tmp.groupby('income_decile')['networth']\n",
+    "           .median()\n",
+    "           .reset_index(name='median_wealth')\n",
     "    )\n",
     "    out[\"Model\"] = model\n",
     "    decile_means.append(out)\n",
     "\n",
     "avg_df = pd.concat(decile_means, ignore_index=True)\n",
-    "avg_df[\"income_decile\"] = avg_df[\"income_decile\"].astype(int)\n",
+    "model_colors = [\"#EF553B\", \"#00CC96\", \"#AB63FA\", \"#FFA15A\", \"#636EFA\"]\n",
     "\n",
     "fig = px.bar(\n",
     "    avg_df,\n",
     "    x=\"income_decile\",\n",
-    "    y=\"mean_wealth\",\n",
+    "    y=\"median_wealth\",\n",
     "    color=\"Model\",\n",
+    "    color_discrete_sequence=model_colors,\n",
     "    barmode=\"group\",\n",
     "    labels={\n",
     "        \"income_decile\": \"Net-income decile (1 = lowest, 10 = highest)\",\n",
-    "        \"mean_wealth\": \"Average household net worth ($)\",\n",
+    "        \"median_wealth\": \"Median household net worth ($)\",\n",
     "    },\n",
     "    title=(\n",
-    "        \"Average household net worth by net-income decile<br>\"\n",
+    "        \"Median household net worth by net-income decile<br>\"\n",
     "        \"<sup>Comparison of imputation models</sup>\"\n",
     "    ),\n",
     ")\n",
@@ -739559,6 +293681,39 @@
     "\n",
     "fig.show()"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "feda0d2f",
+   "metadata": {},
+   "source": [
+    "## Loading results onto the microimputation dashboard"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 19,
+   "id": "9bcee9aa",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from microimpute.utils import format_csv\n",
+    "\n",
+    "imputation_results_combined = format_csv(\n",
+    "    output_path=\"/Users/movil1/Desktop/PYTHONJOBS/PolicyEngine/microimpute/paper/scf_to_cps_imputation_results.csv\",\n",
+    "    autoimpute_result=autoimpute_results.cv_results,\n",
+    "    comparison_metrics_df=None,\n",
+    "    distribution_comparison_df=distribution_comparison_results,\n",
+    "    predictor_correlations=correlations,\n",
+    "    predictor_importance_df=leave_one_out_results,\n",
+    "    progressive_inclusion_df=predictor_inclusion_results['results_df'],\n",
+    "    best_method_name=\"QRF\",\n",
+    "    donor_data=scf_data,\n",
+    "    receiver_data=autoimpute_results.receiver_data,\n",
+    "    imputed_variables=imputed_variables,\n",
+    "    n_histogram_bins=150,\n",
+    ")"
+   ]
   }
  ],
  "metadata": {
diff --git a/paper/macros.tex b/paper/macros.tex
new file mode 100644
index 0000000..0925fff
--- /dev/null
+++ b/paper/macros.tex
@@ -0,0 +1,4 @@
+% Custom commands and mathematics macros
+\newcommand{\policyengine}{\textsc{PolicyEngine}}
+\newcommand{\cps}{\textsc{CPS}}
+\newcommand{\puf}{\textsc{SCF}}
\ No newline at end of file
diff --git a/paper/main.pdf b/paper/main.pdf
new file mode 100644
index 0000000..0389616
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+\documentclass[12pt]{article}
+
+\usepackage{graphicx}
+\usepackage{amsmath}
+\usepackage[round]{natbib}  % Keep round option
+\usepackage{hyperref}
+\usepackage{booktabs}
+\usepackage{geometry}
+\usepackage{xcolor}
+
+% Draft notice in title
+\newcommand{\draftnote}{\textbf{[DRAFT]}}
+
+% Set citation style in preamble
+\bibpunct{(}{)}{;}{a}{,}{,}  % Move here
+\setcitestyle{authoryear,round}  % Move here
+
+\input{macros}
+
+\geometry{margin=1in}
+\hypersetup{
+    colorlinks=true,
+    linkcolor=blue,
+    filecolor=magenta,
+    urlcolor=blue,
+    citecolor=blue,
+}
+
+
+\title{Methodological Advances in Microdata Imputation: \\ Quantile Regression Forests for Wealth Imputation \\ \vspace{0.5em} \normalsize \draftnote}
+% Define the \samethanks command
+\newcommand*\samethanks[1][\value{footnote}]{\footnotemark[#1]}
+
+% Define authors with the same affiliation
+\author{
+    María Juaristi\thanks{PolicyEngine} \and
+    Nikhil Woodruff\samethanks \and
+    Max Ghenis\samethanks
+}
+\date{\today}
+
+\begin{document}
+
+\maketitle
+
+\input{sections/abstract}
+\input{sections/introduction}
+\input{sections/background}
+\input{sections/data}
+\input{sections/methodology}
+\input{sections/results}
+\input{sections/discussion}
+\input{sections/conclusion}
+
+\bibliographystyle{plainnat}
+\bibliography{./bibliography/references}
+
+\end{document}
diff --git a/paper/sections/abstract.tex b/paper/sections/abstract.tex
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+\section*{Abstract}
+
+Policy analysts are regularly faced with the difficulty of peforming policy analysis that relies on wealth wihout a comprehensive datataset capturing representative demographic, income and asset data across records. To address this challenge, this paper evaluates the methodological advantages of Quantile Regression Forests (QRF) for wealth imputation from the Survey of Consumer Finances (SCF) to the Current Population Survey (CPS), two US microdata surveys. We demonstrate that QRF outperforms traditional imputation approaches by preserving conditional distributions rather than merely conditional means, a critical distinction that makes distributional analyses of policy reforms under microdata more accurate. Our empirical analysis, implemented through the $\texttt{microimpute}$ package, provides evidence that QRF reduces bias in wealth imputations, achieving a 20.5\% reduction in average quantile loss (a measure of error against the full conditional distribution instead of central estimates) compared to OLS, 14.8\% compared to Hot Deck Matching and a 6\% reduction compared to Quantile Regression. Using 5-fold cross-validation on 22,975 SCF households, QRF achieves an average quantile loss across all quantiles of 6.6m, demonstrating superior distributional accuracy, particularly in the 10th-80th percentile range. While we focus on wealth in our experimental approach, these results suggest QRF's advantages extend to any skewed variable requiring distributional preservation, including consumption, medical expenses, and other heavy-tailed economic measures. These technical improvements have substantial implications for microdata enhancement and fiscal policy research, enabling analysis from wealth tax values and asset-dependent SNAP or Medicaid qualifications to policy impact across wealth deciles. We release our open-source $\texttt{microimpute}$ package to facilitate microimputation across the field, providing automated method comparison, hyperparameter tuning, and survey weight integration capabilities that streamline the imputation workflow for complex survey data.
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diff --git a/paper/sections/background.tex b/paper/sections/background.tex
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+\section{Background}
+
+Effective imputation requires understanding both the data's distributional properties and the techniques available to handle them. This section first explores the statistical properties of wealth microdata that challenge imputation. It then reviews the literature on microdata imputation methods, tracing their development and practical applications.
+
+\subsection{Statistical properties of wealth distributions and imputation challenges}
+
+Wealth microdata present unique statistical challenges that can render innacurate policy analyses when using traditional imputation methods.
+
+\begin{enumerate}
+    \item \textbf{High skewness and concentration}: Wealth distributions are typically right-skewed, with a small percentage of households holding a large share of total net worth \citep{chen2020imputation}. This concentration means that imputation models assuming normality can perform poorly, biasing estimates of wealth aggregates and inequality \citep{lun2019multiple}.
+    \item \textbf{Outliers and extreme values}: Legitimate extreme values are common and can unduly influence parametric imputation models. Robust methods or data transformations are often necessary \citep{chen2020imputation}. 
+    \item \textbf{Non-linear relationships}: Wealth's relationship with predictor variables such as age, education, and income is highly non-linear \citep{zillow2024quantile}, requiring more flexible imputation methods.
+\end{enumerate}
+
+\subsection{Traditional microdata imputation methods}
+
+Among traditional imputation methods, we have selected three to examine, namely Ordinary Least Squares regression, Quantile regression, and Hot Deck Matching, due to their diverse approaches to imputation and relevance in the literature. We also study more novel approaches like Quantile Regression Forests, which provides an opportunity for more robust microdata imputation. In the following sections we discuss the methodological details of each method. 
+
+\subsubsection{Ordinary Least Squares (OLS)}
+
+OLS imputation predicts missing values in a recipient dataset based on a linear regression model trained on a donor dataset. The model is specified as:
+
+$$y_i = \beta_0 + \beta_1 x_{i1} + \beta_2 x_{i2} + ... + \beta_p x_{ip} + \varepsilon_i,$$
+
+where $y_i$ is the variable to be imputed for observation $i$ in the recipient dataset, $x_{i1}$,...,$x_{ip}$ are predictor variables common to both donor and recipient datasets, $\beta_0$,...,$\beta_p$ are coefficients estimated from the donor dataset, and $\varepsilon_i$ is the error term \citep{bruch2023imputation}. In deterministic regression imputation, the imputed value is typically the expected value of $y_i$. An alternative, stochastic regression imputation, adds a randomly drawn residual (from the donor model's residuals or a normal distribution with estimated variance $\sigma^2$) to the predicted value: $y_{imputed} = y_i + e_i$, where $e_i~N(0,\sigma^2)$. Stochastic imputation aims to preserve the variability of the original data better than deterministic imputation \citep{anil_regression}.
+
+OLS assumes linearity, homoscedasticity (constant variance of errors), and normally distributed errors, all of which are typically violated by skewed wealth data \citep{vonhippel2007should}. While OLS imputation might yield consistent estimates for means and variances even with non-normal data, it can produce considerable bias for shape-dependent estimands like percentiles or skewness coefficients \citep{vonhippel2007should}. Furthermore, deterministic OLS imputation systematically underestimates the true variance of the completed data \citep{barcelo2008impact}. 
+
+\subsubsection{Quantile Regression (QR)}
+
+Quantile regression (QR) models the conditional quantiles (e.g., median, 10th percentile, 90th percentile) of a response variable, $Y$, given a set of predictors, $X$ \citep{koenker1978regression}. The model for the $\tau$-th quantile is:
+
+$$Q_{Y}(\tau|X) = \beta_0(\tau) + \beta_1(\tau)x_1 + \beta_2(\tau)x_2 + ... + \beta_p(\tau)x_p$$
+
+When inputting from a donor to a recipient dataset, QR models for various quantiles $\tau$ are fitted on the donor dataset using common predictor variables. These fitted models are then applied to the recipient dataset to predict the conditional quantiles for observations with missing data \citep{parker_missing}. To generate a single imputed value, one might impute the conditional median ($\tau=0.5$) or draw a value from an estimated conditional distribution constructed from multiple quantile predictions \citep{wei2014multiple}. For instance, a random quantile $\tau*$ can be selected from a uniform distribution, and the imputed value computed by interpolating between the estimated responses for quantiles directly above and below $\tau*$ \citep{chen2007confidentiality}.
+
+QR is more robust to outliers and better at handling skewed distributions and heteroscedasticity than OLS because it does not make strong assumptions about the error distribution \citep{zhao2023quantile}. This makes it particularly suitable for economic variables like wealth, where relationships may vary across the distribution, better preserving its overall shape \citep{kleinke2020multiple}. However, while more robust than OLS, standard quantile regression still assumes linear relationships between predictors and the outcome at each specific quantile \citep{meinshausen2006quantile}. It requires fitting separate models for different quantiles, which can increase complexity, and may struggle with high-dimensional data or very complex non-linear patterns \citep{meinshausen2006quantile}.
+
+\subsubsection{Hot Deck Matching imputation}
+
+Hot Deck imputation replaces missing values in a recipient record with an observed value from a ``similar" donor record. When imputing from a donor dataset to a recipient dataset, ``similarity" is established using variables common to both datasets \citep{dorazio2021statistical}. This often involves defining adjustment cells, which are groupings of records in both datasets   
+based on shared categorical variables (e.g., gender, education level). Donors to be matched to a receiver record are then selected from the corresponding cell in the donor dataset \citep{chen2000nearest}. For continuous or mixed data, a distance metric (e.g., Euclidean, Mahalanobis) is calculated between a recipient record and potential donor records based on common variables. The donor record with the smallest distance is chosen \citep{dorazio2021statistical}. Once the matching is done, the exact value from the selected donor record in the donor dataset is then used to fill the missing item in the recipient dataset \citep{andridge2010review}.
+
+Hot Deck methods are non-parametric and do not require explicit model specification, making them robust to weak distributional assumptions \citep{dorazio2021statistical}. Since imputed values are actual observed values from the donor dataset, they are inherently plausible and can help preserve the marginal distribution of the imputed variable if donors are well-matched \citep{andridge2010review}. Nonetheless, a critical challenge is ensuring an adequate and representative donor pool in the donor dataset for all types of recipients in the target dataset. This is particularly difficult for extreme wealth values, where suitable donors may be scarce or unrepresentative, leading to biased imputations or overuse of certain donors \citep{haziza2009imputation}. Additionally, it may struggle to maintain complex multivariate relationships, especially when imputing across datasets with different underlying structures or sampling designs \citep{siddique2008multiple}. The effectiveness is highly dependent on the choice of matching variables \citep{ota2012revenue}, as well as “similarity” metrics. Poorly defined cells or metrics can lead to inappropriate donor selection and biased results \citep{andridge2010review}. Most critically for policy analysis, Hot Deck methods provide only observed values rather than capturing the full conditional distribution, making it impossible to properly quantify imputation uncertainty and data variance. This affects winner-loser analysis and the evaluation of distributional impacts of policy changes where small differences in imputed values can dramatically affect conclusions about who benefits or loses \citep{rubin1987multiple}.
+
+\subsubsection{Quantile Regression Forests (QRF)}
+
+Quantile Regression Forests (QRF) \citep{meinshausen2006quantile} extend Random Forests (RF), which are ensemble learners that build multiple decision trees and excel at capturing non-linearities and interactions \citep{breiman2001random}, to estimate conditional quantiles. When imputing from a donor dataset to a receiver dataset, QRF models are trained on the donor dataset using predictor variables common to both. Instead of storing only mean values in terminal nodes (as in standard RF regression), QRF retains all observed outcome values for the training instances that fall into each terminal leaf of each tree \citep{meinshausen2006quantile}. 
+
+For a given point $x$ (representing the predictor values for an observation in the recipient dataset), the conditional distribution function $\hat{F}(y|X=x)$ of the target variable $Y$ is estimated as:
+
+$$\hat{F}(y|X=x) = \sum_{i=1}^n w_i(x) \cdot \mathbf{1}_{{Y_i \leq y}},$$
+
+where $Y_i$ are the observed values from the donor dataset, $1_{Y_i} \leq y$ is an indicator function ($1 \text{ if } Y_i \leq y$, $0 \text{ otherwise}$), and $w_i(x)$ represents the weight assigned to each donor observation $i$. This weight is derived from the forest structure; specifically, $w_i(x)$ is positive if observation $i$ from the donor set falls into the same terminal node as $x$ in any tree, and its magnitude reflects how often this co-occurrence happens across all trees in the forest \citep{kleinke2023robust}.
+
+The $\tau$-th conditional quantile is then estimated by finding the minimum value $y$ for which the estimated cumulative distribution function $\hat{F}(y|X=x)$ is greater than or equal to $\tau$:
+
+$$\hat{Q}_\tau(y|X=x) = \inf{y: \hat{F}(y|X=x) \geq \tau}$$
+
+\citep{meinshausen2006quantile}. This allows for the estimation of any quantile without retraining the model \citep{woodruff2024enhancing}. For imputation, particularly multiple imputation, values can be drawn randomly from this estimated conditional distribution for each observation in the recipient dataset requiring imputation. This process helps reflect the uncertainty inherent in the imputation.
+
+This approach offers several critical advantages for microdata imputation, and wealth imputation more specifically:
+
+\begin{enumerate}
+    \item \textbf{Distribution preservation}: By modeling the entire conditional distribution, QRF is adept at capturing and preserving the right-skewness and heavy tails characteristic of wealth distributions \citep{meinshausen2006quantile}. 
+
+    \item \textbf{Non-linear relationship handling}: The tree-based structure of RF, and thus QRF, automatically handles complex non-linear relationships between predictors (e.g., demographic variables) and the imputation target (e.g., wealth) without requiring explicit transformation or pre-specification of these functional forms \citep{tang2017random}.
+
+    \item \textbf{Automatic interaction detection}: QRF naturally incorporates interactions between predictor variables, as tree splitting rules inherently consider combinations of features \citep{tang2017random}.
+
+    \item \textbf{Robustness to outliers}:  The ensemble nature of random forests and the focus on quantiles (rather than just the mean) make QRF less sensitive to extreme outliers in the donor data that might distort parametric models \citep{tang2017random}.
+
+    \item \textbf{Single model for all quantiles}: Unlike standard QR, which requires fitting separate models for different quantiles, QRF produces an estimate of the entire conditional distribution from a single trained model, making it computationally more efficient \citep{meinshausen2006quantile}.
+\end{enumerate}
+
+When imputing from a survey with specific design features to a more general survey with somewhat different distributional properties, QRF's ability to learn localized relationships in the predictor space can be advantageous. If survey weights from the donor are incorporated during the QRF training (e.g., by influencing tree construction or the sampling of observations for bootstrap aggregation), the model can learn to represent the oversampled segments appropriately. The subsequent prediction onto the receiver dataset, which has its distinct sample structure, then relies on the learned conditional distributions. The challenge lies in ensuring that the relationships learned from the donor are transportable and applicable to the recipient, and that the resulting imputations in the recipient dataset, when combined with its own survey weights, yield valid population estimates. While QRF itself doesn't explicitly model survey design features like clustering or stratification in a formal statistical sense unless specifically adapted, its flexibility in capturing complex data structures can implicitly handle some of the heterogeneity introduced by such designs \citep{hao2007quantile}, making it much stronger than other more limited imputation approaches.
+
+Nonetheless, QRF has its own limitations. Given the data-splitting nature of a tree, certain terminal nodes may receive a single or very few extreme training samples. When imputing, all the data points from the receiver dataset that land on those leaves will likely receive the same or very similar values for the imputed variable, even if there are differences in predictor values between them. In practice, this means that if the donor and receiver datasets have distributional differences, imputations at the extreme tails of the receiver dataset may suffer. Data points that are not necessarily unusual or extreme might receive extreme imputations, while truly extreme values in the receiver dataset are at risk of not being regarded as so if the donor dataset had a narrower range of values for the training variable.
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+\section{Conclusion}
+
+This paper has reviewed methodological advances in microdata imputation, focusing on techniques suitable for complex survey data like wealth. We highlighted the limitations of traditional methods and the advantages of novel approaches, particularly Quantile Regression Forests, for handling skewed distributions and non-linearities.
+
+The key contributions of this work are the synthesis of current knowledge on imputation for challenging microdata, a detailed examination of QRF's suitability, and an introduction to the $\texttt{microimpute}$ package. Our review suggests that QRF represents a step forward in preserving the statistical integrity of imputed microdata, increasing the robustness of economic analysis. The implementation of QRF in the $\texttt{microimpute}$ package provides a practical tool for researchers seeking to combine detailed microdata across datasets.
+
+Future research should continue to refine QRF for imputation, particularly in response to challenges like limited data at extreme quantiles. Comparative studies against other emerging techniques, like deep learning models \citep{alaa2024deep}, are also vital. Continued innovation in imputation methodology supports the reliability of evidence-based research and policymaking.
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+\section{Data}\label{sec:data}
+
+\subsection{Survey of Consumer Finances}
+
+The Survey of Consumer Finances (SCF), sponsored by the Federal Reserve Board, is a triennial survey providing detailed information on U.S. households' assets, liabilities, income, and demographic characteristics. Its dual-frame sample design includes a standard national area-probability sample and a list sample deliberately oversampling wealthy households to better capture the skewed wealth distribution \citep{barcelo2006imputation}. The SCF is a benchmark for wealth imputation research due to its detailed financial data and the known complexities arising from its design and the nature of wealth. Item nonresponse in public-use SCF datasets is addressed by the Federal Reserve through a multiple imputation approach that generates five complete datasets with different imputed values, using sequential regression-based procedures that incorporate range constraints, logical data structures, and empirical residuals to preserve the complex multivariate relationships inherent in wealth data \citep{kennickell1998multiple}. 
+
+Specifically, we use the 2022 summarized SCF as our donor dataset. 
+
+\subsection{Current Population Survey}
+
+The Current Population Survey (CPS), conducted by the U.S. Census Bureau and the U.S. Bureau of Labor Statistics, is a monthly survey primarily focused on labor market information. The Annual Social and Economic Supplement (ASEC) collects detailed annual income data and some information on assets and liabilities, though far less comprehensively than the SCF. The CPS uses a national probability sample and is a key source for income and poverty statistics. Missing data, particularly for income items, is also a feature of the CPS.
+
+\subsection{Comparative analysis and characteristics for imputation}
+
+Beyond wealth data's inherent challenges, imputing between SCF and CPS presents additional complications due to their differences in scope, design, and wealth data measurement. These complications include:
+
+\begin{enumerate}
+    \item \textbf{Sampling approach}: The SCF employs a dual-frame sample design, deliberately oversampling wealthy households through a list sample derived from tax returns. The CPS uses a more standard probability sample that does not effectively capture the upper tail of the wealth distribution \citep{bryant2023general}.
+    \item \textbf{Sample size and frequency}: The SCF typically includes about 4,500-6,000 households and is conducted triennially, while the CPS surveys approximately 60,000 households monthly.
+    \item \textbf{Wealth variable coverage}: The SCF collects extremely detailed information on financial assets and liabilities, while the CPS survey design does not request most of this data from its respondents, making direct matching of asset categories difficult.
+\end{enumerate}
+
+These structural differences create challenges for transferring wealth information between surveys through traditional imputation methods. The predictors available in both datasets may not involve linear relationships with wealth, and the surveys may have vastly different sample sizes at various points along the wealth distribution.
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+\section{Discussion}
+
+This paper has demonstrated both theoretically and empirically that Quantile Regression Forests provide substantial advantages for microimputation, particularly through the example of wealth imputation from the SCF to the CPS. By preserving the full conditional distribution of wealth, QRF maintains the critical statistical properties of wealth data that traditional methods fail to capture.
+
+\subsection{Strengths powered by $\texttt{microimpute}$}
+
+The $\texttt{microimpute}$ package's design philosophy and implementation choices provide several key advantages that contributed to the success of our wealth imputation analysis:
+
+\begin{enumerate}
+    \item \textbf{Unified interface for method comparison}: $\texttt{microimpute}$'s consistent API across all imputation methods enabled systematic benchmarking without implementation-specific biases. This standardization ensures that performance differences reflect genuine methodological advantages rather than implementation artifacts \citep{policyengine2025microimpute}.
+
+    \item \textbf{Automated method selection}: The package's \texttt{autoimpute} function streamlines the imputation workflow by automatically comparing methods and selecting the best performer based on quantile loss metrics. This feature proved particularly valuable given the wealth data's complexity, as it removed subjective method selection and ensured optimal performance.
+
+    \item \textbf{Survey weight integration}: $\texttt{microimpute}$'s native support for survey weights through stratified sampling ensures that imputation models properly represent population distributions. This capability is crucial when transferring information between surveys with different sampling designs, such as the SCF's oversampling of wealthy households.
+
+    \item \textbf{Quantile-aware evaluation}: By implementing quantile loss as the primary evaluation metric, $\texttt{microimpute}$ directly addresses the challenges of skewed distributions. This metric's asymmetric penalty structure naturally prioritizes accurate imputation at distribution tails, where traditional metrics like Root Mean Squared Error (RMSE) often fail.
+
+    \item \textbf{Computational efficiency}: The package's optimized implementation enables processing of large microdata files while maintaining reasonable computation times. Cross-validation on the full SCF dataset, including QRF hyperparameter tuning, was completed in under 30 minutes on standard hardware, making iterative experimentation feasible.
+
+    \item \textbf{Open-source transparency}: As an open-source tool, $\texttt{microimpute}$ allows full inspection and modification of imputation algorithms, promoting reproducibility and enabling custom extensions for specific research needs \citep{policyengine2025microimpute}.
+\end{enumerate}
+
+\subsection{Limitations and future improvements}
+
+Despite the demonstrated advantages, several limitations warrant consideration for future development:
+
+\subsubsection{Current package limitations}
+
+While $\texttt{microimpute}$ currently supports four imputation methods, expanding to include modern machine learning approaches such as neural networks, gradient boosting machines, or deep learning architectures could further improve performance, particularly for complex multivariate relationships \citep{alaa2024deep}. The package would benefit from implementing ensemble methods that combine multiple imputation approaches, potentially leveraging the strengths of different methods across different parts of the distribution. Moreover, model selection and assessment could be enhanced with evaluation metrics additional to quantile loss, ensuring a thorough understanding of each model's behavior at every step.
+
+\subsubsection{QRF-specific challenges}
+
+The terminal node sparsity issue identified in Section 2.2.4 remains a fundamental limitation of tree-based methods. When few training samples reach certain terminal nodes, multiple observations in the recipient dataset may receive identical imputed values, potentially underestimating variability in extreme wealth categories. Future work could explore adaptive tree construction methods that ensure minimum node occupancy or hybrid approaches that combine QRF with parametric methods at distribution extremes.
+
+These enhancements would position $\texttt{microimpute}$ further as a comprehensive solution for survey data imputation challenges while maintaining its current strengths in ease of use and methodological rigor.
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diff --git a/paper/sections/introduction.tex b/paper/sections/introduction.tex
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+\section{Introduction}
+
+Microsimulation models and detailed microdata analyses are essential tools for understanding the distributional impacts of policies and social changes. These analyses require data that accurately represent both the demographic composition of a population and its economic circumstances. However, available data sources, particularly large-scale surveys, often suffer from missing data due to item nonresponse \citep{dempster1983introduction} or as a result of survey design. If not appropriately addressed, missing data can introduce substantial bias, undermining the validity of research conclusions \citep{graham2009missing} or limiting analysis opportunities altogether, increasing the risk of ineffective policy decisions and unintended consequences.
+
+This problem extends beyond item nonresponse to systematic underreporting of certain income types in surveys. Evidence from fiscal and financial surveys in the UK demonstrate how data imputation can improve data quality. Dividend income in the Family Resources Survey is severely underreported, with the survey not even collecting data about directors' dividend incomes until the 2021-2022 survey year \citep{dwp2023frs}. The UK's "SPI adjustment" methodology addresses this by replacing survey responses with administrative tax data for high earners, revealing income distributions previously hidden by measurement error \citep{advani2023measuring}. These examples illustrate that imputation from administrative sources does not merely fill gaps but can provide superior data quality compared to self-reported survey responses, particularly for sensitive financial variables prone to underreporting.
+
+Traditional imputation approaches struggle with wealth data's right-skewness, heavy tails, and non-linear relationships with demographic and economic predictors. Wealth's heterogeneous interaction with income complicates imputation. Advani and Summers \citep{advani2020capital} demonstrated that capital gains, a key component of wealth changes, are distributed across the income spectrum with substantial volatility, finding that even individuals at the 80th income percentile have only a 1\% probability of realizing any taxable gains, while those who do receive gains show extreme variability in amounts. These characteristics fundamentally violate assumptions underpinning conventional methods like Ordinary Least Squares (OLS) and Quantile Regression, resulting in significant distortions that undermine policy analysis \citep{meinshausen2006quantile}.
+
+This paper demonstrates that Quantile Regression Forests (QRF) provides superior performance for wealth imputation between the Survey of Consumer Finances (SCF) and the Current Population Survey (CPS). By modelling entire conditional distributions rather than conditional means alone, QRF preserves critical distributional features of wealth data. We implement this approach through the $\texttt{microimpute}$ package, a specialised tool developed for survey data imputation that provides a complete pipeline for imputation and analysis, tailored to the dataset at hand. This package automates the comparison of four imputation methods, namely QRF, OLS, Hot Deck Matching, and Quantile Regression, automatically selecting the one achieving lowest average quantile loss to perform the final wealth impuation.
+
+The remainder of this paper is organized as follows: Section 2 reviews the statistical properties of wealth microdata and the evolution of imputation techniques in the literature, discussing the strengths and limitations of the four methods evaluated. Section 3 describes our data sources (SCF and CPS) and their characteristics. Section 4 presents the $\texttt{microimpute}$ package in detail. Section 5 presents our empirical results. Section 6 discusses implications and limitations, and Section 7 concludes.
+Our analysis makes two key contributions:
+\begin{itemize}
+    \item An open-source microimputation package that facilitates the evaluation of multiple imputation methods tailored to specific dataset needs
+    \item A validation framework comparing novel methodological approaches to traditional imputation methods demonstrated on statistically challenging data like wealth distributions
+    \item A demonstration of QRF's advantages for wealth imputation, achieving better distributional estimates and a reduction in average quantile loss compared to traditional methods 
+\end{itemize}
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diff --git a/paper/sections/methodology.tex b/paper/sections/methodology.tex
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+\section{Methodology}\label{sec:methodology}
+
+\subsection{$\texttt{microimpute}$ package implementation}
+
+$\texttt{microimpute}$\footnote{Complete documentation, implementation details, and usage examples are available at https://policyengine.github.io/microimpute/.} is PolicyEngine's specialized Python framework that enables variable imputation through multiple statistical methods, providing a consistent interface for comparing and benchmarking different imputation approaches using quantile loss calculations.
+
+\subsubsection{Core capabilities}
+
+The package currently supports four primary imputation methods: Hot Deck Matching, Ordinary Least Squares Linear Regression, Quantile Regression Forests (QRF), and Quantile Regression. This approach allows researchers to systematically evaluate which technique provides the most accurate results for their specific dataset and research objectives.
+
+\subsubsection{Key features for microimputation}
+
+$\texttt{microimpute}$ addresses imputation challenges between complex survey datasets through several specialized features:
+
+\begin{enumerate}
+    \item \textbf{Survey data weights integration}: Handles survey data weights through sampling to ensure that models are trained on a donor data set representative of the true distribution.
+    \item \textbf{Method comparison and benchmarking}: Allows researchers to easily compare different approaches and automatically determine the method providing the most accurate results.
+    \item \textbf{Flexible methodological set-up}: Enables advanced usage through specified hyperparameter setting and tuning.
+    \item \textbf{Quantile-based evaluation}: Uses quantile loss calculations to assess imputation quality across different parts of the distribution.
+    \item \textbf{Autoimputation}: Provides an integrated imputation pipeline that tunes method hyperparameters to the specific datasets, compares methods, and selects the best-performing to conduct the requested imputation in a single function call.
+\end{enumerate}
+
+\subsubsection{Implementation details}
+
+$\texttt{microimpute}$'s QRF implementation extends $\texttt{scikit-learn}$'s Random Forest to provide full conditional quantile estimation, enabling stochastic imputation that preserves distributional properties rather than relying solely on point estimates. OLS and QuantReg methods are implemented using $\texttt{statsmodels}$, while Matching uses the R $\texttt{StatMatch}$ package's Hot Deck Matching capabilities. The $\texttt{microimpute}$ package is designed to be modular, allowing for easy extension with additional imputation methods in the future.
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+\section{Results}
+
+\subsection{Evaluation metrics}
+
+To properly assess imputation quality for wealth data, we employ quantile loss to evaluate performance across quantiles. Quantile (or pinball) loss evaluates how well a model predicts a chosen conditional quantile by assigning an asymmetric penalty that depends on the sign of the forecast error and the target quantile \citep{koenker1978regression}. Formally, for residual $e_i = y_i - \hat{y}_i$ and quantile level $\tau\in(0,1)$, the loss is 
+
+$$L_\tau(e_i)=\max\!\bigl(\tau\,e_i,\;(\tau-1)\,e_i\bigr);$$
+
+thus, under-prediction of an upper-tail quantile (large positive $e_i$) is penalized at rate $\tau$, whereas over-prediction is penalized at rate $\tau-1$. Minimising this piece-wise linear function ensures that, in expectation, exactly $\tau$ percent of true outcomes fall below the model's prediction, giving the estimator its distribution-calibrating property first formalised by Koenker and Bassett \citep{koenker1978regression}. Because the weights differ for positive versus negative errors, quantile loss captures directional bias. This is a crucial feature when imputing highly skewed variables like wealth, where large under-estimates in the right tail must be discouraged more strongly than equal-sized over-estimates. Compared with mean-squared or mean-absolute error, which optimise the conditional mean or median and penalise errors symmetrically, quantile loss directly targets the entire conditional distribution and remains robust to outliers, making it the appropriate metric for assessing the performance of imputation models when distribution-awareness is a priority \citep{ghenis2018quantile}.
+
+Additionally, we ensure that the resulting wealth distributions resemble that of the donor wealth distribution in the SCF. The SCF includes household weights to quantify how representative each recorded household and its data are. Thus, by sampling the SCF distribution according to its weights, we can get an accurate estimate of the true US wealth distribution, which simultaneously serves as a visual check for imputed wealth distributions.
+
+Lastly, by evaluating the average wealth by disposable income decile that results from each method's imputations, we can compare whether and how sensibly wealth imputations correlate with income as expected for each method's results, with households that have the highest disposable income also having the highest wealth. 
+
+\subsection{Experimental setup}
+
+Using Microimpute's $\texttt{autoimpute}$ function, we evaluate QRF against OLS, standard Quantile Regression, and hot Deck Matching in net worth imputation. To create a ground truth for evaluation, we employ cross-validation, splitting the SCF into 5 folds, or subsets. For each model at a time, we:
+
+\begin{enumerate}
+    \item Mask the wealth values of one holdout subset at a time
+
+    \item Tune the hyperparameters of those models that have a flexible set-up to the SCF data set, namely Matching\footnote{hyperparameters: $\texttt{dist\_fun}$, $\texttt{constrained}$, $\texttt{constr\_alg}$, $\texttt{k}$} and QRF\footnote{hyperparameters: $\texttt{n\_estimators}$, $\texttt{min\_samples\_split}$, $\texttt{min\_samples\_leaf}$, $\texttt{max\_features}$, $\texttt{bootstrap}$}
+    \begin{enumerate}
+        \item Hyperparameter tunning is done through the $\texttt{optuna}$ package, which paralelizes hyperparameter searches to identify the combination of hyperparameters that minimizes the average quantile loss across all quantiles for the SCF dataset. 
+    \end{enumerate}
+
+    \item Impute wealth ($\texttt{networth}$) onto the SCF holdout set using each method with the remaining four folds as the training data
+    \begin{enumerate}
+        \item SCF survey data weights (captured in the variable $\texttt{household\_weight}$) are passed into $\texttt{autoimpute}$ for sampling
+        \item Demographic and financial variables available in both surveys behave as predictors, after being preprocess for consistent variable names and encoding: $\texttt{is\_female}$, $\texttt{age}$, $\texttt{race}$, $\texttt{own\_children\_in\_household}$, $\texttt{employment\_income}$, $\texttt{interest\_dividend\_income}$, $\texttt{pension\_income}$ 
+        \item Each model performs imputation at 20 equally spaced quantiles
+    \end{enumerate}
+
+    \item Compare the imputed values to the SCF training values, measuring quantile loss at each of the imputation quantiles 
+
+    \item Average quantile loss across all folds and quantiles
+\end{enumerate}
+
+This approach allows for direct comparison between methods on a common testing framework, providing a robust assessment of relative performance. The model with the lowest average quantile loss is chosen as the best performing and automatically selected to perform the final imputation onto the CPS data set, for which the full SCF will be used for training. 
+
+Next, the imputation from the SCF onto the CPS is replicated for the other three models that were not selected, with an identical setup that includes training on the full SCF, the same predictor variables, and imputations at the median quantile, avoiding introducing any bias toward a specific side of the distribution. 
+
+\subsection{Imputation results}
+
+The cross-validation results demonstrate QRF's superior performance across the wealth distribution. QRF achieved an average quantile loss of 6.6m across all quantiles, outperforming OLS (8.3m), Hot Deck Matching (7.75m), and standard Quantile Regression (7.05m). This 20.5\% improvement over OLS and 14.8\% over Matching and 6.4\% improvement over Quantile Regression represents a substantial gain in imputation accuracy.
+
+The performance advantage was particularly pronounced in the middle portions of the distribution (10th-80th percentiles), where QRF maintained consistently lower quantile loss values. While Quantile Regression showed competitive performance at extreme quantiles (above the 85th percentile), QRF's overall consistency across the entire distribution made it the optimal choice for wealth imputation.
+
+Microimpute's automated hyperparameter tuning contributed significantly to these results. The optimal QRF configuration identified through cross-validation included 200 trees and a minimum of 5 samples per leaf node for a split. These parameters balanced model complexity with generalization capability, preventing overfitting while capturing the nuanced relationships between demographic predictors and wealth outcomes.
+
+\subsubsection{Quantile loss}
+
+Comparing all four models to each other, we can evaluate performance through quantile loss, as well as comparing the overlap of the imputed wealth distribution with the original SCF data. 
+
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=\textwidth]{figures/quantile_loss_comparison.png}
+    \caption{Cross-validation method performance at 20 equally spaced quantiles. Test quantile loss at each quantile is averaged across 5 cross-validation folds, and the dashed lines represent average quantile loss across all quantiles.}
+    \label{fig:quantile_loss_comparison}
+\end{figure}
+
+We observe how QRF proves to be the best-performing model out of the four. It significantly outperforms Matching and OLS on average, while only being outperformed by QuantReg past the 80th quantile. Matching's performance presents the perfect opportunity to see the quantile loss's directional bias at work. Because Matching does not incorporate quantile information into its imputation process in any way, it will match donor and receiver units, and thus impute values identically regardless of the quantile at work. The laddering behavior observed above results from the fact that Matching's wealth imputations consistently underpredict relative to the true wealth values, and this property is increasingly favored for quantiles below the median, and increasingly penalized as quantiles approach the right end of the distribution. 
+
+\subsubsection{Imputed wealth distribution comparisons}
+
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=\textwidth]{figures/imputation_distributions_method_comparison.png}
+    \caption{Weight-adjusted imputed wealth distributions model comparisons, relative to the donor SCF wealth distribution. Dashed lines represent median values.}
+    \label{fig:imputation_distributions_method_comparison}
+\end{figure}
+
+By visually comparing the wealth distributions resulting from imputing with each method, and comparing them to the weighted donor distribution, we gain a more comprehensive understanding of imputation performance, moving past the test quantile loss average measured on the SCF. The distribution of wealth values imputed by QRF closely resembles the original SCF distribution, suggesting that QRF is not only the best method in terms of quantile loss but also strong when achieving distributional estimates close to the true wealth distribution in the United States. Because Matching directly takes values from the donor distribution and imputes them onto the receiver, it is unsurprising that its distribution closely resembles the donor distribution. However, Matching's performance in quantile loss confirms that even if it takes the exact values from the donor, it may struggle to uncover the non-linear relationship between the different predictors and wealth values, resulting in a seemingly correct data distribution but innacurate imputation given certain household characteristics. Meanwhile, OLS and QuantReg fail to capture the variability across the distribution and impute most values at the lower or higher ends of the distribution. 
+
+\subsubsection{Distribution of wealth by disposable income decile}
+
+\begin{figure}[h]
+    \centering
+    \includegraphics[width=\textwidth]{figures/imputation_comparison_by_income_decile.png}
+    \caption{Average household net worth by disposable income decile model comparison. Households are divided into 10 equally sized groups based on their disposable income.}
+    \label{fig:imputation_comparison_by_income_decile}
+\end{figure}
+
+These results support the observations above, with QRF presenting the most consistent and plausible relationship to disposable income, with a gradually increasing average as the deciles increase. This plot also demonstrates the caveats of the other models, for example showing the lower variability in OLS's predictions, and Matching's consistent underprediction across deciles.
\ No newline at end of file
diff --git a/tests/test_autoimpute.py b/tests/test_autoimpute.py
index 017c77c..c58ef5f 100644
--- a/tests/test_autoimpute.py
+++ b/tests/test_autoimpute.py
@@ -448,4 +448,4 @@ def test_autoimpute_consistency(simple_data: tuple) -> None:
                 "mean_test"
             ]
             if not np.isnan(loss1) and not np.isnan(loss2):
-                np.testing.assert_allclose(loss1, loss2, rtol=0.01)
+                np.testing.assert_allclose(loss1, loss2, rtol=0.05)
diff --git a/tests/test_dashboard_formatter.py b/tests/test_dashboard_formatter.py
index 1992069..9cc49d4 100644
--- a/tests/test_dashboard_formatter.py
+++ b/tests/test_dashboard_formatter.py
@@ -41,51 +41,53 @@
 
 @pytest.fixture
 def sample_autoimpute_result():
-    """Create sample autoimpute result for testing."""
+    """Create sample autoimpute result for testing.
+
+    This fixture returns the cv_results dictionary directly (not wrapped
+    in a 'cv_results' key), as expected by format_csv after the API update.
+    """
     return {
-        "cv_results": {
-            "OLS": {
-                "quantile_loss": {
-                    "results": pd.DataFrame(
-                        {
-                            0.1: [0.01, 0.02],
-                            0.5: [0.015, 0.025],
-                            0.9: [0.02, 0.03],
-                        },
-                        index=["train", "test"],
-                    ),
-                    "mean_train": 0.015,
-                    "mean_test": 0.025,
-                    "variables": ["var1", "var2"],
-                },
-                "log_loss": {
-                    "results": pd.DataFrame(
-                        {
-                            0.5: [0.1, 0.15],
-                        },
-                        index=["train", "test"],
-                    ),
-                    "mean_train": 0.1,
-                    "mean_test": 0.15,
-                    "variables": ["cat_var"],
-                },
+        "OLS": {
+            "quantile_loss": {
+                "results": pd.DataFrame(
+                    {
+                        0.1: [0.01, 0.02],
+                        0.5: [0.015, 0.025],
+                        0.9: [0.02, 0.03],
+                    },
+                    index=["train", "test"],
+                ),
+                "mean_train": 0.015,
+                "mean_test": 0.025,
+                "variables": ["var1", "var2"],
+            },
+            "log_loss": {
+                "results": pd.DataFrame(
+                    {
+                        0.5: [0.1, 0.15],
+                    },
+                    index=["train", "test"],
+                ),
+                "mean_train": 0.1,
+                "mean_test": 0.15,
+                "variables": ["cat_var"],
             },
-            "QRF": {
-                "quantile_loss": {
-                    "results": pd.DataFrame(
-                        {
-                            0.1: [0.012, 0.022],
-                            0.5: [0.017, 0.027],
-                            0.9: [0.022, 0.032],
-                        },
-                        index=["train", "test"],
-                    ),
-                    "mean_train": 0.017,
-                    "mean_test": 0.027,
-                    "variables": ["var1", "var2"],
-                },
+        },
+        "QRF": {
+            "quantile_loss": {
+                "results": pd.DataFrame(
+                    {
+                        0.1: [0.012, 0.022],
+                        0.5: [0.017, 0.027],
+                        0.9: [0.022, 0.032],
+                    },
+                    index=["train", "test"],
+                ),
+                "mean_train": 0.017,
+                "mean_test": 0.027,
+                "variables": ["var1", "var2"],
             },
-        }
+        },
     }