-(Version 0.2.11, updated on 2024-09-22, [release history](https://sfcheung.github.io/stdmod/news/index.html))
+(Version 0.2.11.1, updated on 2026-01-04, [release history](https://sfcheung.github.io/stdmod/news/index.html))
(Important changes since 0.2.0.0: Bootstrap confidence intervals and
variance-covariance matrix of estimates are the defaults of `confint()`
diff --git a/rebuild_vignettes.R b/rebuild_vignettes.R
index 2c3cfce..8ea81d8 100644
--- a/rebuild_vignettes.R
+++ b/rebuild_vignettes.R
@@ -4,6 +4,8 @@ base_dir <- getwd()
setwd("vignettes/")
knitr::knit("cond_effect.Rmd.original", output = "cond_effect.Rmd")
-# knitr::knit("moderation.Rmd.original", output = "moderation.Rmd")
-# knitr::knit("std_selected.Rmd.original", output = "std_selected.Rmd")
+knitr::knit("moderation.Rmd.original", output = "moderation.Rmd")
+knitr::knit("std_selected.Rmd.original", output = "std_selected.Rmd")
+knitr::knit("stdmod_lavaan.Rmd.original", output = "stdmod_lavaan.Rmd")
+knitr::knit("stdmod.Rmd.original", output = "stdmod.Rmd")
setwd(base_dir)
diff --git a/vignettes/eg2_lm_xwy_std_ci.rds b/vignettes/eg2_lm_xwy_std_ci.rds
deleted file mode 100644
index 356426d..0000000
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deleted file mode 100644
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diff --git a/vignettes/egl_lavaan_boot.rds b/vignettes/egl_lavaan_boot.rds
deleted file mode 100644
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diff --git a/vignettes/mod_reg-1.png b/vignettes/mod_reg-1.png
new file mode 100644
index 0000000..68f7bca
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diff --git a/vignettes/mod_reg_stdall-1.png b/vignettes/mod_reg_stdall-1.png
new file mode 100644
index 0000000..64e5e04
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diff --git a/vignettes/moderation.Rmd b/vignettes/moderation.Rmd
index 3a835ca..c5f7c62 100644
--- a/vignettes/moderation.Rmd
+++ b/vignettes/moderation.Rmd
@@ -1,244 +1,410 @@
----
-title: "Standardized Moderation Effect by std_selected()"
-author: "Shu Fai Cheung and David Weng Ngai Vong"
-date: "`r Sys.Date()`"
-output: rmarkdown::html_vignette
-vignette: >
- %\VignetteIndexEntry{Standardized Moderation Effect by std_selected()}
- %\VignetteEngine{knitr::rmarkdown}
- %\VignetteEncoding{UTF-8}
----
-
-```{r, include = FALSE}
-knitr::opts_chunk$set(
- collapse = TRUE,
- comment = "#>",
- fig.width = 6,
- fig.height = 4,
- fig.align = "center"
-)
-```
-
-# Purpose
-
-This document demonstrates how to use `std_selected()` from
-the `stdmod` package to compute the correct
-standardized solution of moderated regression.
-More about this package can be found
-in `vignette("stdmod", package = "stdmod")`
-or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
-
-# Setup the Environment
-
-```{r setup}
-library(stdmod) # For computing the standardized moderation effect conveniently
-```
-
-# Load the Dataset
-
-```{r load_dataset}
-data(sleep_emo_con)
-head(sleep_emo_con, 3)
-```
-
-This data set has 500 cases of data. The variables are sleep duration, age, gender,
-and the scores from two personality scales, emotional stability and
-conscientiousness of the IPIP Big Five markers. Please refer to
-(citation to be added) for the detail of the data set.
-
-The names of some variables are shortened for readability:
-
-```{r}
-colnames(sleep_emo_con)[3:4] <- c("cons", "emot")
-head(sleep_emo_con, 3)
-```
-
-
-# Moderated Regression
-
-Suppose we are interested in predicting sleep duration by emotional stability,
-after controlling for gender and age. However, we suspect that the effect of
-emotional stability, if any, may be moderated by conscientiousness. Therefore,
-we conduct a moderated regression as follow:
-
-```{r mod_reg}
-lm_out <- lm(sleep_duration ~ age + gender + emot * cons,
- data = sleep_emo_con)
-summary(lm_out)
-plotmod(lm_out,
- x = "emot",
- w = "cons",
- x_label = "Emotional Stability",
- w_label = "Conscientiousness",
- y_label = "Sleep Duration")
-```
-
-The results show that conscientiousness significantly moderates the effect of
-emotional stability on sleep duration.
-
-# Standardized Moderation Effect
-
-To get the correct standardized solution of the moderated regression, with the
-product term formed *after* standardization, we can use `std_selected()`.
-
-- The first argument is the regression output from `lm()`.
-
-- The argument `to_center` specifies variables to be mean
- centered.
-
-- The argument `to_scale` specifies variables to be rescaled
- by their standard deviations after centering.
-
-- In `stdmod` 0.2.6.3, the argument `to_standardize` was introduced
- as a shortcut. Listing a variable in `to_standardize` is
- equivalent to listing it in `to_center` and `to_scale`.
-
-If we want to standardize or mean center all variables, we can use `~ .` as a
-shortcut. Note that `std_selected()` will automatically skip categorical
-variables (i.e., factors or string variables in the regression model of `lm()`).
-
-```{r}
-lm_stdall <- std_selected(lm_out,
- to_standardize = ~ .)
-```
-
-Before 0.2.6.3, to standardize all variables except for
-categorical variables, we need to use both `to_center = ~ .`
-and `to_scale = ~ .`. Since 0.2.6.3,
-we can just use `to_standardize = ~ .`, as shown above.
-If `to_standardize = ~ .` does not work, just use
-`to_center` and `to_scale` as shown below:
-
-```r
-lm_stdall <- std_selected(lm_out,
- to_center = ~ .,
- to_scale = ~ .)
-```
-
-A summary of the results of `std_selected()` can be
-generated by `summary()`:
-
-```{r}
-summary(lm_stdall)
-```
-
-The coefficient in this solution,
-`r round(coef(lm_stdall)["emot:cons"], 5)`,
-can be interpreted as the change in the standardized effect of
-emotional stability for each one standard deviation increase of
-conscientiousness. Naturally, this can be called the
-*standardized moderation effect* of conscientiousness
-([Cheung, Cheung, Lau, Hui, & Vong, 2022](https://doi.org/10.1037/hea0001188)).
-
-The output of `std_selected()` can be passed to other functions that accept the
-output of `lm()`. This package also has a simple function,
-`plotmod()`, for generating a typical plot of the moderation effect:
-
-```{r mod_reg_stdall}
-plotmod(lm_stdall,
- x = "emot",
- w = "cons",
- x_label = "Emotional Stability",
- w_label = "Conscientiousness",
- y_label = "Sleep Duration")
-```
-
-The function `plotmod()` also prints the conditional effects of the predictor
-(focal variable), emotional stability in this example.
-
-# The Common (Incorrect) Standardized Solution
-
-For comparison, this is the results of standardizing all variables, including
-the product term and the categorical variable.
-
-```{r}
-library(lm.beta) # For generating the typical standardized solution
-packageVersion("lm.beta")
-lm_beta <- lm.beta(lm_out)
-summary(lm_beta)
-```
-
-The coefficient of the *standardized* product term is
-`r round(coef(lm_beta)["emot:cons"], 5)`, which
-*cannot* be interpreted as the change in the standardized effect of
-emotional stability for each one standard deviation increase of
-conscientiousness because the product term is standardized and can no longer
-be interpreted as the product of two variables in the model.
-
-# Improved Confidence Intervals
-
-It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6))
-that the standard errors of
-standardized regression coefficients computed just by standardizing the variables
-are biased, and consequently the confidence intervals are also invalid. The
-function `std_selected_boot()` is a wrapper of `std_selected()` that also
-forms the confidence interval of the regression coefficients when standardizing
-is conducted, using nonparametric bootstrapping as suggested by
-Cheung, Cheung, Lau, Hui, and Vong (2022).
-
-We use the same example above that standardizes all variables except for
-categorical variables to illustrate this function. The argument `nboot`
-specifies the number of nonparametric bootstrap samples.
-The level of confidence is set by `conf`. The default is .95, denoting 95%
-confidence intervals. If this is the desired level, this argument can be
-omitted.
-
-```{r echo = FALSE, eval = TRUE}
-if (file.exists("eg2_lm_xwy_std_ci.rds")) {
- lm_xwy_std_ci <- readRDS("eg2_lm_xwy_std_ci.rds")
- } else {
- set.seed(649017)
- lm_xwy_std_ci <- std_selected_boot(lm_out, to_center = ~ .,
- to_scale = ~ .,
- nboot = 2000)
- saveRDS(lm_xwy_std_ci, "eg2_lm_xwy_std_ci.rds", compress = "xz")
- }
-```
-
-```r
-set.seed(649017)
-lm_xwy_std_ci <- std_selected_boot(lm_out,
- to_standardize = ~ .,
- nboot = 2000)
-```
-
-If the default options are acceptable, the only additional argument is `nboot`.
-
-```{r}
-summary(lm_xwy_std_ci)
-```
-
-```{r echo = FALSE}
-tmp <- summary(lm_xwy_std_ci)$coefficients
-```
-
-The standardized moderation effect is
-`r formatC(tmp["emot:cons", "Estimate"], 4, format = "f")`,
-and the 95% nonparametric bootstrap confidence interval is
-`r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
-`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
-
-Note: As a side product, the nonparametric bootstrap percentile confidence of the other
-coefficients are also reported. They can be used for other variables that are
-standardized in the same model, whether they are involved in the moderation or not.
-
-# Further Information
-
-`vignette("plotmod", package = "stdmod")` illustrates how to use `plotmod()` to plot a moderation
-effect. If variables are standardized by `std_selected()`, `plotmod()` can
-indicate this in the plot.
-
-`vignette("cond_effect", package = "stdmod")` illustrates how to use `cond_effect()` to compute
-conditional effects, the effect of a predictor (focal variable) for selected
-levels of the moderator.
-`cond_effect()` supports outputs from `std_selected()`.
-
-# Reference(s)
-
-Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
-Improving an old way to measure moderation effect in standardized units.
-*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
-
-Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
-regression coefficients. *Psychometrika, 76*(4), 670-690.
-https://doi.org/10.1007/s11336-011-9224-6
+---
+title: "Standardized Moderation Effect by std_selected()"
+author: "Shu Fai Cheung and David Weng Ngai Vong"
+date: "2026-01-04"
+output: rmarkdown::html_vignette
+vignette: >
+ %\VignetteIndexEntry{Standardized Moderation Effect by std_selected()}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+
+
+# Purpose
+
+This document demonstrates how to use `std_selected()` from
+the `stdmod` package to compute the correct
+standardized solution of moderated regression.
+More about this package can be found
+in `vignette("stdmod", package = "stdmod")`
+or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
+
+# Setup the Environment
+
+
+``` r
+library(stdmod) # For computing the standardized moderation effect conveniently
+```
+
+# Load the Dataset
+
+
+``` r
+data(sleep_emo_con)
+head(sleep_emo_con, 3)
+#> # A tibble: 3 × 6
+#> case_id sleep_duration conscientiousness emotional_stability age gender
+#>
+
+
+
+The results show that conscientiousness significantly moderates the effect of
+emotional stability on sleep duration.
+
+# Standardized Moderation Effect
+
+To get the correct standardized solution of the moderated regression, with the
+product term formed *after* standardization, we can use `std_selected()`.
+
+- The first argument is the regression output from `lm()`.
+
+- The argument `to_center` specifies variables to be mean
+ centered.
+
+- The argument `to_scale` specifies variables to be rescaled
+ by their standard deviations after centering.
+
+- In `stdmod` 0.2.6.3, the argument `to_standardize` was introduced
+ as a shortcut. Listing a variable in `to_standardize` is
+ equivalent to listing it in `to_center` and `to_scale`.
+
+If we want to standardize or mean center all variables, we can use `~ .` as a
+shortcut. Note that `std_selected()` will automatically skip categorical
+variables (i.e., factors or string variables in the regression model of `lm()`).
+
+
+``` r
+lm_stdall <- std_selected(lm_out,
+ to_standardize = ~ .)
+```
+
+Before 0.2.6.3, to standardize all variables except for
+categorical variables, we need to use both `to_center = ~ .`
+and `to_scale = ~ .`. Since 0.2.6.3,
+we can just use `to_standardize = ~ .`, as shown above.
+If `to_standardize = ~ .` does not work, just use
+`to_center` and `to_scale` as shown below:
+
+```r
+lm_stdall <- std_selected(lm_out,
+ to_center = ~ .,
+ to_scale = ~ .)
+```
+
+A summary of the results of `std_selected()` can be
+generated by `summary()`:
+
+
+``` r
+summary(lm_stdall)
+#>
+#> Call to std_selected():
+#> std_selected(lm_out = lm_out, to_standardize = ~.)
+#>
+#> Selected variable(s) are centered by mean and/or scaled by SD
+#> - Variable(s) centered: sleep_duration age gender emot cons
+#> - Variable(s) scaled: sleep_duration age gender emot cons
+#>
+#> centered_by scaled_by Note
+#> sleep_duration 6.776333 1.4168291 Standardized (mean = 0, SD = 1)
+#> age 22.274000 2.9407857 Standardized (mean = 0, SD = 1)
+#> gender NA NA Nonnumeric
+#> emot 2.713200 0.7629613 Standardized (mean = 0, SD = 1)
+#> cons 3.343200 0.6068198 Standardized (mean = 0, SD = 1)
+#>
+#> Note:
+#> - Categorical variables will not be centered or scaled even if
+#> requested.
+#>
+#> Call:
+#> lm(formula = sleep_duration ~ age + gender + emot * cons, data = dat_mod)
+#>
+#> Residuals:
+#> Min 1Q Median 3Q Max
+#> -4.2941 -0.5563 0.0063 0.6663 4.3187
+#>
+#> Coefficients:
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) 0.0549 0.0488 1.1248 0.26124
+#> age 0.0371 0.0443 0.8384 0.40221
+#> gendermale -0.1844 0.1170 -1.5759 0.11570
+#> emot 0.1150 0.0449 2.5600 0.01076 *
+#> cons 0.1305 0.0452 2.8893 0.00403 **
+#> emot:cons -0.1083 0.0434 -2.4967 0.01286 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+#>
+#> Residual standard error: 0.9771 on 494 degrees of freedom
+#>
+#> R-squared : 0.0548
+#> Adjusted R-squared : 0.0452
+#> ANOVA test of R-squared : F(5, 494) = 5.7277, p < 0.001
+#>
+#> = Test the highest order term =
+#> The highest order term : emot:cons
+#> R-squared increase adding this term: 0.0119
+#> F test of R-squared increase : F(1, 494) = 6.2335, p = 0.013
+#>
+#> Note:
+#> - Estimates and their statistics are based on the data after
+#> mean-centering, scaling, or standardization.
+#> - One or more variables are scaled by SD or standardized. OLS standard
+#> errors and confidence intervals may be biased for their coefficients.
+#> Please use `std_selected_boot()`.
+```
+
+The coefficient in this solution,
+-0.10829,
+can be interpreted as the change in the standardized effect of
+emotional stability for each one standard deviation increase of
+conscientiousness. Naturally, this can be called the
+*standardized moderation effect* of conscientiousness
+([Cheung, Cheung, Lau, Hui, & Vong, 2022](https://doi.org/10.1037/hea0001188)).
+
+The output of `std_selected()` can be passed to other functions that accept the
+output of `lm()`. This package also has a simple function,
+`plotmod()`, for generating a typical plot of the moderation effect:
+
+
+``` r
+plotmod(lm_stdall,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+
+plot of chunk mod_reg
+
+
+
+
+The function `plotmod()` also prints the conditional effects of the predictor
+(focal variable), emotional stability in this example.
+
+# The Common (Incorrect) Standardized Solution
+
+For comparison, this is the results of standardizing all variables, including
+the product term and the categorical variable.
+
+
+``` r
+library(lm.beta) # For generating the typical standardized solution
+packageVersion("lm.beta")
+#> [1] '1.7.3'
+lm_beta <- lm.beta(lm_out)
+summary(lm_beta)
+#>
+#> Call:
+#> lm(formula = sleep_duration ~ age + gender + emot * cons, data = sleep_emo_con)
+#>
+#> Residuals:
+#> Min 1Q Median 3Q Max
+#> -6.0841 -0.7882 0.0089 0.9440 6.1189
+#>
+#> Coefficients:
+#> Estimate Standardized Std. Error t value Pr(>|t|)
+#> (Intercept) 1.85154 NA 1.35224 1.369 0.17155
+#> age 0.01789 0.03712 0.02133 0.838 0.40221
+#> gendermale -0.26127 -0.06934 0.16579 -1.576 0.11570
+#> emot 1.32151 0.71163 0.45039 2.934 0.00350 **
+#> cons 1.20385 0.51560 0.37062 3.248 0.00124 **
+#> emot:cons -0.33140 -0.78201 0.13273 -2.497 0.01286 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+#>
+#> Residual standard error: 1.384 on 494 degrees of freedom
+#> Multiple R-squared: 0.0548, Adjusted R-squared: 0.04523
+#> F-statistic: 5.728 on 5 and 494 DF, p-value: 3.768e-05
+```
+
+The coefficient of the *standardized* product term is
+-0.78201, which
+*cannot* be interpreted as the change in the standardized effect of
+emotional stability for each one standard deviation increase of
+conscientiousness because the product term is standardized and can no longer
+be interpreted as the product of two variables in the model.
+
+# Improved Confidence Intervals
+
+It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6))
+that the standard errors of
+standardized regression coefficients computed just by standardizing the variables
+are biased, and consequently the confidence intervals are also invalid. The
+function `std_selected_boot()` is a wrapper of `std_selected()` that also
+forms the confidence interval of the regression coefficients when standardizing
+is conducted, using nonparametric bootstrapping as suggested by
+Cheung, Cheung, Lau, Hui, and Vong (2022).
+
+We use the same example above that standardizes all variables except for
+categorical variables to illustrate this function. The argument `nboot`
+specifies the number of nonparametric bootstrap samples.
+The level of confidence is set by `conf`. The default is .95, denoting 95%
+confidence intervals. If this is the desired level, this argument can be
+omitted.
+
+
+
+
+``` r
+set.seed(649017)
+lm_xwy_std_ci <- std_selected_boot(lm_out,
+ to_standardize = ~ .,
+ nboot = 2000)
+```
+
+If the default options are acceptable, the only additional argument is `nboot`.
+
+
+``` r
+summary(lm_xwy_std_ci)
+#>
+#> Call to std_selected_boot():
+#> std_selected_boot(lm_out = lm_out, to_standardize = ~., nboot = 2000)
+#>
+#> Selected variable(s) are centered by mean and/or scaled by SD
+#> - Variable(s) centered: sleep_duration age gender emot cons
+#> - Variable(s) scaled: sleep_duration age gender emot cons
+#>
+#> centered_by scaled_by Note
+#> sleep_duration 6.776333 1.4168291 Standardized (mean = 0, SD = 1)
+#> age 22.274000 2.9407857 Standardized (mean = 0, SD = 1)
+#> gender NA NA Nonnumeric
+#> emot 2.713200 0.7629613 Standardized (mean = 0, SD = 1)
+#> cons 3.343200 0.6068198 Standardized (mean = 0, SD = 1)
+#>
+#> Note:
+#> - Categorical variables will not be centered or scaled even if
+#> requested.
+#> - Nonparametric bootstrapping 95% confidence intervals computed.
+#> - The number of bootstrap samples is 2000.
+#>
+#> Call:
+#> lm(formula = sleep_duration ~ age + gender + emot * cons, data = dat_mod)
+#>
+#> Residuals:
+#> Min 1Q Median 3Q Max
+#> -4.2941 -0.5563 0.0063 0.6663 4.3187
+#>
+#> Coefficients:
+#> Estimate CI Lower CI Upper Std. Error t value Pr(>|t|)
+#> (Intercept) 0.0549 0.0030 0.1043 0.0488 1.1248 0.26124
+#> age 0.0371 -0.0363 0.1036 0.0443 0.8384 0.40221
+#> gendermale -0.1844 -0.4389 0.0876 0.1170 -1.5759 0.11570
+#> emot 0.1150 0.0236 0.2024 0.0449 2.5600 0.01076 *
+#> cons 0.1305 0.0324 0.2242 0.0452 2.8893 0.00403 **
+#> emot:cons -0.1083 -0.2040 -0.0097 0.0434 -2.4967 0.01286 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+#>
+#> Residual standard error: 0.9771 on 494 degrees of freedom
+#>
+#> R-squared : 0.0548
+#> Adjusted R-squared : 0.0452
+#> ANOVA test of R-squared : F(5, 494) = 5.7277, p < 0.001
+#>
+#> = Test the highest order term =
+#> The highest order term : emot:cons
+#> R-squared increase adding this term: 0.0119
+#> F test of R-squared increase : F(1, 494) = 6.2335, p = 0.013
+#>
+#> Note:
+#> - Estimates and their statistics are based on the data after
+#> mean-centering, scaling, or standardization.
+#> - [CI Lower, CI Upper] are bootstrap percentile confidence intervals.
+#> - Std. Error are not bootstrap SEs.
+```
+
+
+
+The standardized moderation effect is
+-0.1083,
+and the 95% nonparametric bootstrap confidence interval is
+-0.2040 to
+-0.0097.
+
+Note: As a side product, the nonparametric bootstrap percentile confidence of the other
+coefficients are also reported. They can be used for other variables that are
+standardized in the same model, whether they are involved in the moderation or not.
+
+# Further Information
+
+`vignette("plotmod", package = "stdmod")` illustrates how to use `plotmod()` to plot a moderation
+effect. If variables are standardized by `std_selected()`, `plotmod()` can
+indicate this in the plot.
+
+`vignette("cond_effect", package = "stdmod")` illustrates how to use `cond_effect()` to compute
+conditional effects, the effect of a predictor (focal variable) for selected
+levels of the moderator.
+`cond_effect()` supports outputs from `std_selected()`.
+
+# Reference(s)
+
+Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
+Improving an old way to measure moderation effect in standardized units.
+*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
+
+Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
+regression coefficients. *Psychometrika, 76*(4), 670-690.
+https://doi.org/10.1007/s11336-011-9224-6
diff --git a/vignettes/moderation.Rmd.original b/vignettes/moderation.Rmd.original
new file mode 100644
index 0000000..168f603
--- /dev/null
+++ b/vignettes/moderation.Rmd.original
@@ -0,0 +1,245 @@
+---
+title: "Standardized Moderation Effect by std_selected()"
+author: "Shu Fai Cheung and David Weng Ngai Vong"
+date: "`r Sys.Date()`"
+output: rmarkdown::html_vignette
+vignette: >
+ %\VignetteIndexEntry{Standardized Moderation Effect by std_selected()}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+```{r, include = FALSE}
+knitr::opts_chunk$set(
+ collapse = TRUE,
+ comment = "#>",
+ fig.width = 6,
+ fig.height = 4,
+ fig.align = "center",
+ fig.path = ""
+)
+```
+
+# Purpose
+
+This document demonstrates how to use `std_selected()` from
+the `stdmod` package to compute the correct
+standardized solution of moderated regression.
+More about this package can be found
+in `vignette("stdmod", package = "stdmod")`
+or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
+
+# Setup the Environment
+
+```{r setup}
+library(stdmod) # For computing the standardized moderation effect conveniently
+```
+
+# Load the Dataset
+
+```{r load_dataset}
+data(sleep_emo_con)
+head(sleep_emo_con, 3)
+```
+
+This data set has 500 cases of data. The variables are sleep duration, age, gender,
+and the scores from two personality scales, emotional stability and
+conscientiousness of the IPIP Big Five markers. Please refer to
+(citation to be added) for the detail of the data set.
+
+The names of some variables are shortened for readability:
+
+```{r}
+colnames(sleep_emo_con)[3:4] <- c("cons", "emot")
+head(sleep_emo_con, 3)
+```
+
+
+# Moderated Regression
+
+Suppose we are interested in predicting sleep duration by emotional stability,
+after controlling for gender and age. However, we suspect that the effect of
+emotional stability, if any, may be moderated by conscientiousness. Therefore,
+we conduct a moderated regression as follow:
+
+```{r mod_reg}
+lm_out <- lm(sleep_duration ~ age + gender + emot * cons,
+ data = sleep_emo_con)
+summary(lm_out)
+plotmod(lm_out,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+The results show that conscientiousness significantly moderates the effect of
+emotional stability on sleep duration.
+
+# Standardized Moderation Effect
+
+To get the correct standardized solution of the moderated regression, with the
+product term formed *after* standardization, we can use `std_selected()`.
+
+- The first argument is the regression output from `lm()`.
+
+- The argument `to_center` specifies variables to be mean
+ centered.
+
+- The argument `to_scale` specifies variables to be rescaled
+ by their standard deviations after centering.
+
+- In `stdmod` 0.2.6.3, the argument `to_standardize` was introduced
+ as a shortcut. Listing a variable in `to_standardize` is
+ equivalent to listing it in `to_center` and `to_scale`.
+
+If we want to standardize or mean center all variables, we can use `~ .` as a
+shortcut. Note that `std_selected()` will automatically skip categorical
+variables (i.e., factors or string variables in the regression model of `lm()`).
+
+```{r}
+lm_stdall <- std_selected(lm_out,
+ to_standardize = ~ .)
+```
+
+Before 0.2.6.3, to standardize all variables except for
+categorical variables, we need to use both `to_center = ~ .`
+and `to_scale = ~ .`. Since 0.2.6.3,
+we can just use `to_standardize = ~ .`, as shown above.
+If `to_standardize = ~ .` does not work, just use
+`to_center` and `to_scale` as shown below:
+
+```r
+lm_stdall <- std_selected(lm_out,
+ to_center = ~ .,
+ to_scale = ~ .)
+```
+
+A summary of the results of `std_selected()` can be
+generated by `summary()`:
+
+```{r}
+summary(lm_stdall)
+```
+
+The coefficient in this solution,
+`r round(coef(lm_stdall)["emot:cons"], 5)`,
+can be interpreted as the change in the standardized effect of
+emotional stability for each one standard deviation increase of
+conscientiousness. Naturally, this can be called the
+*standardized moderation effect* of conscientiousness
+([Cheung, Cheung, Lau, Hui, & Vong, 2022](https://doi.org/10.1037/hea0001188)).
+
+The output of `std_selected()` can be passed to other functions that accept the
+output of `lm()`. This package also has a simple function,
+`plotmod()`, for generating a typical plot of the moderation effect:
+
+```{r mod_reg_stdall}
+plotmod(lm_stdall,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+The function `plotmod()` also prints the conditional effects of the predictor
+(focal variable), emotional stability in this example.
+
+# The Common (Incorrect) Standardized Solution
+
+For comparison, this is the results of standardizing all variables, including
+the product term and the categorical variable.
+
+```{r}
+library(lm.beta) # For generating the typical standardized solution
+packageVersion("lm.beta")
+lm_beta <- lm.beta(lm_out)
+summary(lm_beta)
+```
+
+The coefficient of the *standardized* product term is
+`r round(coef(lm_beta)["emot:cons"], 5)`, which
+*cannot* be interpreted as the change in the standardized effect of
+emotional stability for each one standard deviation increase of
+conscientiousness because the product term is standardized and can no longer
+be interpreted as the product of two variables in the model.
+
+# Improved Confidence Intervals
+
+It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6))
+that the standard errors of
+standardized regression coefficients computed just by standardizing the variables
+are biased, and consequently the confidence intervals are also invalid. The
+function `std_selected_boot()` is a wrapper of `std_selected()` that also
+forms the confidence interval of the regression coefficients when standardizing
+is conducted, using nonparametric bootstrapping as suggested by
+Cheung, Cheung, Lau, Hui, and Vong (2022).
+
+We use the same example above that standardizes all variables except for
+categorical variables to illustrate this function. The argument `nboot`
+specifies the number of nonparametric bootstrap samples.
+The level of confidence is set by `conf`. The default is .95, denoting 95%
+confidence intervals. If this is the desired level, this argument can be
+omitted.
+
+```{r echo = FALSE, eval = FALSE}
+if (file.exists("eg2_lm_xwy_std_ci.rds")) {
+ lm_xwy_std_ci <- readRDS("eg2_lm_xwy_std_ci.rds")
+ } else {
+ set.seed(649017)
+ lm_xwy_std_ci <- std_selected_boot(lm_out, to_center = ~ .,
+ to_scale = ~ .,
+ nboot = 2000)
+ saveRDS(lm_xwy_std_ci, "eg2_lm_xwy_std_ci.rds", compress = "xz")
+ }
+```
+
+```{r}
+set.seed(649017)
+lm_xwy_std_ci <- std_selected_boot(lm_out,
+ to_standardize = ~ .,
+ nboot = 2000)
+```
+
+If the default options are acceptable, the only additional argument is `nboot`.
+
+```{r}
+summary(lm_xwy_std_ci)
+```
+
+```{r echo = FALSE}
+tmp <- summary(lm_xwy_std_ci)$coefficients
+```
+
+The standardized moderation effect is
+`r formatC(tmp["emot:cons", "Estimate"], 4, format = "f")`,
+and the 95% nonparametric bootstrap confidence interval is
+`r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
+`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
+
+Note: As a side product, the nonparametric bootstrap percentile confidence of the other
+coefficients are also reported. They can be used for other variables that are
+standardized in the same model, whether they are involved in the moderation or not.
+
+# Further Information
+
+`vignette("plotmod", package = "stdmod")` illustrates how to use `plotmod()` to plot a moderation
+effect. If variables are standardized by `std_selected()`, `plotmod()` can
+indicate this in the plot.
+
+`vignette("cond_effect", package = "stdmod")` illustrates how to use `cond_effect()` to compute
+conditional effects, the effect of a predictor (focal variable) for selected
+levels of the moderator.
+`cond_effect()` supports outputs from `std_selected()`.
+
+# Reference(s)
+
+Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
+Improving an old way to measure moderation effect in standardized units.
+*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
+
+Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
+regression coefficients. *Psychometrika, 76*(4), 670-690.
+https://doi.org/10.1007/s11336-011-9224-6
diff --git a/vignettes/std_selected.Rmd b/vignettes/std_selected.Rmd
index 8e79747..b402167 100644
--- a/vignettes/std_selected.Rmd
+++ b/vignettes/std_selected.Rmd
@@ -1,326 +1,481 @@
----
-title: "Mean Center and Standardize Selected Variable by std_selected()"
-author: "Shu Fai Cheung and David Weng Ngai Vong"
-date: "`r Sys.Date()`"
-output: rmarkdown::html_vignette
-vignette: >
- %\VignetteIndexEntry{Mean Center and Standardize Selected Variable by std_selected()}
- %\VignetteEngine{knitr::rmarkdown}
- %\VignetteEncoding{UTF-8}
----
-
-```{r, include = FALSE}
-knitr::opts_chunk$set(
- collapse = TRUE,
- comment = "#>",
- fig.width = 6,
- fig.height = 4,
- fig.align = "center"
-)
-```
-
-# Purpose
-
-Instead of standardizing all variables, even variables that (a) are categorical
-and should not be standardized, or (b) measured on meaningful unites and do
-not need to be standardized, `std_selected()` from the package
-`stdmod` allows users to have more
-control on how standardization is to be conducted.
-
-A moderated regression model is used as an example but it can also be used for
-regression models without interaction terms.
-
-More about this package can be found
-in `vignette("stdmod", package = "stdmod")`
-or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
-
-# Setup the Environment
-
-```{r setup}
-library(stdmod)
-```
-
-# Load the Dataset
-
-```{r load_dataset}
-data(sleep_emo_con)
-head(sleep_emo_con, 3)
-```
-
-This data set has 500 cases of data. The variables are sleep duration,
-age, gender, and the scores from two personality scales, emotional stability
-and conscientiousness of the IPIP Big Five markers. Please refer to
-(citation to be included) for the detail of the data set.
-
-The names of some variables are shortened for readability:
-
-```{r shorten_names}
-colnames(sleep_emo_con)[3:4] <- c("cons", "emot")
-head(sleep_emo_con, 3)
-```
-
-# Moderated Regression
-
-Suppose we are interested in predicting sleep duration by emotional
-stability, after controlling for gender and age. However, we suspect that the
-effect of emotional stability, if any, may be moderated by conscientiousness.
-Therefore, we conduct a moderated regression as follow:
-
-```{r mod_reg}
-lm_raw <- lm(sleep_duration ~ age + gender + emot * cons,
- data = sleep_emo_con)
-summary(lm_raw)
-```
-
-The results show that conscientiousness significantly moderates the effect of
-emotional stability on sleep duration.
-
-This package has a simple function, `plotmod()`, for generating a typical plot
-of the moderation effect:
-
-```{r std_selected_lm_raw_plot}
-plotmod(lm_raw,
- x = "emot",
- w = "cons",
- x_label = "Emotional Stability",
- w_label = "Conscientiousness",
- y_label = "Sleep Duration")
-```
-
-The function `plotmod()` also prints the conditional effects of the predictor,
-emotional stability in this example.
-
-# Mean Center the Moderator
-
-To know the effect of emotional stability when conscientiousness is equal to its
-mean, we can center conscientiousness by its mean in the data and redo the
-moderated regression. Instead of creating the new variable and rerun the
-regression, we can pass the `lm()` output to `std_selected()` and specify the
-variables to be mean centered:
-
-
-```{r lm_w_centered}
-lm_w_centered <- std_selected(lm_raw,
- to_center = ~ cons)
-printCoefmat(summary(lm_w_centered)$coefficients, digits = 3)
-```
-
-The argument for meaning centering is `to_center`. The variable is specified
-in the formula form, placing them on the right hand side of the formula.
-
-In this example, when conscientiousness
-is at mean level, the effect of emotional stability is
-`r formatC(coef(lm_w_centered)["emot"], 4, format = "f")`.
-
-# Mean Center The Moderator and the Focal Variable
-
-This example demonstrates centering more than one variable. In the following
-model, both emotional stability and conscientiousness are centered. They are
-placed after `~` and joined by `+`.
-
-```{r lm_xw_centered}
-lm_xw_centered <- std_selected(lm_raw,
- to_center = ~ emot + cons)
-printCoefmat(summary(lm_xw_centered)$coefficients, digits = 3)
-```
-
-# Standardize The Moderator and The Focal Variable
-
-To standardize a variable we first mean center it and then scale it by its
-standard deviation. Scaling is done by listing the variable on `to_scale`.
-The input format is identical to that of `to_center`.
-
-```r
-lm_xw_std <- std_selected(lm_raw,
- to_center = ~ emot + cons,
- to_scale = ~ emot + cons)
-```
-
-Since 0.2.6.3 of `stdmod`, `to_standardize` can be used as a shortcut.
-Listing a variable on `to_standardize` is equivalent to listing it
-on both `to_center` and `to_scale`. Therefore, the following
-call can also be used:
-
-```{r lm_xw_std}
-lm_xw_std <- std_selected(lm_raw,
- to_standardize = ~ emot + cons)
-```
-
-```{r lm_xw_std_coef}
-printCoefmat(summary(lm_xw_std)$coefficients, digits = 3)
-```
-
-In this example, when conscientiousness
-is at mean level, for each one standard deviation increase of
-emotional stability, the predicted sleep duration increases by
-`r formatC(coef(lm_xw_std)["emot"], 4, format = "f")` hour.
-
-```{r std_selected_lm_xw_std_plot}
-plotmod(lm_xw_std,
- x = "emot",
- w = "cons",
- x_label = "Emotional Stability",
- w_label = "Conscientiousness",
- y_label = "Sleep Duration")
-```
-
-The function `plotmod()` automatically checks whether a variable is
-standardized. If yes, it will report this in the plot as table note on the
-bottom.
-
-The pattern of
-the plot does not change. However, the conditional effects reported
-in the graph are now
-based on the model with emotional stability and conscientiousness
-standardized.
-
-# Standardize The Moderator, The Focal Variable, and the Outcome Variable
-
-We can also mean center or standardize the outcome variable (dependent
-variable). We
-just add the variable to the right hand side of `~` in `to_center` and
-`to_scale` as appropriate.
-
-```r
-lm_xwy_std <- std_selected(lm_raw,
- to_center = ~ emot + cons + sleep_duration,
- to_scale = ~ emot + cons + sleep_duration)
-```
-
-Since 0.2.6.3, `to_standardize` can be used as a shortcut:
-
-```{r lm_xwy_std}
-lm_xwy_std <- std_selected(lm_raw,
- to_standardize = ~ emot + cons + sleep_duration)
-printCoefmat(summary(lm_xwy_std)$coefficients, digits = 3)
-```
-
-In this example, when conscientiousness
-is at mean level, the standardized moderation effect of
-emotional stability on sleep duration is
-`r formatC(coef(lm_xwy_std)["emot"], 4, format = "f")`.
-
-```{r std_selected_lm_xwy_std_plot}
-plotmod(lm_xwy_std,
- x = "emot",
- w = "cons",
- x_label = "Emotional Stability",
- w_label = "Conscientiousness",
- y_label = "Sleep Duration")
-```
-
-Again, the pattern of
-the plot does not change, but the conditional effects reported
-in the graph are now
-based on the model with emotional stability, conscientiousness,
-and sleep duration standardized.
-
-# Standardize All Variables
-
-If we want to standardize all variables except for categorical variables, if any,
-we can use `~ .` as a shortcut. `std_selected()` will automatically
-skip categorical variables (i.e., factors or string variables in the
-regression model of `lm()`).
-
-```r
-lm_all_std <- std_selected(lm_raw,
- to_center = ~ .,
- to_scale = ~ .)
-```
-
-Since 0.2.6.3, `to_standardize` can be used as a shortcut:
-
-```{r lm_all_std}
-lm_all_std <- std_selected(lm_raw,
- to_standardize = ~ .)
-printCoefmat(summary(lm_all_std)$coefficients, digits = 3)
-```
-
-# The Usual Standardized Solution
-
-For comparison, this is the results of standardizing all variables, including
-the product term and the categorical variable.
-
-```{r lm_beta}
-library(lm.beta) # For generating the typical standardized solution
-packageVersion("lm.beta")
-lm_usual_std <- lm.beta(lm_raw)
-printCoefmat(summary(lm_usual_std)$coefficients, digits = 3)
-```
-
-In moderated regression, the coefficient of *standardized* product term,
-`r formatC(coef(lm_usual_std)["emot:cons"], 4, format = "f")`,
-is not interpretable. The coefficient of *standardized* gender,
-`r formatC(coef(lm_usual_std)["gendermale"], 4, format = "f")`, is also
-difficult to interpret.
-
-# Improved Confidence Interval For "Betas"
-
-It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6)) that the standard errors of
-standardized regression coefficients (betas) computed just by standardizing
-the variables
-are biased, and consequently the confidence intervals are also invalid. The
-function `std_selected_boot()` is a wrapper of `std_selected()` that also
-forms the confidence interval of the regression coefficients when standardization
-is conducted,
-using nonparametric bootstrapping as suggested by
-[Cheung, Cheung, Lau, Hui, and Vong (2022)](https://doi.org/10.1037/hea0001188).
-
-We use the same example above that standardizes emotional stability,
-conscientiousness, and sleep duration, to illustrate this function.
-The argument `nboot` specifies the number of nonparametric bootstrap samples.
-The level of confidence set by `conf`. The default is .95, denoting 95%
-confidence intervals. If this is the desired level, this argument can be omitted.
-
-```{r echo = FALSE, eval = TRUE}
-if (file.exists("eg_lm_xwy_std_ci.rds")) {
- lm_xwy_std_ci <- readRDS("eg_lm_xwy_std_ci.rds")
- } else {
- set.seed(58702)
- lm_xwy_std_ci <- std_selected_boot(lm_raw,
- to_center = ~ emot + cons + sleep_duration,
- to_scale = ~ emot + cons + sleep_duration,
- nboot = 2000)
- saveRDS(lm_xwy_std_ci, "eg_lm_xwy_std_ci.rds", compress = "xz")
- }
-```
-
-```r
-set.seed(58702)
-lm_xwy_std_ci <- std_selected_boot(lm_raw,
- to_standardize = ~ emot + cons + sleep_duration,
- nboot = 2000)
-```
-
-```{r lm_xwy_std_ci_summary}
-summary(lm_xwy_std_ci)
-```
-
-```{r echo = FALSE}
-tmp <- summary(lm_xwy_std_ci)$coefficients
-```
-
-The standardized moderation effect is `r formatC(tmp["emot:cons", "Estimate"], 4, format = "f")`
-, and the 95% nonparametric bootstrap percentile confidence interval is
-`r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
-`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
-
-Note: As a side product, the nonparametric bootstrap confidence of the
-other coefficients are also reported. They can be used for other variables that
-are standardized in the same model, whether they are involved in the moderation or not.
-
-# Further Information
-
-Further information on the functions can be found in their help pages
-(`std_selected()` and `std_selected_boot()`). For example, parallel computation
-can be used when doing bootstrapping, if the number of bootstrapping samples
-requested is large.
-
-# Reference
-
-Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
-Improving an old way to measure moderation effect in standardized units.
-*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
-
-Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
-regression coefficients. *Psychometrika, 76*(4), 670-690. https://doi.org/10.1007/s11336-011-9224-6
+---
+title: "Mean Center and Standardize Selected Variable by std_selected()"
+author: "Shu Fai Cheung and David Weng Ngai Vong"
+date: "2026-01-04"
+output: rmarkdown::html_vignette
+vignette: >
+ %\VignetteIndexEntry{Mean Center and Standardize Selected Variable by std_selected()}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+
+
+# Purpose
+
+Instead of standardizing all variables, even variables that (a) are categorical
+and should not be standardized, or (b) measured on meaningful unites and do
+not need to be standardized, `std_selected()` from the package
+`stdmod` allows users to have more
+control on how standardization is to be conducted.
+
+A moderated regression model is used as an example but it can also be used for
+regression models without interaction terms.
+
+More about this package can be found
+in `vignette("stdmod", package = "stdmod")`
+or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
+
+# Setup the Environment
+
+
+``` r
+library(stdmod)
+```
+
+# Load the Dataset
+
+
+``` r
+data(sleep_emo_con)
+head(sleep_emo_con, 3)
+#> # A tibble: 3 × 6
+#> case_id sleep_duration conscientiousness emotional_stability age gender
+#>
+plot of chunk mod_reg_stdall
+
+
+
+
+The function `plotmod()` also prints the conditional effects of the predictor,
+emotional stability in this example.
+
+# Mean Center the Moderator
+
+To know the effect of emotional stability when conscientiousness is equal to its
+mean, we can center conscientiousness by its mean in the data and redo the
+moderated regression. Instead of creating the new variable and rerun the
+regression, we can pass the `lm()` output to `std_selected()` and specify the
+variables to be mean centered:
+
+
+
+``` r
+lm_w_centered <- std_selected(lm_raw,
+ to_center = ~ cons)
+printCoefmat(summary(lm_w_centered)$coefficients, digits = 3)
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) 5.8763 0.5170 11.37 <2e-16 ***
+#> age 0.0179 0.0213 0.84 0.4022
+#> gendermale -0.2613 0.1658 -1.58 0.1157
+#> emot 0.2136 0.0834 2.56 0.0108 *
+#> cons 1.2039 0.3706 3.25 0.0012 **
+#> emot:cons -0.3314 0.1327 -2.50 0.0129 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+The argument for meaning centering is `to_center`. The variable is specified
+in the formula form, placing them on the right hand side of the formula.
+
+In this example, when conscientiousness
+is at mean level, the effect of emotional stability is
+0.2136.
+
+# Mean Center The Moderator and the Focal Variable
+
+This example demonstrates centering more than one variable. In the following
+model, both emotional stability and conscientiousness are centered. They are
+placed after `~` and joined by `+`.
+
+
+``` r
+lm_xw_centered <- std_selected(lm_raw,
+ to_center = ~ emot + cons)
+printCoefmat(summary(lm_xw_centered)$coefficients, digits = 3)
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) 6.4557 0.4783 13.50 <2e-16 ***
+#> age 0.0179 0.0213 0.84 0.402
+#> gendermale -0.2613 0.1658 -1.58 0.116
+#> emot 0.2136 0.0834 2.56 0.011 *
+#> cons 0.3047 0.1055 2.89 0.004 **
+#> emot:cons -0.3314 0.1327 -2.50 0.013 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+# Standardize The Moderator and The Focal Variable
+
+To standardize a variable we first mean center it and then scale it by its
+standard deviation. Scaling is done by listing the variable on `to_scale`.
+The input format is identical to that of `to_center`.
+
+```r
+lm_xw_std <- std_selected(lm_raw,
+ to_center = ~ emot + cons,
+ to_scale = ~ emot + cons)
+```
+
+Since 0.2.6.3 of `stdmod`, `to_standardize` can be used as a shortcut.
+Listing a variable on `to_standardize` is equivalent to listing it
+on both `to_center` and `to_scale`. Therefore, the following
+call can also be used:
+
+
+``` r
+lm_xw_std <- std_selected(lm_raw,
+ to_standardize = ~ emot + cons)
+```
+
+
+``` r
+printCoefmat(summary(lm_xw_std)$coefficients, digits = 3)
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) 6.4557 0.4783 13.50 <2e-16 ***
+#> age 0.0179 0.0213 0.84 0.402
+#> gendermale -0.2613 0.1658 -1.58 0.116
+#> emot 0.1630 0.0637 2.56 0.011 *
+#> cons 0.1849 0.0640 2.89 0.004 **
+#> emot:cons -0.1534 0.0615 -2.50 0.013 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+In this example, when conscientiousness
+is at mean level, for each one standard deviation increase of
+emotional stability, the predicted sleep duration increases by
+0.1630 hour.
+
+
+``` r
+plotmod(lm_xw_std,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+
+plot of chunk std_selected_lm_raw_plot
+
+
+
+
+The function `plotmod()` automatically checks whether a variable is
+standardized. If yes, it will report this in the plot as table note on the
+bottom.
+
+The pattern of
+the plot does not change. However, the conditional effects reported
+in the graph are now
+based on the model with emotional stability and conscientiousness
+standardized.
+
+# Standardize The Moderator, The Focal Variable, and the Outcome Variable
+
+We can also mean center or standardize the outcome variable (dependent
+variable). We
+just add the variable to the right hand side of `~` in `to_center` and
+`to_scale` as appropriate.
+
+```r
+lm_xwy_std <- std_selected(lm_raw,
+ to_center = ~ emot + cons + sleep_duration,
+ to_scale = ~ emot + cons + sleep_duration)
+```
+
+Since 0.2.6.3, `to_standardize` can be used as a shortcut:
+
+
+``` r
+lm_xwy_std <- std_selected(lm_raw,
+ to_standardize = ~ emot + cons + sleep_duration)
+printCoefmat(summary(lm_xwy_std)$coefficients, digits = 3)
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) -0.2263 0.3376 -0.67 0.503
+#> age 0.0126 0.0151 0.84 0.402
+#> gendermale -0.1844 0.1170 -1.58 0.116
+#> emot 0.1150 0.0449 2.56 0.011 *
+#> cons 0.1305 0.0452 2.89 0.004 **
+#> emot:cons -0.1083 0.0434 -2.50 0.013 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+In this example, when conscientiousness
+is at mean level, the standardized moderation effect of
+emotional stability on sleep duration is
+0.1150.
+
+
+``` r
+plotmod(lm_xwy_std,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+
+plot of chunk std_selected_lm_xw_std_plot
+
+
+
+
+Again, the pattern of
+the plot does not change, but the conditional effects reported
+in the graph are now
+based on the model with emotional stability, conscientiousness,
+and sleep duration standardized.
+
+# Standardize All Variables
+
+If we want to standardize all variables except for categorical variables, if any,
+we can use `~ .` as a shortcut. `std_selected()` will automatically
+skip categorical variables (i.e., factors or string variables in the
+regression model of `lm()`).
+
+```r
+lm_all_std <- std_selected(lm_raw,
+ to_center = ~ .,
+ to_scale = ~ .)
+```
+
+Since 0.2.6.3, `to_standardize` can be used as a shortcut:
+
+
+``` r
+lm_all_std <- std_selected(lm_raw,
+ to_standardize = ~ .)
+printCoefmat(summary(lm_all_std)$coefficients, digits = 3)
+#> Estimate Std. Error t value Pr(>|t|)
+#> (Intercept) 0.0549 0.0488 1.12 0.261
+#> age 0.0371 0.0443 0.84 0.402
+#> gendermale -0.1844 0.1170 -1.58 0.116
+#> emot 0.1150 0.0449 2.56 0.011 *
+#> cons 0.1305 0.0452 2.89 0.004 **
+#> emot:cons -0.1083 0.0434 -2.50 0.013 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+# The Usual Standardized Solution
+
+For comparison, this is the results of standardizing all variables, including
+the product term and the categorical variable.
+
+
+``` r
+library(lm.beta) # For generating the typical standardized solution
+packageVersion("lm.beta")
+#> [1] '1.7.3'
+lm_usual_std <- lm.beta(lm_raw)
+printCoefmat(summary(lm_usual_std)$coefficients, digits = 3)
+#> Estimate Standardized Std. Error t value Pr(>|t|)
+#> (Intercept) 1.8515 NA 1.3522 1.37 0.1715
+#> age 0.0179 0.0371 0.0213 0.84 0.4022
+#> gendermale -0.2613 -0.0693 0.1658 -1.58 0.1157
+#> emot 1.3215 0.7116 0.4504 2.93 0.0035 **
+#> cons 1.2039 0.5156 0.3706 3.25 0.0012 **
+#> emot:cons -0.3314 -0.7820 0.1327 -2.50 0.0129 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+```
+
+In moderated regression, the coefficient of *standardized* product term,
+-0.7820,
+is not interpretable. The coefficient of *standardized* gender,
+-0.0693, is also
+difficult to interpret.
+
+# Improved Confidence Interval For "Betas"
+
+It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6)) that the standard errors of
+standardized regression coefficients (betas) computed just by standardizing
+the variables
+are biased, and consequently the confidence intervals are also invalid. The
+function `std_selected_boot()` is a wrapper of `std_selected()` that also
+forms the confidence interval of the regression coefficients when standardization
+is conducted,
+using nonparametric bootstrapping as suggested by
+[Cheung, Cheung, Lau, Hui, and Vong (2022)](https://doi.org/10.1037/hea0001188).
+
+We use the same example above that standardizes emotional stability,
+conscientiousness, and sleep duration, to illustrate this function.
+The argument `nboot` specifies the number of nonparametric bootstrap samples.
+The level of confidence set by `conf`. The default is .95, denoting 95%
+confidence intervals. If this is the desired level, this argument can be omitted.
+
+
+
+
+``` r
+set.seed(58702)
+lm_xwy_std_ci <- std_selected_boot(lm_raw,
+ to_standardize = ~ emot + cons + sleep_duration,
+ nboot = 2000)
+```
+
+
+``` r
+summary(lm_xwy_std_ci)
+#>
+#> Call to std_selected_boot():
+#> std_selected_boot(lm_out = lm_raw, to_standardize = ~emot + cons +
+#> sleep_duration, nboot = 2000)
+#>
+#> Selected variable(s) are centered by mean and/or scaled by SD
+#> - Variable(s) centered: emot cons sleep_duration
+#> - Variable(s) scaled: emot cons sleep_duration
+#>
+#> centered_by scaled_by Note
+#> sleep_duration 6.776333 1.4168291 Standardized (mean = 0, SD = 1)
+#> age 0.000000 1.0000000
+#> gender NA NA Nonnumeric
+#> emot 2.713200 0.7629613 Standardized (mean = 0, SD = 1)
+#> cons 3.343200 0.6068198 Standardized (mean = 0, SD = 1)
+#>
+#> Note:
+#> - Categorical variables will not be centered or scaled even if
+#> requested.
+#> - Nonparametric bootstrapping 95% confidence intervals computed.
+#> - The number of bootstrap samples is 2000.
+#>
+#> Call:
+#> lm(formula = sleep_duration ~ age + gender + emot * cons, data = dat_mod)
+#>
+#> Residuals:
+#> Min 1Q Median 3Q Max
+#> -4.2941 -0.5563 0.0063 0.6663 4.3187
+#>
+#> Coefficients:
+#> Estimate CI Lower CI Upper Std. Error t value Pr(>|t|)
+#> (Intercept) -0.2263 -0.8315 0.3503 0.3376 -0.6703 0.50298
+#> age 0.0126 -0.0128 0.0397 0.0151 0.8384 0.40221
+#> gendermale -0.1844 -0.4484 0.0723 0.1170 -1.5759 0.11570
+#> emot 0.1150 0.0256 0.2001 0.0449 2.5600 0.01076 *
+#> cons 0.1305 0.0289 0.2323 0.0452 2.8893 0.00403 **
+#> emot:cons -0.1083 -0.2005 -0.0077 0.0434 -2.4967 0.01286 *
+#> ---
+#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
+#>
+#> Residual standard error: 0.9771 on 494 degrees of freedom
+#>
+#> R-squared : 0.0548
+#> Adjusted R-squared : 0.0452
+#> ANOVA test of R-squared : F(5, 494) = 5.7277, p < 0.001
+#>
+#> = Test the highest order term =
+#> The highest order term : emot:cons
+#> R-squared increase adding this term: 0.0119
+#> F test of R-squared increase : F(1, 494) = 6.2335, p = 0.013
+#>
+#> Note:
+#> - Estimates and their statistics are based on the data after
+#> mean-centering, scaling, or standardization.
+#> - [CI Lower, CI Upper] are bootstrap percentile confidence intervals.
+#> - Std. Error are not bootstrap SEs.
+```
+
+
+
+The standardized moderation effect is -0.1083
+, and the 95% nonparametric bootstrap percentile confidence interval is
+-0.2005 to
+-0.0077.
+
+Note: As a side product, the nonparametric bootstrap confidence of the
+other coefficients are also reported. They can be used for other variables that
+are standardized in the same model, whether they are involved in the moderation or not.
+
+# Further Information
+
+Further information on the functions can be found in their help pages
+(`std_selected()` and `std_selected_boot()`). For example, parallel computation
+can be used when doing bootstrapping, if the number of bootstrapping samples
+requested is large.
+
+# Reference
+
+Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
+Improving an old way to measure moderation effect in standardized units.
+*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
+
+Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
+regression coefficients. *Psychometrika, 76*(4), 670-690. https://doi.org/10.1007/s11336-011-9224-6
diff --git a/vignettes/std_selected.Rmd.original b/vignettes/std_selected.Rmd.original
new file mode 100644
index 0000000..6d11eac
--- /dev/null
+++ b/vignettes/std_selected.Rmd.original
@@ -0,0 +1,327 @@
+---
+title: "Mean Center and Standardize Selected Variable by std_selected()"
+author: "Shu Fai Cheung and David Weng Ngai Vong"
+date: "`r Sys.Date()`"
+output: rmarkdown::html_vignette
+vignette: >
+ %\VignetteIndexEntry{Mean Center and Standardize Selected Variable by std_selected()}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+```{r, include = FALSE}
+knitr::opts_chunk$set(
+ collapse = TRUE,
+ comment = "#>",
+ fig.width = 6,
+ fig.height = 4,
+ fig.align = "center",
+ fig.path = ""
+)
+```
+
+# Purpose
+
+Instead of standardizing all variables, even variables that (a) are categorical
+and should not be standardized, or (b) measured on meaningful unites and do
+not need to be standardized, `std_selected()` from the package
+`stdmod` allows users to have more
+control on how standardization is to be conducted.
+
+A moderated regression model is used as an example but it can also be used for
+regression models without interaction terms.
+
+More about this package can be found
+in `vignette("stdmod", package = "stdmod")`
+or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
+
+# Setup the Environment
+
+```{r setup}
+library(stdmod)
+```
+
+# Load the Dataset
+
+```{r load_dataset}
+data(sleep_emo_con)
+head(sleep_emo_con, 3)
+```
+
+This data set has 500 cases of data. The variables are sleep duration,
+age, gender, and the scores from two personality scales, emotional stability
+and conscientiousness of the IPIP Big Five markers. Please refer to
+(citation to be included) for the detail of the data set.
+
+The names of some variables are shortened for readability:
+
+```{r shorten_names}
+colnames(sleep_emo_con)[3:4] <- c("cons", "emot")
+head(sleep_emo_con, 3)
+```
+
+# Moderated Regression
+
+Suppose we are interested in predicting sleep duration by emotional
+stability, after controlling for gender and age. However, we suspect that the
+effect of emotional stability, if any, may be moderated by conscientiousness.
+Therefore, we conduct a moderated regression as follow:
+
+```{r mod_reg}
+lm_raw <- lm(sleep_duration ~ age + gender + emot * cons,
+ data = sleep_emo_con)
+summary(lm_raw)
+```
+
+The results show that conscientiousness significantly moderates the effect of
+emotional stability on sleep duration.
+
+This package has a simple function, `plotmod()`, for generating a typical plot
+of the moderation effect:
+
+```{r std_selected_lm_raw_plot}
+plotmod(lm_raw,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+The function `plotmod()` also prints the conditional effects of the predictor,
+emotional stability in this example.
+
+# Mean Center the Moderator
+
+To know the effect of emotional stability when conscientiousness is equal to its
+mean, we can center conscientiousness by its mean in the data and redo the
+moderated regression. Instead of creating the new variable and rerun the
+regression, we can pass the `lm()` output to `std_selected()` and specify the
+variables to be mean centered:
+
+
+```{r lm_w_centered}
+lm_w_centered <- std_selected(lm_raw,
+ to_center = ~ cons)
+printCoefmat(summary(lm_w_centered)$coefficients, digits = 3)
+```
+
+The argument for meaning centering is `to_center`. The variable is specified
+in the formula form, placing them on the right hand side of the formula.
+
+In this example, when conscientiousness
+is at mean level, the effect of emotional stability is
+`r formatC(coef(lm_w_centered)["emot"], 4, format = "f")`.
+
+# Mean Center The Moderator and the Focal Variable
+
+This example demonstrates centering more than one variable. In the following
+model, both emotional stability and conscientiousness are centered. They are
+placed after `~` and joined by `+`.
+
+```{r lm_xw_centered}
+lm_xw_centered <- std_selected(lm_raw,
+ to_center = ~ emot + cons)
+printCoefmat(summary(lm_xw_centered)$coefficients, digits = 3)
+```
+
+# Standardize The Moderator and The Focal Variable
+
+To standardize a variable we first mean center it and then scale it by its
+standard deviation. Scaling is done by listing the variable on `to_scale`.
+The input format is identical to that of `to_center`.
+
+```r
+lm_xw_std <- std_selected(lm_raw,
+ to_center = ~ emot + cons,
+ to_scale = ~ emot + cons)
+```
+
+Since 0.2.6.3 of `stdmod`, `to_standardize` can be used as a shortcut.
+Listing a variable on `to_standardize` is equivalent to listing it
+on both `to_center` and `to_scale`. Therefore, the following
+call can also be used:
+
+```{r lm_xw_std}
+lm_xw_std <- std_selected(lm_raw,
+ to_standardize = ~ emot + cons)
+```
+
+```{r lm_xw_std_coef}
+printCoefmat(summary(lm_xw_std)$coefficients, digits = 3)
+```
+
+In this example, when conscientiousness
+is at mean level, for each one standard deviation increase of
+emotional stability, the predicted sleep duration increases by
+`r formatC(coef(lm_xw_std)["emot"], 4, format = "f")` hour.
+
+```{r std_selected_lm_xw_std_plot}
+plotmod(lm_xw_std,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+The function `plotmod()` automatically checks whether a variable is
+standardized. If yes, it will report this in the plot as table note on the
+bottom.
+
+The pattern of
+the plot does not change. However, the conditional effects reported
+in the graph are now
+based on the model with emotional stability and conscientiousness
+standardized.
+
+# Standardize The Moderator, The Focal Variable, and the Outcome Variable
+
+We can also mean center or standardize the outcome variable (dependent
+variable). We
+just add the variable to the right hand side of `~` in `to_center` and
+`to_scale` as appropriate.
+
+```r
+lm_xwy_std <- std_selected(lm_raw,
+ to_center = ~ emot + cons + sleep_duration,
+ to_scale = ~ emot + cons + sleep_duration)
+```
+
+Since 0.2.6.3, `to_standardize` can be used as a shortcut:
+
+```{r lm_xwy_std}
+lm_xwy_std <- std_selected(lm_raw,
+ to_standardize = ~ emot + cons + sleep_duration)
+printCoefmat(summary(lm_xwy_std)$coefficients, digits = 3)
+```
+
+In this example, when conscientiousness
+is at mean level, the standardized moderation effect of
+emotional stability on sleep duration is
+`r formatC(coef(lm_xwy_std)["emot"], 4, format = "f")`.
+
+```{r std_selected_lm_xwy_std_plot}
+plotmod(lm_xwy_std,
+ x = "emot",
+ w = "cons",
+ x_label = "Emotional Stability",
+ w_label = "Conscientiousness",
+ y_label = "Sleep Duration")
+```
+
+Again, the pattern of
+the plot does not change, but the conditional effects reported
+in the graph are now
+based on the model with emotional stability, conscientiousness,
+and sleep duration standardized.
+
+# Standardize All Variables
+
+If we want to standardize all variables except for categorical variables, if any,
+we can use `~ .` as a shortcut. `std_selected()` will automatically
+skip categorical variables (i.e., factors or string variables in the
+regression model of `lm()`).
+
+```r
+lm_all_std <- std_selected(lm_raw,
+ to_center = ~ .,
+ to_scale = ~ .)
+```
+
+Since 0.2.6.3, `to_standardize` can be used as a shortcut:
+
+```{r lm_all_std}
+lm_all_std <- std_selected(lm_raw,
+ to_standardize = ~ .)
+printCoefmat(summary(lm_all_std)$coefficients, digits = 3)
+```
+
+# The Usual Standardized Solution
+
+For comparison, this is the results of standardizing all variables, including
+the product term and the categorical variable.
+
+```{r lm_beta}
+library(lm.beta) # For generating the typical standardized solution
+packageVersion("lm.beta")
+lm_usual_std <- lm.beta(lm_raw)
+printCoefmat(summary(lm_usual_std)$coefficients, digits = 3)
+```
+
+In moderated regression, the coefficient of *standardized* product term,
+`r formatC(coef(lm_usual_std)["emot:cons"], 4, format = "f")`,
+is not interpretable. The coefficient of *standardized* gender,
+`r formatC(coef(lm_usual_std)["gendermale"], 4, format = "f")`, is also
+difficult to interpret.
+
+# Improved Confidence Interval For "Betas"
+
+It has been shown (e.g., [Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6)) that the standard errors of
+standardized regression coefficients (betas) computed just by standardizing
+the variables
+are biased, and consequently the confidence intervals are also invalid. The
+function `std_selected_boot()` is a wrapper of `std_selected()` that also
+forms the confidence interval of the regression coefficients when standardization
+is conducted,
+using nonparametric bootstrapping as suggested by
+[Cheung, Cheung, Lau, Hui, and Vong (2022)](https://doi.org/10.1037/hea0001188).
+
+We use the same example above that standardizes emotional stability,
+conscientiousness, and sleep duration, to illustrate this function.
+The argument `nboot` specifies the number of nonparametric bootstrap samples.
+The level of confidence set by `conf`. The default is .95, denoting 95%
+confidence intervals. If this is the desired level, this argument can be omitted.
+
+```{r echo = FALSE, eval = FALSE}
+if (file.exists("eg_lm_xwy_std_ci.rds")) {
+ lm_xwy_std_ci <- readRDS("eg_lm_xwy_std_ci.rds")
+ } else {
+ set.seed(58702)
+ lm_xwy_std_ci <- std_selected_boot(lm_raw,
+ to_center = ~ emot + cons + sleep_duration,
+ to_scale = ~ emot + cons + sleep_duration,
+ nboot = 2000)
+ saveRDS(lm_xwy_std_ci, "eg_lm_xwy_std_ci.rds", compress = "xz")
+ }
+```
+
+```{r}
+set.seed(58702)
+lm_xwy_std_ci <- std_selected_boot(lm_raw,
+ to_standardize = ~ emot + cons + sleep_duration,
+ nboot = 2000)
+```
+
+```{r lm_xwy_std_ci_summary}
+summary(lm_xwy_std_ci)
+```
+
+```{r echo = FALSE}
+tmp <- summary(lm_xwy_std_ci)$coefficients
+```
+
+The standardized moderation effect is `r formatC(tmp["emot:cons", "Estimate"], 4, format = "f")`
+, and the 95% nonparametric bootstrap percentile confidence interval is
+`r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
+`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
+
+Note: As a side product, the nonparametric bootstrap confidence of the
+other coefficients are also reported. They can be used for other variables that
+are standardized in the same model, whether they are involved in the moderation or not.
+
+# Further Information
+
+Further information on the functions can be found in their help pages
+(`std_selected()` and `std_selected_boot()`). For example, parallel computation
+can be used when doing bootstrapping, if the number of bootstrapping samples
+requested is large.
+
+# Reference
+
+Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
+Improving an old way to measure moderation effect in standardized units.
+*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
+
+Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
+regression coefficients. *Psychometrika, 76*(4), 670-690. https://doi.org/10.1007/s11336-011-9224-6
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diff --git a/vignettes/stdmod.Rmd b/vignettes/stdmod.Rmd
index 43bf284..25095ae 100644
--- a/vignettes/stdmod.Rmd
+++ b/vignettes/stdmod.Rmd
@@ -1,316 +1,547 @@
----
-title: "A Quick Start Guide on Using std_selected()"
-author: "Shu Fai Cheung"
-date: "`r Sys.Date()`"
-output: rmarkdown::html_vignette
-vignette: >
- %\VignetteIndexEntry{A Quick Start Guide on Using std_selected()}
- %\VignetteEngine{knitr::rmarkdown}
- %\VignetteEncoding{UTF-8}
----
-
-```{r, include = FALSE}
-knitr::opts_chunk$set(
- collapse = TRUE,
- comment = "#>",
- fig.width = 6,
- fig.height = 4,
- fig.align = "center"
-)
-```
-
-# Introduction
-
-This vignette illustrates how to use
-`std_selected()`, the main function from
-the `stdmod` package.
-More about this package can be found
-in `vignette("stdmod", package = "stdmod")`
-or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
-
-
-# This Guide Shows to use `std_selected()` to:
-
-- get the correct standardized regression coefficients of a moderated
-regression model, and
-
-- form the valid confidence intervals of the standardized regression
-coefficients using nonparametric bootstrapping that takes into account the
-sampling variation due to standardization.
-
-# Sample Dataset
-
-```{r}
-library(stdmod)
-dat <- sleep_emo_con
-head(dat, 3)
-```
-
-This dataset has 500 cases, with sleep duration
-(measured in average hours),
-conscientiousness, emotional stability, age, and gender (a
-`"female"` and `"male"`).
-
-The names of some variables are shortened for readability:
-
-```{r}
-colnames(dat)[2:4] <- c("sleep", "cons", "emot")
-head(dat, 3)
-```
-
-# Model
-
-Suppose this is the moderated regression model:
-
-- Dependent variable (Outcome Variable): sleep duration (`sleep`)
-
-- Independent variable (Predictor / Focal Variable): emotional stability (`emot`)
-
-- Moderator: conscientiousness (`cons`)
-
-- Control variables: `age` and `gender`
-
-`lm()` can be used to fit this model:
-
-```{r}
-lm_out <- lm(sleep ~ age + gender + emot * cons,
- dat = dat)
-summary(lm_out)
-```
-
-The unstandardized moderation effect is significant, B =
-`r formatC(coef(lm_out)["emot:cons"], 4, format = "f")`.
-For each one unit increase of conscientiousness score, the effect of emotional
-stability decreases by `r formatC(-1 * coef(lm_out)["emot:cons"], 4, format = "f")`.
-
-# Correct Standardization For the Moderated Regression
-
-Suppose we want to find the correct standardized solution for the moderated
-regression, that is, all variables
-except for categorical variables are standardized. In a moderated regression model,
-the product term should be formed *after* standardization.
-
-Instead of doing the standardization ourselves before calling `lm()`, we can pass
-the `lm()` output to `std_selected()`, and use `~ .` for
-the arguments `to_scale` and `to_center`.
-
-```r
-lm_stdall <- std_selected(lm_out,
- to_scale = ~ .,
- to_center = ~ .)
-```
-
-Since 0.2.6.3, `to_standardize` can be used as a shortcut:
-
-```{r}
-lm_stdall <- std_selected(lm_out,
- to_standardize = ~ .)
-```
-
-```{r}
-summary(lm_stdall)
-```
-
-
-
-In this example, the coefficient of the product term, which naturally can
-be called the
-**standardized moderation effect**, is significant, B =
-`r formatC(coef(lm_stdall)["emot:cons"], 4, format = "f")`.
-For each one *standard deviation* increase of conscientiousness score, the
-**standardized effect** of emotional stability decreases by
-`r formatC(-1 * coef(lm_stdall)["emot:cons"], 4, format = "f")`.
-
-## The Arguments
-
-Standardization is equivalent to centering by mean and then scaling by
-(dividing by) standard deviation.
-The argument `to_center` specifies the variables to be centered
-by their means, and the argument `to_scale` specifies the variables to be scaled by
-their standard deviations. The formula interface of `lm()` is used in these two
-arguments,
-with the variables on the right hand side being the variables to be
-centered and/or scaled.
-
-The "`.`" on the right hand side represents all variables in the model,
-including the outcome variable (sleep duration in this example).
-
-`std_selected()` will also skip categorical variables automatically skipped
-because standardizing them will make their coefficients not easy to interpret.
-
-Since 0.2.6.3, `to_standardize` is added as a shortcut. Listing a variable
-on `to_standardize` is equivalent to listing this variable
-on both `to_center` and `to_scale`.
-
-## Advantage
-
-Using `std_selected` minimizes impact on the workflow. Do regression
-as usual. Get the correct standardized coefficients only when we need to
-interpret them.
-
-## Nonparametric Bootstrap Confidence Intervals
-
-There is one problem with standardized coefficients. The confidence intervals
-based on ordinary least squares (OLS) fitted to the standardized
-variables do not take into account the sampling variation of
-the sample means and standard deviations ([Yuan & Chan, 2011](https://doi.org/10.1007/s11336-011-9224-6)).
-[Cheung, Cheung, Lau, Hui, and Vong (2022)](https://doi.org/10.1037/hea0001188)
-suggest using nonparametric bootstrapping, with standardization conducted
-in each bootstrap sample.
-
-This can be done by `std_selected_boot()`, a wrapper of `std_selected()`:
-
-```{r echo = FALSE}
-if (file.exists("stdmod_lm_stdall_boot.rds")) {
- lm_stdall_boot <- readRDS("stdmod_lm_stdall_boot.rds")
- } else {
- set.seed(870432)
- lm_stdall_boot <- std_selected_boot(lm_out,
- to_scale = ~ .,
- to_center = ~ .,
- nboot = 5000)
- saveRDS(lm_stdall_boot, "stdmod_lm_stdall_boot.rds", compress = "xz")
- }
-```
-
-```{r eval = FALSE}
-set.seed(870432)
-lm_stdall_boot <- std_selected_boot(lm_out,
- to_scale = ~ .,
- to_center = ~ .,
- nboot = 5000)
-```
-
-Since 0.2.6.3, `to_standardize` can be used as a shortcut:
-
-```r
-lm_stdall_boot <- std_selected_boot(lm_out,
- to_standardize = ~ .
- nboot = 5000)
-```
-
-
-The minimum additional argument is `nboot`, the number of bootstrap samples.
-
-```{r}
-summary(lm_stdall_boot)
-```
-
-The output is similar to that of `std_selected()`, with additional information
-on the bootstrapping process.
-
-```{r echo = FALSE}
-tmp <- summary(lm_stdall_boot)$coefficients
-```
-
-The 95% bootstrap percentile confidence interval of the standardized
-moderation effect is `r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
-`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
-
-# Standardize Independent Variable (Focal Variable) and Moderator
-
-`std_selected()` and `std_selected_boot()` can also be used to standardize only
-selected variables. There are cases in which we do not want to standardize
-some continuous variables because they are measured on interpretable units,
-such as hours.
-
-Suppose we want to standardize only emotional stability and conscientiousness,
-and do not standardize sleep
-duration. We just list `emot` and `cons` on
-`to_center` and `to_scale`:
-
-```r
-lm_std1 <- std_selected(lm_out,
- to_scale = ~ emot + cons,
- to_center = ~ emot + cons)
-```
-
-Since 0.2.6.3, `to_standardize` can be used a shortuct:
-
-```{r}
-lm_std1 <- std_selected(lm_out,
- to_standardize = ~ emot + cons)
-```
-
-```{r}
-summary(lm_std1)
-```
-
-The *partially* standardized moderation effect is
-`r formatC(coef(lm_std1)["emot:cons"], 4, format = "f")`.
-For each one *standard deviation* increase of conscientiousness score, the
-*partially* standardized effect of emotional stability decreases by
-`r formatC(-1 * coef(lm_std1)["emot:cons"], 4, format = "f")`.
-
-## Nonparametric Bootstrap Confidence Intervals
-
-The function `std_selected_boot()` can also be used to form the nonparametric
-bootstrap confidence interval when only some of the variables are standardized:
-
-```{r echo = FALSE}
-if (file.exists("stdmod_lm_std1_boot.rds")) {
- lm_std1_boot <- readRDS("stdmod_lm_std1_boot.rds")
- } else {
- set.seed(870432)
- lm_std1_boot <- std_selected_boot(lm_out,
- to_scale = ~ emot + cons,
- to_center = ~ emot + cons,
- nboot = 5000)
- saveRDS(lm_std1_boot, "stdmod_lm_std1_boot.rds", compress = "xz")
- }
-```
-
-```{r eval = FALSE}
-set.seed(870432)
-lm_std1_boot <- std_selected_boot(lm_out,
- to_scale = ~ emot + cons,
- to_center = ~ emot + cons,
- nboot = 5000)
-```
-
-Since 0.2.6.3, `to_standardize` can be used as a shortcut:
-
-```r
-lm_std1_boot <- std_selected_boot(lm_out,
- to_standardize = ~ emot + cons,
- nboot = 5000)
-```
-
-Again, the only additional argument is `nboot`.
-
-```{r}
-summary(lm_std1_boot)
-```
-
-```{r echo = FALSE}
-tmp <- summary(lm_std1_boot)$coefficients
-```
-
-The 95% bootstrap percentile confidence interval of the partially standardized
-moderation effect is `r formatC(tmp["emot:cons", "CI Lower"], 4, format = "f")` to
-`r formatC(tmp["emot:cons", "CI Upper"], 4, format = "f")`.
-
-# Further Information
-
-A more detailed illustration can be found at
-`vignette("moderation", package = "stdmod")`.
-
-`vignette("std_selected", package = "stdmod")` illustrates how `std_selected()` can be used
-to form nonparametric bootstrap percentile confidence interval for
-standardized regression coefficients ("betas") for regression models
-without a product term.
-
-Further information on the functions can be found in their help pages
-(`std_selected()` and `std_selected_boot()`). For example, parallel computation
-can be used when doing bootstrapping, if the number of bootstrapping samples
-request is large.
-
-# Reference(s)
-
-Cheung, S. F., Cheung, S.-H., Lau, E. Y. Y., Hui, C. H., & Vong, W. N. (2022)
-Improving an old way to measure moderation effect in standardized units.
-*Health Psychology*, *41*(7), 502-505. https://doi.org/10.1037/hea0001188.
-
-Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized
-regression coefficients. *Psychometrika, 76*(4), 670-690.
-https://doi.org/10.1007/s11336-011-9224-6
\ No newline at end of file
+---
+title: "A Quick Start Guide on Using std_selected()"
+author: "Shu Fai Cheung"
+date: "2026-01-04"
+output: rmarkdown::html_vignette
+vignette: >
+ %\VignetteIndexEntry{A Quick Start Guide on Using std_selected()}
+ %\VignetteEngine{knitr::rmarkdown}
+ %\VignetteEncoding{UTF-8}
+---
+
+
+
+# Introduction
+
+This vignette illustrates how to use
+`std_selected()`, the main function from
+the `stdmod` package.
+More about this package can be found
+in `vignette("stdmod", package = "stdmod")`
+or at [https://sfcheung.github.io/stdmod/](https://sfcheung.github.io/stdmod/).
+
+
+# This Guide Shows to use `std_selected()` to:
+
+- get the correct standardized regression coefficients of a moderated
+regression model, and
+
+- form the valid confidence intervals of the standardized regression
+coefficients using nonparametric bootstrapping that takes into account the
+sampling variation due to standardization.
+
+# Sample Dataset
+
+
+``` r
+library(stdmod)
+dat <- sleep_emo_con
+head(dat, 3)
+#> # A tibble: 3 × 6
+#> case_id sleep_duration cons emot age gender
+#>
+plot of chunk std_selected_lm_xwy_std_plot
+