Corrected Goodness-of-Fit Test in Covariance Structure Analysis

Many previous studies report simulation evidence that the goodness-of-fit test in covariance structure analysis or structural equation modeling suffers from the over-rejection problem when the number of manifest variables is large compared with the sample size. In this study, we demonstrate that one of the tests considered in Browne(1974) can address this long-standing problem. We also propose a simple modification of Satorra and Bentler's mean and variance adjusted test for non-normal data. A Monte Carlo simulation is carried out to investigate the performance of the corrected tests in the context of a confirmatory factor model, a panel autoregressive model, and a cross-lagged panel (panel vector autoregressive) model. The simulation results reveal that the corrected tests overcome the over-rejection problem and outperform existing tests in most cases