A Comparison of Four Estimators of a Population Measure of Model Fit in Covariance Structure Analysis

Abstract

A major issue in the utilization of covariance structure analysis is model fit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indexes, most of which are actually based on or closely related to F ₀, a measure of model fit in the population. This study aims to provide a systematic investigation about the performance of 4 available estimators of F ₀. [Fcirc]₀₁ is the conventional estimator and is based on noncentral chi-square approximation. [Fcirc]₀₂ is newly proposed and does not assume noncentral chi-square approximation. [Fcirc]₀₃ and [Fcirc]₀₄ are variations of [Fcirc]₀₂. A Monte Carlo simulation study is conducted to examine how these four estimators of F ₀ perform across varying model misspecifications, data distributions, model sizes, and sample sizes. The results show that under normality all 4 quantities estimate F ₀ equally well, and under nonnormality [Fcirc]₀₂, [Fcirc]₀₃, and [Fcirc]₀₄ outperform [Fcirc]₀₁. Issues related to these findings are discussed.

ACKNOWLEDGMENTS

I wish to thank Ke-Hai Yuan, Scott Maxwell, and Steve Boker for their helpful comments on an earlier version of this article.