Performance of Bootstrapping Approaches to Model Test Statistics and Parameter Standard Error Estimation in Structural Equation Modeling

TLDR

The default maximum likelihood estimator in SEM assumes multivariate normality, yet researchers frequently encounter nonnormal data and small samples, prompting the integration of alternative methods into popular software. The study evaluates the bootstrap method across varying levels of nonnormality, sample size, model specification, and bootstrap sample numbers. Bootstrap resampling in AMOS was employed to estimate model test statistic p values and parameter standard errors, with accuracy assessed via model rejection rates and bias/variability of the standard errors. The evaluation examined the accuracy of bootstrap estimates, reporting model rejection rates for p values and bias and variability for standard errors under the different conditions.

Abstract

Though the common default maximum likelihood estimator used in structural equation modeling is predicated on the assumption of multivariate normality, applied researchers often find themselves with data clearly violating this assumption and without sufficient sample size to utilize distribution-free estimation methods. Fortunately, promising alternatives are being integrated into popular software packages. Bootstrap resampling, which is offered in AMOS (Arbuckle, 1997), is one potential solution for estimating model test statistic p values and parameter standard errors under nonnormal data conditions. This study is an evaluation of the bootstrap method under varied conditions of nonnormality, sample size, model specification, and number of bootstrap samples drawn from the resampling space. Accuracy of the test statistic p values is evaluated in terms of model rejection rates, whereas accuracy of bootstrap standard error estimates takes the form of bias and variability of the standard error estimates thems...