Bootstrapping a Lavaan Model — bootstrapLavaan • lavaan

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

bootstrapLavaan(object, R = 1000L, type = "ordinary", verbose = FALSE, 
                FUN = "coef", keep.idx = FALSE,
                parallel = c("no", "multicore", "snow"),
                ncpus =  max(1L, parallel::detectCores() - 2L), 
                cl = NULL, iseed = NULL, h0.rmsea = NULL, ...)

bootstrapLRT(h0 = NULL, h1 = NULL, R = 1000L, type="bollen.stine", 
             verbose = FALSE, return.LRT = FALSE, double.bootstrap = "no", 
             double.bootstrap.R = 500L, double.bootstrap.alpha = 0.05, 
             parallel = c("no", "multicore", "snow"),
             ncpus =  max(1L, parallel::detectCores() - 2L), 
             cl = NULL, iseed = NULL)

Arguments

object: An object of class lavaan.
h0: An object of class lavaan. The restricted model.
h1: An object of class lavaan. The unrestricted model.
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.
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.
return.LRT: If TRUE, return the LRT values as an attribute to the pvalue.
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 bootstrapLavaan or bootstrapLRT 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.
double.bootstrap: If "standard" the genuine double bootstrap is used to compute an additional set of plug-in p-values for each boostrap sample. If "FDB", the fast double bootstrap is used to compute second level LRT-values for each bootstrap sample. If "no", no double bootstrap is used. The default is set to "FDB".
double.bootstrap.R: Integer. The number of bootstrap draws to be use for the double bootstrap.
double.bootstrap.alpha: The significance level to compute the adjusted alpha based on the plugin p-values.

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 bootstrapLavaan(), the bootstrap distribution of the value(s) returned by FUN, when the object can be simplified to a vector. For bootstrapLRT(), a bootstrap p value, calculated as the proportion of bootstrap samples with a LRT statistic at least as large as the LRT statistic for the original data.

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.

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.

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 sample in this example; in practice
# you may wish to use a much higher number
T.boot <- bootstrapLavaan(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)