semhelpinghands (version 0.1.14)

standardizedSolution_boot_ci: Bootstrap CIs for Standardized Solution

Description

Functions for forming bootstrap confidence intervals for the standardized solution.

Usage

standardizedSolution_boot_ci(
  object,
  level = 0.95,
  type = "std.all",
  save_boot_est_std = TRUE,
  force_run = FALSE,
  boot_delta_ratio = FALSE,
  boot_ci_type = c("perc", "bc", "bca.simple"),
  ...
)
store_boot_est_std(object, type = "std.all", force_run = FALSE, ...)
get_boot_est_std(object)

Value

The output of lavaan::standardizedSolution(), with bootstrap confidence intervals appended to the right, with class set to std_solution_boot (since version 0.1.8.4). It has a print method (print.std_solution_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.

store_boot_est_std() returns the fit object set to object, with the bootstrap values of standardized solution in the bootstrap samples, as a matrix, stored in the slot external under the name shh_boot_est_std.

get_boot_est_std() returns a matrix of the stored bootstrap estimates of standardized solution. If none is stored, NULL is returned.

store_boot_est_std() is usually used with diagnostic functions such as plot_boot().

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".

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.

force_run

If TRUE, will skip checks and run models without checking the estimates. For internal use. Default is FALSE.

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").

...

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

Author

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.

Details

NOTE: A new package, semboottools (Yang & Cheung, 2026), can do what standardizedSolution_boot_ci() does, with more features, as well as some diagnostic functions. The function standardizedSolution_boot_ci(), as well as its helpers, such as store_boot_def() and plot_boot(), will stay in this package, but will not be further developed. Users are recommended to use semboottools::standardizedSolution_boot() and other functions in semboottools instead of this function.

standardizedSolution_boot_ci() 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.

A more reliable way is to use function like lavaan::bootstrapLavaan(). Nevertheless, this simple function is good enough for some simple scenarios, and does not require repeating the bootstrapping step.

store_boot_est_std() computes the standardized solution for each bootstrap sample, stores them the lavaan::lavaan object, and returns it. These estimates can be used by other functions, such as plot_boot(), to examine the estimates, without the need to repeat the computation.

get_boot_est_std() retrieves the bootstrap estimates of the standardized solution stored by store_boot_est_std().

References

Yang, W., & Cheung, S. F. (2026). Forming bootstrap confidence intervals and examining bootstrap distributions of standardized coefficients in structural equation modelling: A simplified workflow using the R package semboottools. Behavior Research Methods, 58(2), 38. tools:::Rd_expr_doi("10.3758/s13428-025-02911-z")

See Also

lavaan::standardizedSolution(), plot_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_ci(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)

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


# store_boot_est_std() is usually used with plot_boot()
# First, store the bootstrap estimates of the
# standardized solution
fit_with_boot_std <- store_boot_est_std(fit)
# Second, plot the distribution of the bootstrap estimates of
# standardized 'ab'
plot_boot(fit_with_boot_std, "ab", standardized = TRUE)