Title: Bootstrapping Helpers for Structural Equation Modelling
Version: 0.1.0
Description: A collection of helper functions for forming bootstrapping confidence intervals and examining bootstrap estimates in structural equation modelling. Currently supports models fitted by the 'lavaan' package by Rosseel (2012) <doi:10.18637/jss.v048.i02>.
License: GPL (≥ 3)
Encoding: UTF-8
RoxygenNote: 7.3.2
Suggests: knitr, rmarkdown, testthat (≥ 3.0.0)
Config/testthat/edition: 3
Config/testthat/parallel: true
VignetteBuilder: knitr
Imports: boot, lavaan, psych, lavaan.printer
URL: https://Yangzhen1999.github.io/semboottools/
BugReports: https://github.com/Yangzhen1999/semboottools/issues
NeedsCompilation: no
Packaged: 2025-03-30 14:06:57 UTC; Administrator
Author: Wendie Yang ORCID iD [aut, cre], Shu Fai Cheung ORCID iD [aut]
Maintainer: Wendie Yang <1581075494q@gmail.com>
Repository: CRAN
Date/Publication: 2025-04-01 16:40:06 UTC

semboottools: Bootstrapping Helpers for Structural Equation Modelling

Description

A collection of helper functions for forming bootstrapping confidence intervals and examining bootstrap estimates in structural equation modelling. Currently supports models fitted by the 'lavaan' package by Rosseel (2012) doi: 10.18637/jss.v048.i02.

Author(s)

Maintainer: Wendie Yang 1581075494q@gmail.com (ORCID)

Authors:

See Also

Useful links:

Diagnostic Plots of Bootstrap Estimates in 'lavaan'

Description

Plots for examining the distribution of bootstrap estimates in a model fitted by lavaan.

Usage

hist_qq_boot(
  object,
  param,
  standardized = NULL,
  nclass = NULL,
  hist_color = "#5DADE233",
  hist_linewidth = 1.5,
  hist_border_color = "#1B4F72",
  density_line_type = "solid",
  density_line_color = "#8B0000CC",
  density_line_linewidth = 2,
  est_line_color = "#154360",
  est_line_type = "dashed",
  est_line_linewidth = 2,
  qq_dot_pch = 21,
  qq_dot_color = "#1B4F72",
  qq_dot_fill = "#5DADE233",
  qq_dot_size = 1.3,
  qq_line_color = "#8B0000CC",
  qq_line_linewidth = 2.1,
  qq_line_linetype = "solid"
)

scatter_boot(
  object,
  params,
  standardized = NULL,
  main = "Bootstrap Estimates",
  ...
)

Arguments

object

Either a lavaan-class object with bootstrap estimates stored, or the output of standardizedSolution_boot(). For standardized solution and user-defined parameters, if the object is a 'lavaan-class“ object, the estimates need to be stored by store_boot().

param

String. The name of the parameter to be plotted, which should be the name as appeared in a call to coef().

standardized

Logical. Whether the estimates from the standardized solution are to be plotted. Default is NULL. If object is a lavaan object, then this is a required parameter and users need to explicitly set it to TRUE or FALSE. If object is the output of standardizedSolution_boot(), then this argument is ignored ( forced to be TRUE internally).

nclass

The number of breaks. This argument will be passed to hist(). Default is NULL.

hist_color

String. The color of the bars in the histogram. It will be passed to hist() for the argument col. Default is light blue (scales::alpha("#5DADE2", 0.2)).

hist_linewidth

The width of the borders of the bars in the histogram. Default is 1.5.

hist_border_color

String. The color of the borders (outline) of the bars in the histogram. It will be passed to hist() for the argument border. Default is a dark blue color ("#1B4F72").

density_line_type

String. The type of the line of the density curve in the histogram. It will be passed to lines() for the argument lty. Default is "solid".

density_line_color

String. The color of the density curve in the histogram. It will be passed to lines() for the argument col. Default is "blue".

density_line_linewidth

The width of the density curve in the histogram. It will be passed to lines() for the argument lwd. Default is 2.

est_line_color

String. The color of the vertical line showing the point estimate in the histogram. It will be passed to abline() for the argument col.

est_line_type

String. The type of the vertical line in the histogram showing the point estimate of the parameter. It will be passed to abline() for the argument lty. Default is "dashed",

est_line_linewidth

The width of the vertical line showing the point estimate in the histogram. It will be passed to hist() for the argument lwd. Default is 2.

qq_dot_pch

Numeric. The shape of the points in the normal QQ-plot. It will be passed to qqnorm() for the argument pch. Default is 21.

qq_dot_color

String. The color of the points in the normal QQ-plot. It will be passed to qqnorm() for the argument col.

qq_dot_fill

String. The fill color of the points in the normal QQ-plot. Only applicable when qq_dot_pch is set to a symbol that allows fill color (e.g., pch = 21). It will be passed to qqnorm() for the argument bg. Default is a semi-transparent light blue (scales::alpha("#5DADE2", 0.2)).

qq_dot_size

The size of the points in the normal QQ-plot. It will be passed to qqnorm() for the argument cex. Default is 2.

qq_line_color

String. The color of the diagonal line to be drawn in the normal QQ-plot. It will be passed to qqline() for the argument col.

qq_line_linewidth

The width of the diagonal line to be drawn in the normal QQ-plot. It will be passed to qqline() for the argument lwd. Default is 2.1.

qq_line_linetype

The type of the diagonal line to be drawn in the normal QQ-plot. Default is "solid".

params

The vector of the names of the parameters to be plotted, which should be the names as appeared in a call to coef(). The function scatter_boot() requires two or more parameters selected by this argument.

main

The title of the scatterplot matrix. Default is "Bootstrap Estimates".

...

Arguments to be passed to psych::pairs.panels(). Please refer to the help page of psych::pairs.panels() for arguments to customize the plot.

Details

Rousselet, Pernet, and Wilcox (2021) argued that when using bootstrapping, it is necessary to examine the distribution of bootstrap estimates. This can be done when boot::boot() is used because it has a plot method for its output. This cannot be easily done in model fitted by lavaan::lavaan(), such as lavaan::sem() and lavaan::cfa().

The function hist_qq_boot() is used for plotting the distribution of bootstrap estimates for a model fitted by lavaan in a format similar to that of the output of boot::boot(), with a histogram on the left and a normal QQ-plot on the right.

For free parameters in a model (unstandardized), it can be called directly on the output of lavaan and retrieves the stored estimates.

For estimates of user-defined parameters, call store_boot() first to compute and store the bootstrap estimates first.

For estimates in standardized solution, for both free and user-defined parameters, call store_boot() first to compute and store the bootstrap estimates in the standardized solution.

It can also plot bootstrap estimates in the output of standardizedSolution_boot() or parameterEstimates_boot().

The function scatter_boot() is used to generate a scatterplot matrix of the bootstrap estimates of two or more parameters. The function psych::pairs.panels() from the package psych is used.

Like hist_qq_boot(), it can also be used on the output of standardizedSolution_boot() or parameterEstimates_boot().

Value

Return the original lavaan::lavaan object invisibly. Called for its side-effect (plotting the graphs).

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

References

Rousselet, G. A., Pernet, C. R., & Wilcox, R. R. (2021). The percentile bootstrap: A primer with step-by-step instructions in R. Advances in Methods and Practices in Psychological Science, 4(1), 1–10. doi:10.1177/2515245920911881

See Also

store_boot() and standardizedSolution_boot().

Examples


library(lavaan)

set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)

mod <-
"
m ~ a * x
y ~ b * m + x
ab := a * b
"
fit <- sem(mod,
           data = dat,
           se = "bootstrap",
           bootstrap = 50,
           iseed = 985714)

# Can plot bootstrap estimates for
# free parameters directly
# Note that 'standardized' must be always be set to
# either TRUE or FALSE. No default value.
hist_qq_boot(fit, "a", standardized = FALSE)

# For estimates of user-defined parameters,
# call store_boot() first.
fit <- store_boot(fit)
hist_qq_boot(fit, "ab", standardized = FALSE)

# For estimates in standardized solution,
# call store_boot() first.
fit <- store_boot(fit)
hist_qq_boot(fit, "a", standardized = TRUE)
hist_qq_boot(fit, "ab", standardized = TRUE)

# It can also plot the estimates stored
# in the output of standardizedSolution_boot().
std_boot <- standardizedSolution_boot(fit)
hist_qq_boot(std_boot, "ab")
hist_qq_boot(fit, "ab", standardized = TRUE)



# Scatterplot matrix of bootstrap estimates for
# two or more free parameters
scatter_boot(fit, c("a", "b", "ab"), standardized = FALSE)

# Can include user-defined parameters in
# scatterplot matrix, if their bootstrap
# estimates have been stored
scatter_boot(fit, c("ab", "a", "b"), standardized = FALSE)

# scatter_boot also supports the
# standardized solution
scatter_boot(fit, c("a", "b", "ab"), standardized = TRUE)

Bootstrap CIs for Parameter Estimates

Description

Functions for forming bootstrap confidence intervals for the parameter estimates.

Usage

parameterEstimates_boot(
  object,
  level = 0.95,
  boot_org_ratio = FALSE,
  boot_ci_type = c("perc", "bc", "bca.simple"),
  save_boot_est = TRUE,
  boot_pvalue = TRUE,
  boot_pvalue_min_size = 1000,
  standardized = FALSE,
  ...
)

Arguments

object

A 'lavaan'-class object, fitted with 'se = "boot"'.

level

The level of confidence of the confidence intervals. Default is .95.

boot_org_ratio

The ratio of (a) the distance of the bootstrap confidence limit from the point estimate to (b) the distance of the original confidence limit in object from the point estimate. Default is FALSE.

boot_ci_type

The type of the bootstrapping confidence intervals. Support percentile confidence intervals ("perc", the default) and bias-corrected confidence intervals ("bc" or "bca.simple").

save_boot_est

Whether the bootstrap estimates of the parameter estimates are saved. If saved, the bootstrap estimates of the free parameters will be stored in the attribute boot_est_ustd, while the bootstrap estimates of user-defined parameters, if any, will be stored in the attribute boot_def. Default is TRUE.

boot_pvalue

Whether asymmetric bootstrap p-values are computed. Default is TRUE.

boot_pvalue_min_size

Integer. The asymmetric bootstrap p-values will be computed only if the number of valid bootstrap estimates is at least this value. Otherwise, NA will be returned. If the number of valid bootstrap samples is less than this value, then boot_pvalue will be set to FALSE.

standardized

The type of standardized estimates. The same argument of lavaan::parameterEstimates(), and support all values supported by lavaan::parameterEstimates(). It is recommended to use standardizedSolution_boot() or lavaan::standardizedSolution() because this function only report the point estimates of the standardized solution, without standard errors or confidence intervals.

...

Other arguments to be passed to lavaan::parameterEstimates().

Details

parameterEstimates_boot() receives a lavaan::lavaan object and form bootstrap confidence intervals for the parameter estimates.

The function store_boot() should be called first to compute and store bootstrap estimates. This function will then retrieve them.

Bootstrap Confidence Intervals

It supports percentile and bias-corrected bootstrap confidence intervals.

Bootstrap Standard Errors

The standard errors are the standard deviation of the bootstrap estimates.

Bootstrap Asymmetric p-Values

If percentile bootstrap confidence interval is requested, asymmetric bootstrap p-values are also computed, using the method presented in Asparouhov and Muthén (2021).

Value

The output of lavaan::parameterEstimates(), with bootstrap confidence intervals appended to the right, with class set to sbt_ustd_boot. It has a print method (print.sbt_ustd_boot()) that can be used to print the parameter estimates in a format similar to that of the printout of the summary() of a lavaan::lavaan object.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

See Also

lavaan::parameterEstimates(), store_boot()

Examples


library(lavaan)
set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)
model <-
'
m ~ a*x
y ~ b*m
ab := a*b
'

# Should set bootstrap to at least 2000 in real studies
fit <- sem(model, data = dat, fixed.x = FALSE)
summary(fit)
fit <- store_boot(fit,
                  do_bootstrapping = TRUE,
                  R = 100,
                  iseed = 1234)
est <- parameterEstimates_boot(fit)
est

Print a 'sbt_std_boot' Object

Description

Print method for a 'sbt_std_boot' object, which is the output of standardizedSolution_boot().

Usage

## S3 method for class 'sbt_std_boot'
print(
  x,
  ...,
  nd = 3,
  output = c("lavaan.printer", "text", "table"),
  standardized_only = TRUE,
  boot_ci_only = FALSE,
  drop_cols = "Z"
)

Arguments

x

Object of the class sbt_std_boot, the output of standardizedSolution_boot().

...

Optional arguments to be passed to print() methods.

nd

The number of digits after the decimal place. Default is 3.

output

String. How the results are printed. If set to "table", the results are printed in a table format similar to that of lavaan::standardizedSolution(). If set to "text", the results will be printed in a text format similar to the printout of the output of summary() of a 'lavaan'-class object. If set to "lavaan.printer", the default, lavaan.printer will be used to print a more compact version of the "text" output.

standardized_only

Logical. If TRUE, the default, only the results for the standardized solution will be printed. If FALSE, then the standardized solution is printed alongside the unstandardized solution, as in the printout of the output of summary() of a 'lavaan'-class object.

boot_ci_only

Logical. Whether only bootstrap confidence intervals are printed. If FALSE, the default, the delta method confidence intervals by lavaan::standardizedSolution() are also printed.

drop_cols

The name(s) of the column(s) to drop if output format is "lavaan.printer". Default is "Z", to fit the print out to the usual screen width of 80.

Details

The default format of the printout, "lavaan.printer", is a compact version of the lavaan-style printout, generated by lavaan.printer. Alternatively, users can request a format similar to that of the printout of the summary of a lavaan output by setting output to "text". This format can be used if "lavaan.printer" failed.

Users can also print the content just as a data frame by setting output to "table". Not easy to read much more compact.

For the "text" or "lavaan.printer" format, users can also select whether only the standardized solution is printed (the default) or whether the standardized solution is appended to the right of the printout.

Value

x is returned invisibly. Called for its side effect.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also

standardizedSolution_boot()

Examples

library(lavaan)
set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)
model <-
'
m ~ a*x
y ~ b*m
ab := a*b
'

# Should set bootstrap to at least 2000 in real studies
fit <- sem(model, data = dat, fixed.x = FALSE,
           se = "boot",
           bootstrap = 50)
std_out <- standardizedSolution_boot(fit)
std_out
print(std_out, standardized_only = FALSE)

Print a 'sbt_ustd_boot' Object

Description

Print method for a 'sbt_ustd_boot' object, which is the output of parameterEstimates_boot().

Usage

## S3 method for class 'sbt_ustd_boot'
print(
  x,
  ...,
  nd = 3,
  output = c("lavaan.printer", "text", "table"),
  drop_cols = "Z"
)

Arguments

x

Object of the class sbt_ustd_boot, the output of parameterEstimates_boot().

...

Optional arguments to be passed to print() methods.

nd

The number of digits after the decimal place. Default is 3.

output

String. How the results are printed. If set to "table", the results are printed in a table format similar to that of lavaan::parameterEstimates(). If set to "text", the results will be printed in a text format similar to the printout of the output of summary() of a 'lavaan'-class object. If set to "lavaan.printer", the default, lavaan.printer will be used to print a more compact version of the "text" output.

drop_cols

The name(s) of the column(s) to drop if output format is "lavaan.printer". Default is "Z", to fit the print out to the usual screen width of 80.

Details

The default format of the printout, "lavaan.printer", is a compact version of the lavaan-style printout, generated by lavaan.printer. Alternatively, users can request a format similar to that of the printout of the summary of a lavaan output by setting output to "text". This format can be used if "lavaan.printer" failed.

Users can also print the content just as a data frame by setting output to "table". Not easy to read much more compact.

Value

x is returned invisibly. Called for its side effect.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448

See Also

parameterEstimates_boot()

Examples

library(lavaan)
set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)
model <-
'
m ~ a*x
y ~ b*m
ab := a*b
'

# Should set bootstrap to at least 2000 in real studies
fit <- sem(model, data = dat, fixed.x = FALSE)

fit <- store_boot(fit,
                  do_bootstrapping = TRUE,
                  R = 100,
                  iseed = 1234)

est <- parameterEstimates_boot(fit)
est

Bootstrap CIs for Standardized Solution

Description

Functions for forming bootstrap confidence intervals for the standardized solution.

Usage

standardizedSolution_boot(
  object,
  level = 0.95,
  type = "std.all",
  boot_delta_ratio = FALSE,
  boot_ci_type = c("perc", "bc", "bca.simple"),
  save_boot_est_std = TRUE,
  boot_pvalue = TRUE,
  boot_pvalue_min_size = 1000,
  ...
)

Arguments

object

A 'lavaan'-class object, fitted with 'se = "boot"'.

level

The level of confidence of the confidence intervals. Default is .95.

type

The type of standard estimates. The same argument of lavaan::standardizedSolution(), and support all values supported by lavaan::standardizedSolution(). Default is "std.all".

boot_delta_ratio

The ratio of (a) the distance of the bootstrap confidence limit from the point estimate to (b) the distance of the delta-method limit from the point estimate. Default is FALSE.

boot_ci_type

The type of the bootstrapping confidence intervals. Support percentile confidence intervals ("perc", the default) and bias-corrected confidence intervals ("bc" or "bca.simple").

save_boot_est_std

Whether the bootstrap estimates of the standardized solution are saved. If saved, they will be stored in the attribute boot_est_std. Default is TRUE.

boot_pvalue

Whether asymmetric bootstrap p-values are computed. Default is TRUE.

boot_pvalue_min_size

Integer. The asymmetric bootstrap p-values will be computed only if the number of valid bootstrap estimates is at least this value. Otherwise, NA will be returned. If the number of valid bootstrap samples is less than this value, then boot_pvalue will be set to FALSE.

...

Other arguments to be passed to lavaan::standardizedSolution().

Details

standardizedSolution_boot() receives a lavaan::lavaan object fitted with bootstrapping standard errors requested and forms the confidence intervals for the standardized solution.

It works by calling lavaan::standardizedSolution() with the bootstrap estimates of free parameters in each bootstrap sample to compute the standardized estimates in each sample.

Alternative, call store_boot() to computes and store bootstrap estimates of the standardized solution. This function will then retrieve them, even if se was not set to "boot" or "bootstrap" when fitting the model.

Bootstrap Confidence Intervals

It supports percentile and bias-corrected bootstrap confidence intervals.

Bootstrap Standard Errors

The standard errors are the standard deviation of the bootstrap estimates, which can be different from the delta-method standard errors.

Bootstrap Asymmetric p-Values

If percentile bootstrap confidence interval is requested, asymmetric bootstrap p-values are also computed, using the method presented in Asparouhov and Muthén (2021).

Value

The output of lavaan::standardizedSolution(), with bootstrap confidence intervals appended to the right, with class set to sbt_std_boot. It has a print method (print.sbt_std_boot()) that can be used to print the standardized solution in a format similar to that of the printout of the summary() of a lavaan::lavaan object.

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448. Originally proposed in an issue at GitHub https://github.com/simsem/semTools/issues/101#issue-1021974657, inspired by a discussion at the Google group for lavaan https://groups.google.com/g/lavaan/c/qQBXSz5cd0o/m/R8YT5HxNAgAJ. boot::boot.ci() is used to form the percentile confidence intervals in this version.

References

Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf

See Also

lavaan::standardizedSolution(), store_boot()

Examples


library(lavaan)
set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)
model <-
'
m ~ a*x
y ~ b*m
ab := a*b
'

# Should set bootstrap to at least 2000 in real studies
fit <- sem(model, data = dat, fixed.x = FALSE,
           se = "boot",
           bootstrap = 100)
summary(fit)

std <- standardizedSolution_boot(fit)
std

# Print in a friendly format with only standardized solution
print(std, output = "text")

# Print in a friendly format with both unstandardized
# and standardized solution
print(std, output = "text", standardized_only = FALSE)

# hist_qq_boot() can be used to examine the bootstrap estimates
# of a parameter
hist_qq_boot(std, param = "ab")

# scatter_boot() can be used to examine the bootstrap estimates
# of two or more parameters
scatter_boot(std, params = c("ab", "a", "b"))

Compute and Store Bootstrap Estimates

Description

This function computes bootstrap estimates of a fitted structural equation model and stores the estimates for further processing.

Usage

store_boot(
  object,
  type = "std.all",
  do_bootstrapping = TRUE,
  R = 1000,
  boot_type = "ordinary",
  parallel = c("no", "multicore", "snow"),
  ncpus = parallel::detectCores(logical = FALSE) - 1,
  iseed = NULL,
  keep.idx = FALSE,
  bootstrapLavaan_args = list()
)

Arguments

object

A 'lavaan'-class object, fitted with 'se = "boot"'.

type

The type of standard estimates. The same argument of lavaan::standardizedSolution(), and support all values supported by lavaan::standardizedSolution(). Default is "std.all".

do_bootstrapping

If TRUE and bootstrapping was not requested when fitting the model, bootstrapping will be done using lavaan::bootstrapLavaan(). Default is TRUE.

R

If lavaan::bootstrapLavaan() is called (see do_bootstrapping), this is the number of bootstrap samples, to be used by lavaan::bootstrapLavaan().

boot_type

If lavaan::bootstrapLavaan() is called (see do_bootstrapping), this is type of bootstrapping, to be passed to the argument type of lavaan::bootstrapLavaan(). Default is "ordinary". See the help page of lavaan::bootstrapLavaan() for details.

parallel

If lavaan::bootstrapLavaan() is called (see do_bootstrapping), whether parallel processing will be used. to be passed to the argument of the same name in lavaan::bootstrapLavaan(). Default is "no". Can be "snow" or "multicore". See the help page of lavaan::bootstrapLavaan() for details.

ncpus

If lavaan::bootstrapLavaan() is called (see do_bootstrapping), and parallel processing is to be used, this is the number of CPU cores to use, to be passed to the argument of the same name in lavaan::bootstrapLavaan(). Default is parallel::detectCores(logical = FALSE) - 1, the number of physical cores minus 1, different from the default of lavaan::bootstrapLavaan() but identical to the default of lavaan::sem() and lavaan::cfa().

iseed

If lavaan::bootstrapLavaan() is called (see do_bootstrapping), this should be an integer used to generate reproducible bootstrap results, to be passed to the argument of the same name in lavaan::bootstrapLavaan(). Default is NULL but it should nearly always be set to an arbitrary integer. See the help page of lavaan::bootstrapLavaan() for details.

keep.idx

Whether the indices of cases selected in each bootstrap sample is to be stored. To be passed to the argument of the same name in lavaan::bootstrapLavaan(). Default is FALSE.

bootstrapLavaan_args

A named list of additional arguments to be passed to lavaan::bootstrapLavaan(). Note that the other arguments in store_boot() takes precedence, overriding arguments of the same names in this list, if any.

Details

The function store_boot() receives a lavaan::lavaan object, optionally fitted with bootstrapping standard errors requested, and compute and store the bootstrap estimates of user-defined parameters and estimates in the standardized solution.

If bootstrapping was not requested when fitting the model (i.e., se not set to "boot" or "bootstrap"), then bootstrapping will be conducted using lavaan::bootstrapLavaan() to compute bootstrap estimates of free parameters. Otherwise, the stored bootstrap estimates will be used in subsequent steps.

For standardized solution bootstrap estimates, it works by calling lavaan::standardizedSolution() with the bootstrap estimates of free parameters in each bootstrap sample to compute the standardized estimates in each sample.

For user-defined parameters, it works by calling the function used to compute user-defined parameters with the bootstrap estimates of free parameters in each bootstrap samples to compute the user-defined parameters.

The bootstrap estimates are then stored in the external slot of the fit object for further processing.

Value

The original lavaan object is returned with the following objects stored in the external slot:

Author(s)

Shu Fai Cheung https://orcid.org/0000-0002-9871-9448. Based on semhelpinghands::standardizedSolution_boot_ci(), which was originally proposed in an issue at GitHub https://github.com/simsem/semTools/issues/101#issue-1021974657, inspired by a discussion at the Google group for lavaan https://groups.google.com/g/lavaan/c/qQBXSz5cd0o/m/R8YT5HxNAgAJ. Unlike semhelpinghands::standardizedSolution_boot_ci(), this function only computes and stores the bootstrap estimates.

Examples


library(lavaan)
set.seed(5478374)
n <- 50
x <- runif(n) - .5
m <- .40 * x + rnorm(n, 0, sqrt(1 - .40))
y <- .30 * m + rnorm(n, 0, sqrt(1 - .30))
dat <- data.frame(x = x, y = y, m = m)
model <-
'
m ~ a*x
y ~ b*m
ab := a*b
'

# Should set bootstrap to at least 2000 in real studies
fit <- sem(model, data = dat, fixed.x = FALSE,
           se = "boot",
           bootstrap = 100)
summary(fit)

fit <- store_boot(fit)