The Search for "Optimal" Cutoff Properties: Fit Index Criteria in Structural Equation Modeling

ABSTRACT. This study is a partial replication of L. Hu and P. M. Bentler's (1999) fit criteria work. The purpose of this study was twofold: (a) to determine whether cut-off values vary according to which model is the true population model for a dataset and (b) to identify which of 13 fit indexes behave optimally by retaining all of the correct models while simultaneously rejecting all of the misspecified models in a manner invariant across sample size and data distribution. The authors found that for most indexes the results do not vary depending on which model serves as the correct model. Furthermore, the search for an optimal cut-off value led to a new discovery about the nature of McDonald's measure of centrality and the root mean square error of approximation. Unlike all other indexes considered in this study, the cut-off value of both indexes actually decreases for incorrect models as sample size increases. This may suggest that power calculations are more likely to be optimal when based on those indices.