Stepwise estimation of latent variable models: An overview of approaches

Stepwise approaches for the estimation of latent variable models are becoming increasingly popular, both in the context of models for continuous (factor analysis and latent trait models) and discrete (latent class and latent profile models) latent variables. Examples include two-stage path analysis, structural-after-measurement and Croon’s bias-corrected estimation of structural equation models, and two- and three-step latent class and latent Markov modelling. These methods have in common that the measurement/clustering part of the model is estimated first, followed by the estimation of a—possibly complex—structural model. In this article, we review the existing approaches, which differ in how the information on the latent variable(s) is used when estimating the structural model. We show that based on these differences, stepwise latent variable modelling approaches can be classified into three main types: the fixed parameters, the single indicator and the bias adjustment approach. We discuss similarities and differences between these approaches, as well as between approaches proposed specifically for either continuous or discrete latent variables. Special attention is paid to heterogeneous measurement error resulting from missing data or measurement non-invariance, standard error estimation and software implementations.