# Latent Variable Modeling

## Selected Topics in Structural Equation Modeling and Multivariate Scaling

NOTE: Usually taught every other year. Last taught in Spring 2022.

Topics covered include: summated scales; exploratory factor analysis; confirmatory factor analysis; item response theory; latent class analysis; structural equation modeling; measurement invariance and differential item functioning

### Course Description

Many constructs of fundamental interest to social scientists are not directly observable. A person's political ideology, their level of racial prejudice, someone's personality traits, the propensity to engage in risky behavior, the presence or absence of a mental illness, a person's ability, someone's health lifestyle, and more are all examples of latent variables.

To start, we will learn several different multivariate scaling techniques for modeling latent variables from multiple observed indicators. We will consider scaling strategies that allow continuous, count, ordinal, nominal, and binary observed indicators. We will also consider scaling techniques for both continuous and nominal latent variables. Specific techniques for scaling we cover include exploratory factor analysis, confirmatory factor analysis, latent class analysis, item response theory, and some variants of each of these. We also cover issues of measurement invariance and differential item functioning which applies to all of these methods.

Next, the class covers how to incorporate latent variables into the regression framework. We consider how to estimate and interpret a regression model when either the dependent or independent variable is latent. The course ends by covering methods for simultaneous model estimation. Simultaneously estimating models allows for comparisons of the effects of observed and/or latent variables across multiple models. We will also consider how multiple groups (observed or latent) can be incorporated into a simultaneous equation framework. These types of methods are useful, e.g., when the process being examined may differ across observed groups (e.g. men and women) or across groups that are latent.