A Comparison of Methods for Testing for Interaction Effects in Structural Equation Modeling

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## Abstract

The current study aimed to determine the best method for estimating latent variable interactions as a function of the size of the interaction effect, sample size, the loadings of the indicators, the size of the relation between the first-order latent variables, and normality. Data were simulated from known population parameters, and data were analyzed using nine latent variable methods of testing for interaction effects. Evaluation criteria used for comparing the methods included proportion of relative bias, the standard deviation of parameter estimates, the mean standard error estimate, a relative ratio of the mean standard error estimate to the standard deviation of parameter estimates, the percent of converged solutions, Type I error rates, and empirical power. It was found that when data were normally distributed and the sample size was 250 or more, the constrained approach results in the least biased estimates of the interaction effect, had the most accurate standard error estimates, high convergence rates, and adequate type I error rates and power. However, when sample sizes were small and the loadings were of adequate size, the latent variable scores approach may be preferable to the constrained approach. When data were severely non-normal, all of the methods were biased, had inaccurate standard error estimates, low power, and high Type I error rates. Thus, when data were non-normal, relative comparisons were made regarding the approaches rather than absolute comparisons. In relative terms, the marginal-maximum likelihood approach performed the least poorly of the methods for estimating the interaction effect, but requires sample sizes of 500 or greater. However, when data were non-normal, the latent moderated structure analysis resulted in the least biased estimates of the first-order effects and had bias similar to that of the marginal-maximum likelihood approach. Recommendations are made for researchers who wish to test for latent variable interaction effects.