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

• Published in: Structural equation modeling Vol. 22; no. 2; pp. 276 - 287
• Main Authors: Gerhard, Carla, Klein, Andreas G., Schermelleh-Engel, Karin, Moosbrugger, Helfried, Gäde, Jana, Brandt, Holger
• Format: Journal Article
• Language: English
• Published: Hove Routledge 03.04.2015; Psychology Press
• Subjects: interaction effects; likelihood-ratio test; Monte Carlo simulation; Monte Carlo study; nonlinear SEM; Predictor Variables; robust difference test; Sample size; Statistics; strictly positive difference test; Structural Equation Models; Variables
• ISSN: 1070-5511; 1532-8007
• DOI: 10.1080/10705511.2014.935752

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 T D , 2 robust statistics have been developed in the literature to ensure valid results under the conditions of nonnormality or small sample sizes: the robust T DR and the "strictly positive" T DRP . 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 T D is preferable to both T DR and T DRP . Under the condition of strong nonlinear effects and nonnormal predictors, T DR often produced negative differences and T DRP showed no desirable power.