Robust Statistical Tests for Evaluating the Hypothesis of Close Fit of Misspecified Mean and Covariance Structural Models

Model close fit is one key issue in the mean and covariance structure analysis. In this article, we utilize the latest results on the general distribution of likelihood ratio statistic in this methodology and propose several distribution free root mean square error of approximation (RMSEA) tests for evaluating the hypothesis of close fit of misspecified models. Simulation studies show that three of these tests have robust and desirable performance in spite of severe nonnormality across the examples when sample size is as large as 300. A new two-stage procedure which combines model exact fit tests and the proposed RMSEA tests for model close fit is further proposed for overall model fit evaluation.