Bootstrapping for the bias-corrected percentile method factor loading confidence intervals

[Jing Yu]

Hi Lavaan group,

I am trying to use the Lavaan to do the bootstrapping for the bias-corrected of the factor loading confidence intervals, and I have this code for the estimated standardized loadings below, but I can not figure out how to write the code for the bias-corrected factor loading confidence intervals. Does someone give me some suggestions? I appreciate your help. Thanks

out <- bootstrapLavaan(fit, R = 100, FUN = function(x) { 

standardizedSolution(x)$est }, verbose = TRUE) 

[Terrence Jorgensen]

The bootstrapLavaan() function only returns the bootstrap distribution of the statistic(s), so I don't think you can get the bias-corrected CI this way.  You can get it using the boot function (from the boot package that comes with R by default).  For example:

## Define a function that fits a model to your data and returns the

## Std. estimates. The boot function requires the first argument to

## be the data.frame, and the second argument to be an index to

## select rows (i.e., to do bootstrap sampling)

getSTDs <- function(data, rowIndices) {

  library(lavaan)

  mySyntax <- ' visual  =~ x1 + x2 + x3

                textual =~ x4 + x5 + x6

                speed   =~ x7 + x8 + x9 '

  fit <- cfa(mySyntax, data = data[rowIndices, ] )

  standardizedSolution(fit)$est

}

## run bootstrap

out.boot <- boot(data = HolzingerSwineford1939, statistic = getSTDs, R = 2000)

## get bias-corrected CI, for one parameter (index) at a time

boot.ci(out.boot, type = "bca", index = 1)

## note the index corresponds to the actual order in which

## the parameters appear in the output:

example(cfa)

standardizedSolution(fit)

## You can request a set of BCa CIs

lapply(1:3, function(x) boot.ci(out.boot, type = "bca", index = x))

You need a lot more than 100 bootstrap samples to get a stable bias-corrected CI -- try 2000-5000.  You can use boot's built-in parallel options to make it go faster:

out.boot <- boot(data = HolzingerSwineford1939, statistic = getSTDs, R = 2000,

                 parallel = "snow", ncpus = parallel::detectCores() - 1)

If you just want bias-corrected CIs for raw parameters, you can get those using the arguments in the lavaan() and parameterEstimates() functions

fit <- lavaan(mySyntax, myData, ..., bootstrap = 1000L)

parameterEstimates(fit, boot.ci.type = "bca.simple")

Terry

[Jing Yu]

Hi Terry,

Thank you for your careful description of the syntax. I would like to try it as you suggested.

Many thanks,

Jing

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