Estimation of nonlinear structural equation models with dichotomous indicator variables: a Monte Carlo comparison of methods

Nonlinear structural equation models (SEMs), which include interactions among latent predictors, as well as quadratic or higher order terms, have been the focus of research over the last three decades, beginning with Kenny and Judd (1984). The great majority of that work has focused on the case where the indicator variables are continuous in nature. However, in practice many nonlinear SEMs will involve the use of responses to items on scales, which are categorical. The focus of the current simulation study was on comparing several methods for modelling nonlinear SEMs when indicator variables were dichotomous. Results of the study showed that a Bayesian approach, as well as a method based on 2-stage least squares, provided the most accurate parameter estimates, the highest power, and the best control over the Type I error rate for the interaction effect. Implications of these findings for practice are discussed.