A maximum likelihood approach for multisample nonlinear structural equation models with missing continuous and dichotomous data

Structural equation models are widely appreciated in social-psychological research and other behavioral research to model relations between latent constructs and manifest variables and to control for measurement error. Most applications of SEMs are based on fully observed continuous normal data and models with a linear structural equation. However, discrete nonnormal data and missing data are rather common, and sometimes it is necessary to incorporate nonlinear structural equations for assessing the impact of nonlinear terms of the exogenous latent variables to the endogenous latent variables. Moreover, to study the behaviors of different populations, it is necessary to extend from a single sample model to a multisample model. In this article, a maximum likelihood (ML) approach is developed for analyzing a multisample nonlinear structural equation model, in the context of mixed continuous and dichotomous data that involve data that are missing at random. The article demonstrates the newly developed methods for estimation and model comparison by a simulation study, a synthetic data application, and a real application to study latent psychological constructs of job attitude, emotion, and benefit attitude that are related to organizational and management research.