Introduction to Latent Variables and Structural Equation Modeling

This short course will make latent variable modeling accessible to both new and experienced researchers across many disciplines. Latent variables are indirectly observed variables (e.g. depression, quality of life) and underlie many concepts in behavioral and health research. In this introductory short course, we will show how to take observed data points, such as responses taken from multi-item scales, and model them as continuous and categorical latent variables. We will cover latent variable modeling within the structural equation modeling (SEM) framework. SEM is a multivariate technique that allows relationships among variables to be examined. Several special cases of SEM techniques have advantageous analytic properties in this measurement modeling context. For example, confirmatory factor analysis can be used to establish psychometric properties of a scale and test for measurement invariance across groups (e.g. race/ethnicity or sex/gender groups). Additionally, mixture modeling is a multivariate clustering technique that is related to SEM, where the clusters represent discrete unobserved subgroupings based on indicators of interest (e.g. empirical subgroups among patients with multiple sclerosis). We will address mixture modeling as implemented through latent class analysis and latent profile analysis. Throughout our presentation, we will provide real-world demonstrations using R and Mplus.