Performance of Bootstrapping Approaches to Model Test Statistics and Parameter Standard Error Estimation in Structural Equation Modeling. Structural Equation Modeling 8(3

Though the common default maximum likelihood estimator used in structural equa-tion modeling is predicated on the assumption of multivariate normality, applied re-searchers often find themselves with data clearly violating this assumption and with-out 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 es-timates themselves. For a system of p measured variables, let Σ0 represent the true population covariance matrix underlying the variables of interest. Then, a covariance structure model represents the elements ofΣ 0 as functions of model parameters with null hy-pothesis H0: Σ 0 = Σ (θ), in which θ is a vector of q model parameters. An hypothe-sized model may be fit to a p × p sample covariance matrix (S), and for any vector of model parameter estimates (θ) the hypothesized model can be used to evaluate the model implied covariance matrix, Σ(θ) = Σ. The goal in parameter estimation is t