,
David Weng Ngai Vong [ctb]| Title: | Standardized Moderation Effect and Its Confidence Interval |
|---|---|
| Description: | Functions for computing a standardized moderation effect in moderated regression and forming its confidence interval by nonparametric bootstrapping as proposed in Cheung, Cheung, Lau, Hui, and Vong (2022) <doi:10.1037/hea0001188>. Also includes simple-to-use functions for computing conditional effects (unstandardized or standardized) and plotting moderation effects. |
| Authors: | Shu Fai Cheung [aut, cre] ,
David Weng Ngai Vong [ctb] |
| Maintainer: | Shu Fai Cheung <[email protected]> |
| License: | GPL-3 |
| Version: | 0.2.11 |
| Built: | 2024-11-21 05:21:38 UTC |
| Source: | https://github.com/sfcheung/stdmod |
Intercept the add1() method and raise an error.
## S3 method for class 'std_selected' add1(object, ...)## S3 method for class 'std_selected' add1(object, ...)
object |
The output of |
... |
Additional arguments. They will be ignored. |
add1() should not be used after the output of lm() is
processed by std_selected() or std_selected_boot().
It returns nothing. It is called for its side effect.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
Return the estimates of the conditional
effects
in the output of
cond_effect() or cond_effect_boot().
## S3 method for class 'cond_effect' coef(object, ...)## S3 method for class 'cond_effect' coef(object, ...)
object |
The output of |
... |
Optional arguments. Ignored by the function. |
It just extracts and returns the column of
conditional effects in a cond_effect-class object.
A numeric vector: The estimates of the conditional
effects in a cond_effect-class object.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) out <- cond_effect(lm_raw, x = iv, w = mod) out coef(out) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) out <- cond_effect(lm_std, x = iv, w = mod) out coef(out) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) out <- cond_effect(lm_cat, x = iv, w = cat1) out coef(out)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) out <- cond_effect(lm_raw, x = iv, w = mod) out coef(out) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) out <- cond_effect(lm_std, x = iv, w = mod) out coef(out) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) out <- cond_effect(lm_cat, x = iv, w = cat1) out coef(out)
Return the estimate of the standardized
moderation effect
in the output of stdmod_lavaan().
## S3 method for class 'stdmod_lavaan' coef(object, ...)## S3 method for class 'stdmod_lavaan' coef(object, ...)
object |
The output of |
... |
Optional arguments. Ignored by the function. |
It just extracts and returns the element stdmod.
A scalar: The estimate of the standardized moderation effect.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") coef(out_noboot) # Compute the standardized moderation effect and # its confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) coef(out_boot)# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") coef(out_noboot) # Compute the standardized moderation effect and # its confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) coef(out_boot)
Compute the conditional effects in a moderated regression model.
cond_effect( output, x = NULL, w = NULL, w_method = c("sd", "percentile"), w_percentiles = c(0.16, 0.5, 0.84), w_sd_to_percentiles = NA, w_from_mean_in_sd = 1, w_values = NULL ) cond_effect_boot( output, x = NULL, w = NULL, ..., conf = 0.95, nboot = 100, boot_args = NULL, save_boot_est = TRUE, full_output = FALSE, do_boot = TRUE )cond_effect( output, x = NULL, w = NULL, w_method = c("sd", "percentile"), w_percentiles = c(0.16, 0.5, 0.84), w_sd_to_percentiles = NA, w_from_mean_in_sd = 1, w_values = NULL ) cond_effect_boot( output, x = NULL, w = NULL, ..., conf = 0.95, nboot = 100, boot_args = NULL, save_boot_est = TRUE, full_output = FALSE, do_boot = TRUE )
output |
The output from |
x |
The focal variable (independent variable), that is, the variable with its effect on the outcome variable (dependent) being moderated. It must be a numeric variable. |
w |
The moderator. Both numeric variables and categorical variables (character or factor) are supported. |
w_method |
How to define "low", "medium", and "high" for the moderator
levels.
Default is in terms of mean and
standard deviation (SD) of the moderator, |
w_percentiles |
If |
w_sd_to_percentiles |
If |
w_from_mean_in_sd |
How many SD from mean is used to define
"low" and
"high" for the moderator. Default is 1.
Ignored if |
w_values |
The values of |
... |
Arguments to be passed to |
conf |
The level of confidence for the confidence interval. Default is .95, to get 95% confidence intervals. |
nboot |
The number of bootstrap samples. Default is 100. |
boot_args |
A named list of arguments to be passed to |
save_boot_est |
If |
full_output |
Whether the full output from |
do_boot |
Whether bootstrapping confidence intervals will be formed.
Default is |
cond_effect() uses the centering approach to find the conditional
effect of the focal variable. For each level of the moderator, the value for
this level is subtracted from the moderator scores, and the model is
fitted to the modified data.
The coefficient of the focal variable is then the conditional effect of the
focal variable when the moderator's score is equal this value.
cond_effect_boot() function is a wrapper of cond_effect().
It calls cond_effect()
once for each bootstrap sample, and then computes the nonparametric
bootstrap percentile confidence intervals (Cheung, Cheung, Lau, Hui,
& Vong, 2022). If the output object is the output of std_selected()
or std_selected_boot(), in which mean-centering and/or standardization
have been conducted, they will be repeated in each bootstrap sample.
Therefore, like std_selected_boot(), it can be used for form
nonparametric bootstrap confidence intervals for standardized
effects, though cond_effect_boot() does this for the standardized
conditional effects.
This function ignores bootstrapping done by std_selected_boot(). It will
do its own bootstrapping.
If do_boot is FALSE, then the object it returns is identical to that
by cond_effect().
This function intentionally does not have an argument for setting the seed
for
random number. Users are recommended to set the seed, e.g., using
set.seed()
before calling it, to ensure reproducibility.
cond_effect() returns a data-frame-like object of the conditional effects.
The class is
cond_effect and the print method will print additional information of
the conditional effects. Additional information is stored in the
following attributes:
call: The original call.
output: The output object, such as the output from lm().
x, y, and w: The three variables used to compute the conditional
effects: focal variable (x), outcome variable (y),
and the moderator (w).
w_method: The method used to determine the values of the moderator
at the selected levels.
w_percentiles The percentiles to use if w_method = "percentile".
w_sd_to_percentiles: If not equal to NA, this is a scalar, the
number of standard deviation from the mean used to
determine the percentiles for the "low" and "high"
levels of the moderator.
w_from_mean_in_sd: The number of SD above or below the mean, for
determining the "low" and "high" levels of the
moderator if w_method is "sd".
w_empirical_percentiles: The actual percentile levels in the dataset
for the selected
levels of the moderator. A numeric vector.
w_empirical_z: The actual distance from the mean, in SD, of each
selected level of the moderator. A numeric vector.
y_standardized, x_standardized, and w_standardized: Each of them
is a logical scalar, indicating whether the outcome
variable, focal variable, and moderator are standardized.
cond_effect_boot() also returns a data-frame-like object of the
conditional effects of the class
cond_effect, with additional information from the bootstrapping stored
in these attributes:
boot_ci: A data frame of the bootstrap confidence intervals of the
conditional effects.
nboot: The number of bootstrap samples requested.
conf: The level of confidence, in proportion.
boot_est: A matrix of the bootstrap estimates of the conditional effects.
The number of rows equal to nboot, and the number of columns
equal to the number of levels of the moderator.
cond_effect_boot_call: The call to cond_effect_boot().
boot_out: If available, the original output from boot::boot().
cond_effect_boot(): A wrapper of cond_effect() that forms
nonparametric bootstrap confidence intervals.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) cond_effect(lm_raw, x = iv, w = mod) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) cond_effect(lm_cat, x = iv, w = cat1) # Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod) # Form nonparametric bootstrap confidence intervals # Use 2000 or even 5000 for nboot in real research out <- cond_effect_boot(lm_std, x = iv, w = mod, nboot = 50) out# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) cond_effect(lm_raw, x = iv, w = mod) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) cond_effect(lm_cat, x = iv, w = cat1) # Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod) # Form nonparametric bootstrap confidence intervals # Use 2000 or even 5000 for nboot in real research out <- cond_effect_boot(lm_std, x = iv, w = mod, nboot = 50) out
Return the confidence intervals of estimates
conditional effect in the output of
cond_effect() or cond_effect_boot().
## S3 method for class 'cond_effect' confint(object, parm, level = 0.95, type, ...)## S3 method for class 'cond_effect' confint(object, parm, level = 0.95, type, ...)
object |
The output of |
parm |
Ignored by this function. The confidence intervals for all available levels will be returned. |
level |
The level of confidence. For the confidence intervals returned
by |
type |
The type of the confidence intervals. If est to |
... |
Additional arguments. Ignored. |
If bootstrapping is used to form the confidence interval by
cond_effect_boot(),
users can request the percentile confidence intervals of
the bootstrap estimates. This method does not do the bootstrapping itself.
A matrix of the confidence intervals.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) out <- cond_effect(lm_raw, x = iv, w = mod) print(out, t_ci = TRUE) confint(out) lm_std <- std_selected(lm_raw, to_center = ~ iv + mod, to_scale = ~ iv + mod) # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) out <- cond_effect(lm_std, x = iv, w = mod) print(out, t_ci = TRUE) confint(out) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) out <- cond_effect(lm_cat, x = iv, w = cat1) print(out, t_ci = TRUE) confint(out)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) out <- cond_effect(lm_raw, x = iv, w = mod) print(out, t_ci = TRUE) confint(out) lm_std <- std_selected(lm_raw, to_center = ~ iv + mod, to_scale = ~ iv + mod) # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_raw, to_standardize = ~ iv + mod) out <- cond_effect(lm_std, x = iv, w = mod) print(out, t_ci = TRUE) confint(out) # Categorical moderator lm_cat <- lm(dv ~ iv*cat1 + v1, dat) summary(lm_cat) out <- cond_effect(lm_cat, x = iv, w = cat1) print(out, t_ci = TRUE) confint(out)
Return the confidence intervals of estimates
in the output of std_selected() or std_selected_boot().
## S3 method for class 'std_selected' confint(object, parm, level = 0.95, type, ...)## S3 method for class 'std_selected' confint(object, parm, level = 0.95, type, ...)
object |
The output of |
parm |
The parameters (coefficients) for which confidence intervals should be returned. If missing, the confidence intervals of all parameters will be returned. |
level |
The level of confidence. For the confidence intervals returned
by |
type |
The type of the confidence intervals. If est to |
... |
Arguments to be passed to |
If bootstrapping is used to form the confidence interval by
std_selected_boot(),
users can request the percentile confidence intervals of
the bootstrap estimates. This method does not do the bootstrapping itself.
A matrix of the confidence intervals.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_center = ~ ., to_scale = ~ .) # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_raw, to_standardize = ~ .) summary(lm_std) confint(lm_std) # Use to_standardize as a shortcut lm_std2 <- std_selected(lm_raw, to_standardize = ~ .) # The results are the same confint(lm_std) confint(lm_std2) all.equal(confint(lm_std), confint(lm_std2)) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. set.seed(89572) lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot) # Bootstrap percentile intervals, default when bootstrap was conduced confint(lm_std_boot) # Force OLS confidence intervals confint(lm_std_boot, type = "lm") # Use to_standardize as a shortcut set.seed(89572) lm_std_boot2 <- std_selected_boot(lm_raw, to_standardize = ~ ., nboot = 100) # The results are the same confint(lm_std_boot) confint(lm_std_boot2) all.equal(confint(lm_std_boot), confint(lm_std_boot2))# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_center = ~ ., to_scale = ~ .) # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_raw, to_standardize = ~ .) summary(lm_std) confint(lm_std) # Use to_standardize as a shortcut lm_std2 <- std_selected(lm_raw, to_standardize = ~ .) # The results are the same confint(lm_std) confint(lm_std2) all.equal(confint(lm_std), confint(lm_std2)) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. set.seed(89572) lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot) # Bootstrap percentile intervals, default when bootstrap was conduced confint(lm_std_boot) # Force OLS confidence intervals confint(lm_std_boot, type = "lm") # Use to_standardize as a shortcut set.seed(89572) lm_std_boot2 <- std_selected_boot(lm_raw, to_standardize = ~ ., nboot = 100) # The results are the same confint(lm_std_boot) confint(lm_std_boot2) all.equal(confint(lm_std_boot), confint(lm_std_boot2))
Return the confidence interval of the standardized
moderation effect
in the output of stdmod_lavaan().
## S3 method for class 'stdmod_lavaan' confint(object, parm, level = 0.95, ...)## S3 method for class 'stdmod_lavaan' confint(object, parm, level = 0.95, ...)
object |
The output of |
parm |
Ignored. Always return the bootstrap confidence interval of the standardized moderation effect. |
level |
The level of confidence, default is .95, returning the 95% confidence interval. |
... |
Additional arguments. Ignored by the function. |
If bootstrapping is used to form the confidence interval by
stdmod_lavaan(),
users can request the percentile confidence interval of
using the stored bootstrap estimate.
A one-row matrix of the confidence intervals.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect and # its confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) confint(out_boot)# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect and # its confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) confint(out_boot)
Plot the moderation effect in a regression model
plotmod( output, x, w, x_label, w_label, y_label, title, digits = 3, x_from_mean_in_sd = 1, w_from_mean_in_sd = 1, w_method = c("sd", "percentile"), w_percentiles = c(0.16, 0.84), x_method = c("sd", "percentile"), x_percentiles = c(0.16, 0.84), w_sd_to_percentiles = NA, x_sd_to_percentiles = NA, w_values = NULL, note_standardized = TRUE, no_title = FALSE, line_width = 1, point_size = 5, graph_type = c("default", "tumble") )plotmod( output, x, w, x_label, w_label, y_label, title, digits = 3, x_from_mean_in_sd = 1, w_from_mean_in_sd = 1, w_method = c("sd", "percentile"), w_percentiles = c(0.16, 0.84), x_method = c("sd", "percentile"), x_percentiles = c(0.16, 0.84), w_sd_to_percentiles = NA, x_sd_to_percentiles = NA, w_values = NULL, note_standardized = TRUE, no_title = FALSE, line_width = 1, point_size = 5, graph_type = c("default", "tumble") )
output |
The output
of |
x |
The name of the focal variable (x-axis) in 'output“. It can be the name of the variable, with or without quotes. Currently only numeric variables are supported. |
w |
The name of the moderator in |
x_label |
The label for the X-axis. Default is the value of |
w_label |
The label for the legend for the lines.
Default is the value of |
y_label |
The label for the Y-axis. Default is the name of the response variable in the model. |
title |
The title of the graph. If not supplied, it will be
generated from the variable
names or labels (in |
digits |
Number of decimal places to print. Default is 3. |
x_from_mean_in_sd |
How many SD from mean is used to define "low" and "high" for the focal variable. Default is 1. |
w_from_mean_in_sd |
How many SD from mean is used to define
"low" and
"high" for the moderator. Default is 1.
Ignored if |
w_method |
How to define "high" and "low" for the moderator levels.
Default is in terms of the
standard deviation of the moderator, |
w_percentiles |
If |
x_method |
How to define "high" and "low" for the focal
variable levels.
Default is in terms of the
standard deviation of the focal variable, |
x_percentiles |
If |
w_sd_to_percentiles |
If |
x_sd_to_percentiles |
If |
w_values |
The values of |
note_standardized |
If |
no_title |
If |
line_width |
The width of the lines as used in
|
point_size |
The size of the points as used in |
graph_type |
If |
This function generate a basic ggplot2 graph
typically found in psychology manuscripts. It tries to
check whether one or more variables are standardized, and
report this in the plot if required.
This function only has features for typical plots of moderation effects. It is not intended to be a flexible tool for a fine control on the plots.
A ggplot2 graph. Plotted if not assigned to a name. It can
be further modified like a usual ggplot2 graph.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
Bodner, T. E. (2016). Tumble graphs: Avoiding misleading end point extrapolation when graphing interactions from a moderated multiple regression analysis. Journal of Educational and Behavioral Statistics, 41(6), 593-604. doi:10.3102/1076998616657080
# Do a moderated regression by lm lm_out <- lm(sleep_duration ~ age + gender + emotional_stability*conscientiousness, sleep_emo_con) plotmod(lm_out, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration") # Standardize all variables except for categorical variables # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_out, # to_standardize = ~ .) lm_std <- std_selected(lm_out, to_scale = ~ ., to_center = ~ .) plotmod(lm_std, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration") # Tumble Graph plotmod(lm_std, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration", graph_type = "tumble")# Do a moderated regression by lm lm_out <- lm(sleep_duration ~ age + gender + emotional_stability*conscientiousness, sleep_emo_con) plotmod(lm_out, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration") # Standardize all variables except for categorical variables # Alternative: use to_standardize as a shortcut # lm_std <- std_selected(lm_out, # to_standardize = ~ .) lm_std <- std_selected(lm_out, to_scale = ~ ., to_center = ~ .) plotmod(lm_std, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration") # Tumble Graph plotmod(lm_std, x = emotional_stability, w = conscientiousness, x_label = "Emotional Stability", w_label = "Conscientiousness", y_label = "Sleep Duration", graph_type = "tumble")
Print the output of cond_effect() or cond_effect_boot().
## S3 method for class 'cond_effect' print( x, nd = 3, nd_stat = 3, nd_p = 3, title = TRUE, model = TRUE, level_info = TRUE, standardized = TRUE, boot_info = TRUE, table_only = FALSE, t_ci = FALSE, t_ci_level = 0.95, ... )## S3 method for class 'cond_effect' print( x, nd = 3, nd_stat = 3, nd_p = 3, title = TRUE, model = TRUE, level_info = TRUE, standardized = TRUE, boot_info = TRUE, table_only = FALSE, t_ci = FALSE, t_ci_level = 0.95, ... )
x |
The output of |
nd |
The number of digits for the variables. |
nd_stat |
The number of digits for test statistics (e.g., t). |
nd_p |
The number of digits for p-values. |
title |
If |
model |
If |
level_info |
If |
standardized |
If |
boot_info |
If |
table_only |
If |
t_ci |
If |
t_ci_level |
The level of confidence of the confidence intervals based on t statistics. Default is .95. |
... |
Additional arguments. Ignored by this function. |
x is returned invisibility.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) cond_effect(lm_raw, x = iv, w = mod) lm_std <- std_selected(lm_raw, to_scale = ~ iv + mod, to_center = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) cond_effect(lm_raw, x = iv, w = mod) lm_std <- std_selected(lm_raw, to_scale = ~ iv + mod, to_center = ~ iv + mod) cond_effect(lm_std, x = iv, w = mod)
Provide information of centering and scaling, along with
basic model information printed by the print() method of lm().
## S3 method for class 'std_selected' print(x, ...)## S3 method for class 'std_selected' print(x, ...)
x |
The output of |
... |
x is returned invisibly.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) lm_std # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) lm_std_boot# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) lm_std # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) lm_std_boot
Print the output of stdmod_lavaan().
## S3 method for class 'stdmod_lavaan' print(x, conf = 0.95, nd = 3, ...)## S3 method for class 'stdmod_lavaan' print(x, conf = 0.95, nd = 3, ...)
x |
The output of |
conf |
If nonparametric bootstrapping has been conducted by
|
nd |
The number of digits to be printed. |
... |
Optional arguments. Ignored. |
x is returned invisibly.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") out_noboot # Compute the standardized moderation effect and # its percentile confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) out_boot# Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) coef(fit) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") out_noboot # Compute the standardized moderation effect and # its percentile confidence interval based on nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) out_boot
Print the summary generated by summary() on the output
of std_selected() or std_selected_boot().
## S3 method for class 'summary.std_selected' print( x, ..., est_digits = 4, t_digits = 4, pvalue_less_than = 0.001, default_style = FALSE )## S3 method for class 'summary.std_selected' print( x, ..., est_digits = 4, t_digits = 4, pvalue_less_than = 0.001, default_style = FALSE )
x |
The output of |
... |
Arguments to be passed to |
est_digits |
The number of digits
after the decimal to be displayed for
the coefficient estimates, their
standard errors, and bootstrap
confidence intervals (if present). Note
that the values will be rounded to
this number of digits before printing.
If all digits at this position are
zero for all values, the values may
be displayed with fewer digits.
Note that the coefficient table is
printed by |
t_digits |
The number of digits
after the decimal to be displayed
for the t statistic (in the column
|
pvalue_less_than |
If a p-value
is less than this value, it will be
displayed with |
default_style |
Logical. If
|
x is returned invisibly.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot)
A random subset from a real dataset. For illustration.
sleep_emo_consleep_emo_con
A data frame with 500 rows and six variables:
Case ID, integer
Sleep duration in hours
Conscientiousness score, continuous
Emotional stability score, continuous
Age in years
Gender, string, "female" or "male"
Standardize, mean center, or scale by standard deviation selected variables in a regression model and refit the model
std_selected(lm_out, to_scale = NULL, to_center = NULL, to_standardize = NULL) std_selected_boot( lm_out, to_scale = NULL, to_center = NULL, to_standardize = NULL, conf = 0.95, nboot = 100, boot_args = NULL, save_boot_est = TRUE, full_output = FALSE, do_boot = TRUE )std_selected(lm_out, to_scale = NULL, to_center = NULL, to_standardize = NULL) std_selected_boot( lm_out, to_scale = NULL, to_center = NULL, to_standardize = NULL, conf = 0.95, nboot = 100, boot_args = NULL, save_boot_est = TRUE, full_output = FALSE, do_boot = TRUE )
lm_out |
The output from |
to_scale |
The terms to be rescaled by standard deviation,
specified by a formula as in |
to_center |
The terms to be mean centered, specified by a formula
as in |
to_standardize |
The terms to be standardized, specified by a formula
as in |
conf |
The level of confidence for the confidence interval. Default is .95. |
nboot |
The number of bootstrap samples. Default is 100. |
boot_args |
A named list of arguments to be passed to |
save_boot_est |
If |
full_output |
Whether the full output from |
do_boot |
Whether bootstrapping confidence intervals will be formed.
Default is |
std_selected() was originally developed to compute the standardized
moderation effect and the standardized coefficients for other predictors
given an lm() output (Cheung, Cheung, Lau, Hui, & Vong, 2022).
It has been extended such that users can specify
which variables in a regression model are to be mean-centered and/or
rescaled by
their standard deviations. If the model has one or more interaction terms,
they will be formed after the transformation, yielding the correct
standardized solution for a moderated regression model. Moreover,
categorical predictors will be automatically skipped in mean-centering
and rescaling.
Standardization is conducted when a variable is mean-centered and then rescaled by its standard deviation. Therefore, if the goal is to get the standardized solution of a moderated regression, users just instruct the function to standardize all non-categorical variables in the regression model.
std_selected_boot() is a wrapper of std_selected(). It calls
std_selected()
once
for each bootstrap sample, and then computes the nonparametric
bootstrap
percentile confidence intervals (Cheung, Cheung, Lau, Hui, & Vong, 2022).
If do_boot is FALSE, then the object it returns is identical to that
by std_selected().
This function intentionally does not have an argument for setting the seed
for
random number. Users are recommended to set the seed, e.g., using
set.seed()
before calling it, to ensure reproducibility.
The updated lm() output, with the class std_selected added. It will be
treated as a usual lm() object by most functions. These are the major
additional element in the list:
scaled_terms: If not NULL, a character vector of the variables scaled.
centered_terms: If not NULL, a character vector of the variables mean-centered.
scaled_by: A numeric vector of the scaling factors for all the variables in
the model. The value is 1 for terms not scaled.
centered_by: A numeric vector of the numbers used for centering for all
the variables in the model. The value is 0 for
terms not centered.
std_selected_call: The original call.
lm_out_call: The call in lm_out.
Like std_selected(), std_selected_boot() returns the updated lm()
output, with the class std_selected added. The output of std_selected_boot()
contain these additional elements in the list:
boot_ci: A data frame of the bootstrap confidence intervals of the
regression coefficient.
nboot: The number of bootstrap samples requested.
conf: The level of confidence, in proportion.
boot_est: A matrix of the bootstrap estimates of the regression coefficients.
The number of rows equal to nboot, and the number of columns
equal to the number of terms in the regression model.
std_selected_boot_call: The call to std_selected_boot().
boot_out: If available, the original output from boot::boot().
std_selected(): The base function to center or
scale selected variables in a regression model
std_selected_boot(): A wrapper of std_selected() that forms
nonparametric bootstrap confidence intervals.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
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. doi:10.1037/hea0001188
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Mean center mod only lm_cw <- std_selected(lm_raw, to_center = ~ mod) summary(lm_cw) # Mean center mod and iv lm_cwx <- std_selected(lm_raw, to_center = ~ mod + iv) summary(lm_cwx) # Standardize both mod and iv lm_stdwx <- std_selected(lm_raw, to_scale = ~ mod + iv, to_center = ~ mod + iv) summary(lm_stdwx) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # Use to_standardize as a shortcut lm_stdwx2 <- std_selected(lm_raw, to_standardize = ~ mod + iv) # The results are the same coef(lm_stdwx) coef(lm_stdwx2) all.equal(coef(lm_stdwx), coef(lm_stdwx2)) dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables as in std_selected above, and compute the # nonparametric bootstrapping percentile confidence intervals. set.seed(87053) lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., conf = .95, nboot = 100) # In real analysis, nboot should be at least 2000. summary(lm_std_boot) # Use to_standardize as a shortcut set.seed(87053) lm_std_boot2 <- std_selected_boot(lm_raw, to_standardize = ~ ., conf = .95, nboot = 100) # The results are the same confint(lm_std_boot) confint(lm_std_boot2) all.equal(confint(lm_std_boot), confint(lm_std_boot2))# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Mean center mod only lm_cw <- std_selected(lm_raw, to_center = ~ mod) summary(lm_cw) # Mean center mod and iv lm_cwx <- std_selected(lm_raw, to_center = ~ mod + iv) summary(lm_cwx) # Standardize both mod and iv lm_stdwx <- std_selected(lm_raw, to_scale = ~ mod + iv, to_center = ~ mod + iv) summary(lm_stdwx) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # Use to_standardize as a shortcut lm_stdwx2 <- std_selected(lm_raw, to_standardize = ~ mod + iv) # The results are the same coef(lm_stdwx) coef(lm_stdwx2) all.equal(coef(lm_stdwx), coef(lm_stdwx2)) dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables as in std_selected above, and compute the # nonparametric bootstrapping percentile confidence intervals. set.seed(87053) lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., conf = .95, nboot = 100) # In real analysis, nboot should be at least 2000. summary(lm_std_boot) # Use to_standardize as a shortcut set.seed(87053) lm_std_boot2 <- std_selected_boot(lm_raw, to_standardize = ~ ., conf = .95, nboot = 100) # The results are the same confint(lm_std_boot) confint(lm_std_boot2) all.equal(confint(lm_std_boot), confint(lm_std_boot2))
Compute the standardized moderation effect in a moderated regression model.
stdmod( lm_out, x = NULL, w = NULL, y = NULL, x_rescale = TRUE, w_rescale = TRUE, y_rescale = TRUE ) stdmod_boot( lm_out, ..., nboot = 100, conf = 0.95, boot_args = NULL, full_output = FALSE )stdmod( lm_out, x = NULL, w = NULL, y = NULL, x_rescale = TRUE, w_rescale = TRUE, y_rescale = TRUE ) stdmod_boot( lm_out, ..., nboot = 100, conf = 0.95, boot_args = NULL, full_output = FALSE )
lm_out |
The output from |
x |
The focal variable, that is, the variable with its effect
being moderated. If supplied, its standard deviation will be
used
for rescaling. Also called the independent variable in some
models. Default is |
w |
The moderator. If supplied, its standard deviation will be
used
for rescaling. Default is |
y |
The outcome variable (dependent variable) . If supplied, its standard deviation will be used for rescaling. Default is NULL. |
x_rescale |
If |
w_rescale |
If |
y_rescale |
If |
... |
Parameters to be passed to |
nboot |
The number of bootstrap samples. Default is 100. |
conf |
The level of confidence for the confidence interval. Default is .95. |
boot_args |
A named list of arguments to be passed to |
full_output |
Whether the full output from |
Two more general functions, std_selected() and
std_selected_boot(), have been developed and can do what these functions
do and more. Users are recommended to use them instead of stdmod() and
stdmod_boot(). These two functions will not be updated in the near
future.
Nevertheless, if computing the standardized moderation effect and forming its nonparametric bootstrap interval are all required, then these functions can still be used.
stdmod() computes the standardized moderation effect given an
lm() output using the formula from Cheung, Cheung, Lau, Hui, and Vong
(2022). Users specify
the moderator, the focal variable (the variable with its effect on
the outcome variable moderated), the outcome variable (dependent variable)
, and the corresponding
standardized moderation
effect. Users can also select which variable(s) will be standardized.
stdmod_boot() is a wrapper of stdmod(). It computes the nonparametric
bootstrap confidence interval of the standardized moderation effect, as
suggested by Cheung, Cheung, Lau, Hui, and Vong (2022), given
the output of lm()
Percentile interval from boot::boot.ci() is returned by this function.
If other types of
confidence intervals are desired, set full_output = TRUE and use
boot::boot.ci() on the element boot_out in the output of this
function.
stdmod() returns a scalar: The standardized moderation effect.
stdmod_boot() returns a list with two elements. The element ci is
a numeric vector of the bootstrap confidence interval. The element boot_out,
if not NA, is the output of boot::boot(), which is used to do the
bootstrapping.
stdmod(): The base function for computing standardized
moderation effect
stdmod_boot(): A wrapper of stdmod() that computes the nonparametric
bootstrap confidence interval of the standardized
moderation effect.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
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. doi:10.1037/hea0001188
# Load a test data of 500 cases dat <- test_x_1_w_1_v_2_n_500 # Do regression as usual: lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat) summary(lm_raw) # The standard deviations of iv, dv, and mod: sds <- apply(dat, 2, sd) sds # Compute the standardized moderation effect: stdmod_xyw <- stdmod(lm_raw, x = iv, y = dv, w = mod) stdmod_xyw # By default, all three variables will be standardized. # Check against self-computed standardized moderation effect: coef(lm_raw)["iv:mod"] * sds["iv"] * sds["mod"] / sds["dv"] # Standardize only the iv, i.e., do not standardized dv and the moderator: stdmod_x <- stdmod(lm_raw, x = iv, y = dv, w = mod, x_rescale = TRUE, y_rescale = FALSE, w_rescale = FALSE) stdmod_x # Check against self-computed moderation effect with only iv standardized: coef(lm_raw)["iv:mod"] * sds["iv"] dat <- test_x_1_w_1_v_2_n_500 # Do regression as usual: lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat) # Compute the standardized moderation effect. # Form its confidence interval by nonparametric bootstrapping. set.seed(85740917) stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 100) # In real analysis, nboot should be at least 2000. # Print the ci stdmod_xyw_boot$ci # Repeat the analysis but keep the results from boot: set.seed(85740917) stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 200, full_output = TRUE) # In real analysis, nboot should be at least 2000. # Print the 95% percentile confidence interval stdmod_xyw_boot$ci# Load a test data of 500 cases dat <- test_x_1_w_1_v_2_n_500 # Do regression as usual: lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat) summary(lm_raw) # The standard deviations of iv, dv, and mod: sds <- apply(dat, 2, sd) sds # Compute the standardized moderation effect: stdmod_xyw <- stdmod(lm_raw, x = iv, y = dv, w = mod) stdmod_xyw # By default, all three variables will be standardized. # Check against self-computed standardized moderation effect: coef(lm_raw)["iv:mod"] * sds["iv"] * sds["mod"] / sds["dv"] # Standardize only the iv, i.e., do not standardized dv and the moderator: stdmod_x <- stdmod(lm_raw, x = iv, y = dv, w = mod, x_rescale = TRUE, y_rescale = FALSE, w_rescale = FALSE) stdmod_x # Check against self-computed moderation effect with only iv standardized: coef(lm_raw)["iv:mod"] * sds["iv"] dat <- test_x_1_w_1_v_2_n_500 # Do regression as usual: lm_raw <- lm(dv ~ iv*mod + v1 + v2, dat) # Compute the standardized moderation effect. # Form its confidence interval by nonparametric bootstrapping. set.seed(85740917) stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 100) # In real analysis, nboot should be at least 2000. # Print the ci stdmod_xyw_boot$ci # Repeat the analysis but keep the results from boot: set.seed(85740917) stdmod_xyw_boot <- stdmod_boot(lm_raw, x = iv, w = mod, y = dv, nboot = 200, full_output = TRUE) # In real analysis, nboot should be at least 2000. # Print the 95% percentile confidence interval stdmod_xyw_boot$ci
Compute the standardized moderation effect in a structural
equation model fitted by lavaan::lavaan() or its wrappers and
form the nonparametric bootstrap confidence interval.
stdmod_lavaan( fit, x, y, w, x_w, standardized_x = TRUE, standardized_y = TRUE, standardized_w = TRUE, boot_ci = FALSE, boot_out = NULL, R = 100, conf = 0.95, use_old_version = FALSE, ... )stdmod_lavaan( fit, x, y, w, x_w, standardized_x = TRUE, standardized_y = TRUE, standardized_w = TRUE, boot_ci = FALSE, boot_out = NULL, R = 100, conf = 0.95, use_old_version = FALSE, ... )
fit |
The SEM output by |
x |
The name of the focal variable in the model, the variable with its effect on the outcome variable being moderated. |
y |
The name of the outcome variable (dependent variable) in the model. |
w |
The name of the moderator in the model. |
x_w |
The name of the product term (x * w) in the model. It can be
the variable generated by the colon operator, e.g., |
standardized_x |
If |
standardized_y |
If |
standardized_w |
If |
boot_ci |
Boolean. Whether nonparametric bootstrapping will be
conducted. Default is |
boot_out |
If set to the output of |
R |
(Not used in the current version. Used when |
conf |
The level of confidence. Default is .95, i.e., 95%. |
use_old_version |
If set to |
... |
(Not used in the current version. Used when |
Starting from Version 0.2.7.5, of stdmod_lavaan() adopts an approach
to bootstrapping different from that in the previous
versions (0.2.7.4 and before),
yielding bootstrapping results different from those in
previous versions (for reasons explained later).
To reproduce results from the older version of this function,
set use_old_version to TRUE.
stdmod_lavaan() accepts a lavaan::lavaan object, the
structural equation model output returned
by lavaan::lavaan() and its wrappers (e.g, lavaan::sem()) and computes
the standardized moderation effect using the formula in the appendix of
Cheung, Cheung, Lau, Hui, and Vong (2022).
The standard deviations of the focal variable (the variable with its effect
on the outcome variable being moderated), moderator, and outcome
variable (dependent variable) are computed from the implied
covariance matrix returned by
lavaan::lavInspect(). Therefore, models fitted to data sets with missing
data (e.g., with missing = "fiml") are also supported.
Partial standardization can also be requested. For example, standardization can be requested for only the focal variable and the outcome variable.
There are two ways to request nonparametric bootstrap
confidence interval. First, the model is fitted with se = "boot"
or se = "bootstrap" in lavaan. The stored bootstrap
estimates will then be retrieved automatically to compute the
standardized moderation effect. This is the most efficient approach
if the bootstrap confidence intervals are also needed for
other parameters in the model. Bootstrapping needs to be
done only once.
Second, bootstrap estimates can be generated by manymome::do_boot().
The output is then supplied through the argument boot_out.
Bootstrapping also only needs to be done once. This approach
is appropriate when bootstrapping confidence intervals are
not needed for other model parameters, or another type
of confidence interval is needed when fitting the model.
Please refer to the help page of manymome::do_boot()
on how to use this function.
In both approaches, the standard deviations are also computed in each bootstrap samples. This ensures that the sampling variability of the standard deviations is also taken into account in computing the bootstrap confidence interval of the standardized moderation effect.
In older versions, stdmod_lavaan() does not allow for
partial standardization. Moreover,
it uses boot::boot() to do the bootstrapping. Even with
the same seed, the results from boot::boot() are not
identical to those of lavaan with se = "boot"
because they differ in the way the indices
of resampling are generated. Both approaches are correct,
They just use the generated random numbers differently.
To have results consistent with those from lavaan,
the current version of stdmod_lavaan() adopts a
resampling algorithm identical to that of lavaan.
Last, in older versions, stdmod_lavaan() does
bootstrapping every time it is called. This is
inefficient.
The bootstrapping results in the current version are not
identical to those in older versions due to the use
of different resampling algorithms, To reproduce
previous results, set use_old_version to TRUE
A list of class stdmod_lavaan with these elements:
stdmod: The standardized moderation effect.
ci: The nonparametric bootstrap confidence interval. NA if
confidence interval not requested.
boot_out: The raw output from boot::boot(). NA if
confidence interval not requested.
fit: The original fit object.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
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. doi:10.1037/hea0001188
#Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") out_noboot # Compute the standardized moderation effect and # its percentile confidence interval using # nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) out_boot#Load a test data of 500 cases dat <- test_mod1 library(lavaan) mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 " fit <- sem(mod, dat) # Compute the standardized moderation effect out_noboot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod") out_noboot # Compute the standardized moderation effect and # its percentile confidence interval using # nonparametric bootstrapping # Fit the model with bootstrap confidence intervals # At least 2000 bootstrap samples should be used # in real research. 50 is used here only for # illustration. fit <- sem(mod, dat, se = "boot", bootstrap = 50, iseed = 89574) out_boot <- stdmod_lavaan(fit = fit, x = "iv", y = "med", w = "mod", x_w = "iv:mod", boot_ci = TRUE) out_boot
Summarize the results of std_selected() or
std_selected_boot().
## S3 method for class 'std_selected' summary(object, ...)## S3 method for class 'std_selected' summary(object, ...)
object |
The output of |
... |
Additional arguments. Ignored by this function. |
An object of class summary.std_selected, with
bootstrap confidence intervals added if present in the object.
The object is a list. Its main element coefficients is similar to
the
coefficient table in the summary() printout of lm().
This object is for printing summary information of the results
from std_selected() or std_selected_boot().
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # With bootstrapping # nboot = 100 just for illustration. nboot >= 2000 should be used in read # research. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., nboot = 100) summary(lm_std_boot)
For testing. Generated from the following model.
mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 "
test_mod1test_mod1
A data frame with 300 rows and 6 variables:
Dependent variable, continuous
Independent variable, continuous
Mediator, continuous
Moderator, continuous
Covariate, continuous
Covariate, continuous
For testing. Generated from the following model.
mod <- " med ~ iv + cov1 dv ~ med + mod + med:mod + cov2 "
test_mod2test_mod2
A data frame with 300 rows and 6 variables:
Dependent variable, continuous
Independent variable, continuous
Mediator, continuous
Moderator, continuous
Covariate, continuous
Covariate, continuous
For testing the handling of warnings
in stdmod_lavaan(). Generated from the following
model. dv has about 88% missing. A warning on missing
data will be raised in some bootstrap samples.
mod <- " med ~ iv + mod + iv:mod + cov1 dv ~ med + cov2 "
test_mod3_misstest_mod3_miss
A data frame with 500 rows and 6 variables:
Dependent variable, continuous
Independent variable, continuous
Mediator, continuous
Moderator, continuous
Covariate, continuous
Covariate, continuous
A covariate (cat1) is categorical. For testing.
test_x_1_w_1_v_1_cat1_n_500test_x_1_w_1_v_1_cat1_n_500
A data frame with 500 rows and five variables:
Dependent variable, continuous
Independent variable, continuous
Moderator variable, continuous
Covariate, continuous
Covariate, categorical (string) with three values: "gp1", "gp2", and "gp3"
The independent variable and the moderator are associated. For demonstrating the use of tumble graph.
test_x_1_w_1_v_1_cat1_xw_cov_n_500test_x_1_w_1_v_1_cat1_xw_cov_n_500
A data frame with 500 rows and 5 variables:
Dependent variable, continuous
Independent variable, continuous
Moderator variable, continuous
Covariate, continuous
Covariate, categorical (string) with three values, "gp1", "gp2", and "gp3"
The independent variable and the categorical moderator are associated. For demonstrating the use of tumble graph.
test_x_1_w_1_v_1_cat1_xw_cov_wcat3_n_500test_x_1_w_1_v_1_cat1_xw_cov_wcat3_n_500
A data frame with 500 rows and 5 variables:
Dependent variable, continuous
Independent variable, continuous
Moderator variable, categorical (string) with three categories, "City Alpha", "City Gamma", and "City Beta"
Covariate, continuous
Covariate, categorical (string) with three values, "gp1", "gp2", and "gp3"
All variables are continuous. For testing.
test_x_1_w_1_v_2_n_500test_x_1_w_1_v_2_n_500
A data frame with 500 rows and five variables:
Dependent variable, continuous
Independent variable, continuous
Moderator variable, continuous
Covariate, continuous
Covariate, continuous
This should be used only to update the call to lm(),
not to the call to std_selected() or std_selected_boot().
## S3 method for class 'std_selected' update(object, formula., ..., evaluate = TRUE)## S3 method for class 'std_selected' update(object, formula., ..., evaluate = TRUE)
object |
The output of the class |
formula. |
Changes to the formula. |
... |
Optional arguments to be changed. |
evaluate |
Whether the call will be evaluated. |
Although supported, it is not recommended to update an analysis
processed by std_selected() or std_selected_boot(). It is
recommended to call lm() again and pass the output to
std_selected() or std_selected_boot().
If evaluate = TRUE, it returns the updated fitted object,
otherwise, the updated call.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # Update the model lm_std2 <- update(lm_std, . ~ . - v1) summary(lm_std2)# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) summary(lm_raw) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) summary(lm_std) # Update the model lm_std2 <- update(lm_std, . ~ . - v1) summary(lm_std2)
Compute the variance-covariance matrix
of estimates in the output of std_selected() or
std_selected_boot().
## S3 method for class 'std_selected' vcov(object, type, ...)## S3 method for class 'std_selected' vcov(object, type, ...)
object |
The output of |
type |
The type of variance-covariance matrix. If set to |
... |
Arguments to be passed to |
If bootstrapping was used to form the confidence intervals, users can request the variance-covariance matrix of the bootstrap estimates.
A matrix of the variances and covariances of the parameter estimates.
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448
# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) # VCOV of lm output vcov(lm_std) # Standardize all variables as in std_selected above, and compute the # nonparametric bootstrapping percentile confidence intervals. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., conf = .95, nboot = 100) # In real analysis, nboot should be at least 2000. # VCOV of bootstrap estimates, default when bootstrap was conducted vcov(lm_std_boot) # For OLS VCOV vcov(lm_std_boot, type = "lm")# Load a sample data set dat <- test_x_1_w_1_v_1_cat1_n_500 head(dat) # Do a moderated regression by lm lm_raw <- lm(dv ~ iv*mod + v1 + cat1, dat) # Standardize all variables except for categorical variables. # Interaction terms are formed after standardization. lm_std <- std_selected(lm_raw, to_scale = ~ ., to_center = ~ .) # VCOV of lm output vcov(lm_std) # Standardize all variables as in std_selected above, and compute the # nonparametric bootstrapping percentile confidence intervals. lm_std_boot <- std_selected_boot(lm_raw, to_scale = ~ ., to_center = ~ ., conf = .95, nboot = 100) # In real analysis, nboot should be at least 2000. # VCOV of bootstrap estimates, default when bootstrap was conducted vcov(lm_std_boot) # For OLS VCOV vcov(lm_std_boot, type = "lm")