Using Monte Carlo Normal Distributions to Evaluate Structural Models With Nonnormal Data

Abstract

Statistical theories of goodness-of-fit tests in structural equation modeling are based on asymptotic distributions of test statistics. When the model includes a large number of variables or the population is not from a multivariate normal distribution, the asymptotic distributions do not approximate the distribution of the test statistics very well at small sample sizes. A variety of methods have been developed to improve the accuracy of hypothesis testing at small sample sizes. However, all these methods have their limitations, specially for nonnormal distributed data. We propose a Monte Carlo test that is able to control Type I error with more accuracy compared to existing approaches in both normal and nonnormally distributed data at small sample sizes. Extensive simulation studies show that the suggested Monte Carlo test has a more accurate observed significance level as compared to other tests with a reasonable power to reject misspecified models.

Keywords:

• goodness-of-fit test
• Monte Carlo test
• nonnormality
• Satorra–Bentler test statistic
• small sample size
• structural equation models

Notes

¹ The Hoffman2 cluster is a campus computing resource at UCLA, maintained by the Institute for Digital Research and Education (IDRE).