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

Jonathan Nevitt, Gregory Hancock
2001 Structural Equation Modeling  
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
more » ... 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 themselves. For a system of p measured variables, let Σ 0 represent the true population covariance matrix underlying the variables of interest. Then, a covariance structure model represents the elements of Σ 0 as functions of model parameters with null hypothesis H 0 : Σ 0 = Σ (θ), in which θ is a vector of q model parameters. An hypothesized 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 to STRUCTURAL EQUATION MODELING, 8(3), 353-377
doi:10.1207/s15328007sem0803_2 fatcat:zosbryevjrfk3np7z4szfrqyzq