standardizedSolution_boot: 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,
  ...
)

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.

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().

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

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).

References

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

Examples

Run this code


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"))

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