Sensitivity of Probit Dynamic Structural Equation Models to Non-Normality of the Latent Variable Assumed to Underlie Categorical Responses

Dynamic structural equation models (DSEM) were recently developed for intensive longitudinal data (ILD), whose popularity has sharply increased. Many initial methodological developments in DSEM concerned continuous outcomes. However, a recent review found that 79% of empirical studies collect categorical ILD, with 44% having 5 or fewer categories. Probit DSEM was proposed to accommodate categorical ILD, but its properties have not yet been thoroughly studied. Specifically, probit DSEM assumes that a normal latent variable underlies observed categorical data. However, several topics commonly studied with ILD (e.g., substance use, self-regulation) may not necessarily follow a normal distribution. Therefore, the goal of this paper is to evaluate the sensitivity of probit DSEM to non-normality in the underlying latent variable. Results from simulated data were somewhat robust to non-normality of the underlying latent variable, but sensitivity varied across conditions and results were less promising for smaller samples, binary data, and asymmetric response distributions.