On the Performance of Likelihood-Based Difference Tests in Nonlinear Structural Equation Models

Abstract

This article investigates likelihood-based difference statistics for testing nonlinear effects in structural equation modeling using the latent moderated structural equations (LMS) approach. In addition to the standard difference statistic TD, 2 robust statistics have been developed in the literature to ensure valid results under the conditions of nonnormality or small sample sizes: the robust TDR and the “strictly positive” TDRP. These robust statistics have not been examined in combination with LMS yet. In 2 Monte Carlo studies we investigate the performance of these methods for testing quadratic or interaction effects subject to different sources of nonnormality, nonnormality due to the nonlinear terms, and nonnormality due to the distribution of the predictor variables. The results indicate that TD is preferable to both TDR and TDRP. Under the condition of strong nonlinear effects and nonnormal predictors, TDR often produced negative differences and TDRP showed no desirable power.