parameterEstimates

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parameterEstimates_boot

This vignette is a quick guide to use parameterEstimates_boot() in the package semboottools, described in Yang & Cheung (2026), to form bootstrap confidence intervals for the unstandardized estimates in a model fitted by lavaan.

Function Syntax

parameterEstimates_boot(object,
                        level = .95,
                        standardized = FALSE,
                        boot_org_ratio = FALSE,
                        boot_ci_type = c("perc", "bc", "bca.simple"),
                        save_boot_est = TRUE,
                        boot_pvalue = TRUE,
                        boot_pvalue_min_size = 1000,
                        ...)

Arguments

Argument	Description
`object`	A model fitted by `lavaan`.
`level`	Confidence level for the confidence intervals. For example, `.95` gives 95% confidence intervals.
`standardized`	Whether to return standardized estimates. Same as in `lavaan::parameterEstimates()`. You can use `"std.all"`, `"std.lv"`, etc. For detailed standardized results with CIs, use `standardizedSolution_boot()` instead.
`boot_org_ratio`	Whether to calculate how wide the bootstrap confidence interval is compared to the original confidence interval (from delta method). Useful to compare the two methods.
`boot_ci_type`	Method for forming bootstrap confidence intervals. `"perc"` gives percentile intervals; `"bc"` and `"bca.simple"` give bias-corrected intervals.
`save_boot_est`	Whether to save the bootstrap estimates in the result. Saved in attributes `boot_est_ustd` (free parameters) and `boot_def` (user-defined parameters) if `TRUE`.
`boot_pvalue`	Whether to compute asymmetric p-values based on bootstrap results. Only available when percentile confidence intervals are used.
`boot_pvalue_min_size`	Minimum number of valid bootstrap samples needed to compute asymmetric p-values. If fewer samples are available, p-values will not be computed and will be shown as `NA`.
`...`	Additional arguments passed to `lavaan::parameterEstimates()`.

Example

Data and Model

# Set seed for reproducibility
set.seed(1234)

# Generate data
n <- 1000
x <- runif(n) - 0.5
m <- 0.20 * x + rnorm(n)
y <- 0.17 * m + rnorm(n)
dat <- data.frame(x, y, m)

# Specify mediation model in lavaan syntax
mod <- '
  m ~ a * x
  y ~ b * m + cp * x
  ab := a * b
  total := a * b + cp
'

Basic usage: default settings

The function parameterEstimates_boot() can be used to add bootstrap estimates to an output of lavaan. This method is useful when both the default standard errors and p-values, such as those by maximum likelihood (ML), and the bootstrap standard errors and p-values are desired.

# Ensure bootstrap estimates are stored
# `R`, the number of bootstrap samples, should be ≥2000 in real studies.
# `parallel` should be used unless fitting the model is fast.
# Set `ncpus` to a larger value or omit it in real studies.
# `iseed` is set to make the results reproducible.
fit <- sem(mod,
           data = dat,
           fixed.x = FALSE)
fit <- store_boot(fit,
                  R = 500,
                  parallel = "snow",
                  ncpus = 2,
                  iseed = 1248)
est_boot <- parameterEstimates_boot(fit)
#> Warning in parameterEstimates_boot(fit): The number of bootstrap samples (500)
#> is less than 'boot_pvalue_min_size' (1000). Bootstrap p-values are not
#> computed.
print(est_boot)
#> 
#> Bootstrapping:
#>                                     
#>  Valid Bootstrap Samples: 500       
#>  Level of Confidence:     95.0%     
#>  CI Type:                 Percentile
#> 
#> Parameter Estimates Settings:
#>                                              
#>  Standard errors:                  Standard  
#>  Information:                      Expected  
#>  Information saturated (h1) model: Structured
#> 
#> Regressions:
#>                Estimate    SE     p  CI.Lo CI.Up   bSE bCI.Lo bCI.Up
#>  m ~                                                                
#>   x (a)           0.089 0.103 0.386 -0.113 0.291 0.100 -0.136  0.264
#>  y ~                                                                
#>   m (b)           0.192 0.034 0.000  0.125 0.260 0.036  0.123  0.264
#>   x (cp)         -0.018 0.112 0.871 -0.238 0.202 0.112 -0.228  0.205
#> 
#> Variances:
#>                Estimate    SE     p  CI.Lo CI.Up   bSE bCI.Lo bCI.Up
#>   .m              0.898 0.040 0.000  0.819 0.977 0.038  0.829  0.970
#>   .y              1.065 0.048 0.000  0.972 1.159 0.046  0.972  1.147
#>    x              0.085 0.004 0.000  0.077 0.092 0.002  0.080  0.090
#> 
#> Defined Parameters:
#>                Estimate    SE     p  CI.Lo CI.Up   bSE bCI.Lo bCI.Up
#>  ab (ab)          0.017 0.020 0.392 -0.022 0.056 0.019 -0.028  0.053
#>  total (total)   -0.001 0.114 0.993 -0.224 0.222 0.113 -0.211  0.213
#> 
#> Footnote:
#> - SE: Original standard errors.
#> - p: Original p-values.
#> - CI.Lo, CI.Up: Original confidence intervals.
#> - bSE: Bootstrap standard errors.
#> - bCI.Lo, bCI.Up: Bootstrap confidence intervals.

parameterEstimates_boot(): Different Options

Additional options to customize the output of parameterEstimates_boot().


# Change confidence level to 99%
est_boot <- parameterEstimates_boot(fit,
                                    level = 0.99)
# Use bias-corrected (BC) bootstrap confidence intervals
est_boot <- parameterEstimates_boot(fit,
                                    boot_ci_type = "bc")
# Turn off asymmetric bootstrap p-values
est_boot <- parameterEstimates_boot(fit,
                                    boot_pvalue = FALSE)
# Do not save bootstrap estimates (for memory saving)
est_boot <- parameterEstimates_boot(fit,
                                    save_boot_est = FALSE)
# Compute and display bootstrap-to-original CI ratio
est_boot <- parameterEstimates_boot(fit,
                                    boot_org_ratio = TRUE)
# Combine options: BC CI, 99% level, no p-values
est_boot <- parameterEstimates_boot(fit,
                                    level = 0.99,
                                    boot_ci_type = "bc",
                                    boot_pvalue = FALSE)

print(): Options

Additional options to customize the printout of the output of parameterEstimates_boot().

# Print with more decimal places (e.g., 5 digits)
print(est_boot,
      nd = 5)
# Print in lavaan-style text format (similar to summary())
print(est_boot,
      output = "text")
# Print as a clean data frame table
print(est_boot,
      output = "table")
# Drop specific columns (e.g., "Z") in lavaan.printer format
print(est_boot,
      drop_cols = "Z")
# Combine options: 5 decimal digits, text format
print(est_boot,
      nd = 5,
      output = "text")

Reference(s)

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. https://doi.org/10.3758/s13428-025-02911-z

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