A Semiparametric Approach to Modeling Nonlinear Relations Among Latent Variables

To date, finite mixtures of structural equation models (SEMMs) have been developed and applied almost exclusively for the purpose of providing model-based cluster analyses. This type of analysis constitutes a direct application of the model wherein the estimated component distributions of the latent classes are thought to represent the characteristics of distinct unobserved subgroups of the population. This article instead considers an indirect application of the SEMM in which the latent classes are estimated only in the service of more flexibly modeling the characteristics of the aggregate population as a whole. More specifically, the SEMM is used to semiparametrically model nonlinear latent variable regression functions. This approach is first developed analytically and then demonstrated empirically through analyses of simulated and real data.