Structural Equation Modeling with Categorical Variables

Structural equation modeling (SEM) is a versatile framework for fitting various statistical models, including linear regression, multivariate path models, psychometric models, and latent growth models, just to name a few. To date, standard SEM has primarily been a linear model with normally distributed outcomes, with limited applications to nominal variables. Over the past two decades, there have been important advancements in expanding SEM for categorical variables. The purpose of this workshop is to present a comprehensive treatment of SEM for binary and ordinal outcomes to extend the application of SEM. This workshop will start by doing a high-level overview of logistic and probit regression and path models as a foundation for discussion. Then, the workshop will introduce estimators for binary and ordinal variables within the SEM framework. Specifically, we will introduce the robust weighted least squares (WLS) approach using the WLSMV estimator and the full maximum likelihood estimator. The Bayesian approach (involving Markov Chain Monte Carlo) will be reviewed conceptually as a complement to the two estimation approaches mentioned earlier. Furthermore, this workshop will also cover confirmatory factor models for binary and ordinal indicators, including the 2-parameter logistic model and graded response model, with hands-on practical examples/applications. In addition, model fit indices specific to the WLSMV and the full maximum likelihood estimation will be introduced and discussed; and we will focus on the likelihood ratio test for nested models using modified/adjusted model fit indices. Finally, this workshop will consider missing data estimation with non-normal and/or categorical data using full information maximum likelihood (FIML) or bootstrapping methods. Though unlikely, if time permits, this workshop will also discuss estimation methods for count variables, such as Poisson, negative binomial, or multinomial logistic regression in SEM. The workshop will include a mixture of lecture/presentation, software demonstration, and hands-on application using real-world data. This workshop is intended for an intermediate-level audience. Foundational knowledge of SEM is assumed, and familiarity with logistic regression and SEM application is preferred. Materials, including slides, datasets, and codes, will be shared with attendees electronically. Examples will be available using both Mplus and R Statistical Software.