Comparison of approaches in estimating interaction and quadratic effects of latent variables

Various approaches using the maximum likelihood (ML) option of the LISREL program and products of indicators have been proposed to analyze structural equation models with non-linear latent effects on the basis of Kenny and Judd's formulation. Recently, some methods based on the Bayesian approach and the exact ML approaches have been developed. This article reviews, elaborates and compares several approaches for analyzing nonlinear models with interaction and/or quadratic effects. A total of four approaches are examined, including the product indicator ML approaches proposed by Jaccard and Wan (1995) and Joreskog and Yang (1996), a Bayesian approach and an exact ML approach. The empirical performances of these approaches are assessed using simulation studies in terms of their capabilities in producing reliable parameter and standard error estimates. It is found that whilst the Bayesian and the exact ML approaches produce satisfactory results in all the settings under consideration, and are in general very reliable; the product indicator ML approaches can only produce reasonable results in simple models with large sample sizes.