Bootstrap CIs for Parameter Estimates
Source:R/parameterEstimates_boot.R
parameterEstimates_boot.RdFunctions 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
objectfrom the point estimate. Default isFALSE.- 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 attributeboot_def. Default isTRUE.- 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,
NAwill be returned. If the number of valid bootstrap samples is less than this value, thenboot_pvaluewill be set toFALSE.- standardized
The type of standardized estimates. The same argument of
lavaan::parameterEstimates(), and support all values supported bylavaan::parameterEstimates(). It is recommended to usestandardizedSolution_boot()orlavaan::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().
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.
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.
References
Asparouhov, A., & Muthén, B. (2021). Bootstrap p-value computation. Retrieved from https://www.statmodel.com/download/FAQ-Bootstrap%20-%20Pvalue.pdf
Author
Shu Fai Cheung https://orcid.org/0000-0002-9871-9448.
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)
#> lavaan 0.6-19 ended normally after 1 iteration
#>
#> Estimator ML
#> Optimization method NLMINB
#> Number of model parameters 5
#>
#> Number of observations 50
#>
#> Model Test User Model:
#>
#> Test statistic 0.020
#> Degrees of freedom 1
#> P-value (Chi-square) 0.887
#>
#> Parameter Estimates:
#>
#> Standard errors Standard
#> Information Expected
#> Information saturated (h1) model Structured
#>
#> Regressions:
#> Estimate Std.Err z-value P(>|z|)
#> m ~
#> x (a) 0.569 0.343 1.660 0.097
#> y ~
#> m (b) 0.219 0.153 1.430 0.153
#>
#> Variances:
#> Estimate Std.Err z-value P(>|z|)
#> .m 0.460 0.092 5.000 0.000
#> .y 0.570 0.114 5.000 0.000
#> x 0.078 0.016 5.000 0.000
#>
#> Defined Parameters:
#> Estimate Std.Err z-value P(>|z|)
#> ab 0.125 0.115 1.083 0.279
#>
fit <- store_boot(fit,
do_bootstrapping = TRUE,
R = 100,
iseed = 1234)
est <- parameterEstimates_boot(fit)
#> Warning: The number of bootstrap samples (100) is less than 'boot_pvalue_min_size' (1000). Bootstrap p-values are not computed.
est
#>
#> Bootstrapping:
#>
#> Valid Bootstrap Samples: 100
#> 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) 0.569 0.343 0.097 -0.103 1.240 0.326 -0.054 1.276
#> y ~
#> m (b) 0.219 0.153 0.153 -0.081 0.519 0.151 -0.060 0.572
#>
#> Variances:
#> Estimate SE p CI.Lo CI.Up bSE bCI.Lo bCI.Up
#> .m 0.460 0.092 0.000 0.280 0.641 0.093 0.248 0.673
#> .y 0.570 0.114 0.000 0.347 0.794 0.104 0.386 0.806
#> x 0.078 0.016 0.000 0.048 0.109 0.012 0.052 0.106
#>
#> Defined Parameters:
#> Estimate SE p CI.Lo CI.Up bSE bCI.Lo bCI.Up
#> ab (ab) 0.125 0.115 0.279 -0.101 0.350 0.135 -0.027 0.446
#>
#> 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.