Bootstrapping a Lavaan Model

Bootstrap the LRT, or any other statistic (or vector of statistics) you can extract from a fitted lavaan object.

Usage

lavBootstrap(object, r = 1000L, type = "ordinary", verbose = FALSE, 
                fun = "coef", keep_idx = FALSE,
                parallel = c("no", "multicore", "snow"),
                ncpus =  max(1L, parallel::detectCores() - 2L, na.rm = TRUE),
                cl = NULL, iseed = NULL, h0_rmsea = NULL, ...)
bootstrapLavaan(object, r = 1000L, type = "ordinary", verbose = FALSE, 
                fun = "coef", keep_idx = FALSE,
                parallel = c("no", "multicore", "snow"),
                ncpus =  max(1L, parallel::detectCores() - 2L, na.rm = TRUE),
                cl = NULL, iseed = NULL, h0_rmsea = NULL, ...)

Arguments

object

An object of class lavaan.

r

Integer. The number of bootstrap draws.

type

If "ordinary" or "nonparametric", the usual (naive) bootstrap method is used. If "bollen.stine", the data is first transformed such that the null hypothesis holds exactly in the resampling space. If "yuan", the data is first transformed by combining data and theory (model), such that the resampling space is closer to the population space. Note that both "bollen.stine" and "yuan" require the data to be continuous. They will not work with ordinal data. If "parametric", the parametric bootstrap approach is used; currently, this is only valid for continuous data following a multivariate normal distribution. See references for more details. If the fitted model uses clustered or multilevel data (that is, a cluster= argument was used, either for a two-level model or to obtain cluster-robust standard errors), only the "ordinary" (nonparametric) bootstrap is available, and whole clusters (rather than individual observations) are resampled; see Details.

fun

A function which when applied to the lavaan object returns a vector containing the statistic(s) of interest. The default is fun="coef", returning the estimated values of the free parameters in the model.

...

Other named arguments for fun which are passed unchanged each time it is called.

verbose

If TRUE, show information for each bootstrap draw.

keep_idx

If TRUE, store the indices of each bootstrap run (i.e., the observations that were used for this bootstrap run) as an attribute.

parallel

The type of parallel operation to be used (if any). If missing, the default is "no".

ncpus

Integer: number of processes to be used in parallel operation. By default this is the number of cores (as detected by parallel::detectCores()) minus one.

cl

An optional parallel or snow cluster for use if parallel = "snow". If not supplied, a cluster on the local machine is created for the duration of the lavBootstrap call.

iseed

An integer to set the seed. Or NULL if no reproducible results are needed. This works for both serial (non-parallel) and parallel settings. Internally, RNGkind() is set to "L'Ecuyer-CMRG" if parallel = "multicore". If parallel = "snow" (under windows), parallel::clusterSetRNGStream() is called which automatically switches to "L'Ecuyer-CMRG". When iseed is not NULL, .Random.seed (if it exists) in the global environment is left untouched.

h0_rmsea

Only used if type="yuan". Allows one to do the Yuan bootstrap under the hypothesis that the population RMSEA equals a specified value.

Author

Yves Rosseel and Leonard Vanbrabant. Ed Merkle contributed Yuan's bootstrap. Improvements to Yuan's bootstrap were contributed by Hao Wu and Chuchu Cheng. The handling of iseed was contributed by Shu Fai Cheung.

Value

For lavBootstrap(), the bootstrap distribution of the value(s) returned by fun, when the object can be simplified to a vector.

Details

The fun function can return either a scalar or a numeric vector. This function can be an existing function (for example coef) or can be a custom defined function. For example:

myFUN <- function(x) {
    # require(lavaan)
    modelImpliedCov <- fitted(x)$cov
    vech(modelImpliedCov)
}

If parallel="snow", it is imperative that the require(lavaan) is included in the custom function.

When the fitted model was estimated with clustered or multilevel data (i.e., a cluster= argument was used), the bootstrap automatically switches to a cluster bootstrap: instead of resampling individual observations, whole (level-2) clusters are resampled with replacement, keeping all level-1 observations within a selected cluster together. The number of clusters is held fixed (equal to the number of clusters in the original data), while the total number of observations may vary from one bootstrap sample to the next. A cluster that is drawn more than once is treated as several distinct clusters. This resampling scheme preserves the within-cluster dependence and is the appropriate bootstrap both for two-level models and for single-level models with cluster-robust standard errors. It is currently only available for a single cluster (level-2) variable, and the "bca" confidence interval type (in parameterEstimates) is not supported in this case.

When the fitted model contains rotated exploratory factors (EFA or ESEM; that is, the model syntax uses the efa() modifier together with a rotation= method other than "none"), bootstrap standard errors and confidence intervals (requested via se = "bootstrap" when fitting the model) are computed for the rotated solution. Each bootstrap sample is refit and rotated, and its factors are then aligned (reordered and reflected) to the original (full-sample) rotated solution before their variability is used. This alignment resolves the rotational indeterminacy (the sign and order of the exploratory factors), which would otherwise inflate the standard errors. Note that the raw bootstrap coefficients returned by lavBootstrap(object, fun = "coef") are not aligned to a reference solution in this way.

References

Bollen, K. and Stine, r. (1992) Bootstrapping Goodness of Fit Measures in Structural Equation Models. Sociological Methods and Research, 21, 205–229.

Yuan, K.-H., Hayashi, K., & Yanagihara, H. (2007). A class of population covariance matrices in the bootstrap approach to covariance structure analysis. Multivariate Behavioral Research, 42, 261–281.

Field, C. A., & Welsh, A. H. (2007). Bootstrapping clustered data. Journal of the Royal Statistical Society: Series B, 69, 369–390.

Examples

# fit the Holzinger and Swineford (1939) example
HS.model <- ' visual  =~ x1 + x2 + x3
              textual =~ x4 + x5 + x6
              speed   =~ x7 + x8 + x9 '

fit <- cfa(HS.model, data=HolzingerSwineford1939, se="none")

# get the test statistic for the original sample
T.orig <- fitMeasures(fit, "chisq")

# bootstrap to get bootstrap test statistics
# we only generate 10 bootstrap samples in this example; in practice
# you may wish to use a much higher number
T.boot <- lavBootstrap(fit, r=10, type="bollen.stine",
                          fun=fitMeasures, fit.measures="chisq")

# compute a bootstrap based p-value
pvalue.boot <- length(which(T.boot > T.orig))/length(T.boot)