Beyond SEM: General Latent Variable Modeling

Abstract

This article gives an overview of statistical analysis with latent variables. Using traditional structural equation modeling as a starting point, it shows how the idea of latent variables captures a wide variety of statistical concepts. including random effects, missing data. sources of variation in hierarchical data. finite mixtures. latent classes. and clusters. These latent variable applications go beyond the traditional latent variable useage in psychometrics with its focus on measurement error and hypothetical constructs measured by multiple indicators. The article argues for the value of integrating statistical and psychometric modeling ideas. Different applications are discussed in a unifying framework that brings together in one general model such different analysis types as factor models, growth curve models, multilevel models, latent class models and discrete-time survival models. Several possible combinations and extensions of these models are made clear due to the unifying framework.