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

A major issue in the utilization of covariance structure analysis is model misfit evaluation. Recent years have witnessed increasing interest in various test statistics and so-called fit indices, most of which are actually based on or closely related to F0, a measure of model misfit in the population. The present study aims to provide a systematic investigation about the performance of four estimators of F0 available. F01 is the conventional estimator and is based on noncentral chi-square approximation. F02 is newly proposed and does not assume noncentral chi-square approximation. F03 and F04 are derivatives of F02. A Monte Carlo simulation study is conducted to examine how the above four estimators of F0 perform across varying model misspecifications, data distributions, model complexities, and sample sizes. Although all four quantities estimate F0 satisfactorily under normality, the results favor F02 due to its relative robustness to data nonnormality. Issues related to our findings are discussed.