Fixed and Random Effects in Panel Data Using Structural Equations Models

Applications of classic fixed and random effects models for panel data are common in sociology and in ASR. A primary advantage of these models is the ability to control for time-invariant omitted variables that may bias observed relationships. This paper shows how to incorporate fixed and random effects models into structural equation models(SEMs)and how to extend the standard models to a wide variety of more flexible models. For instance, a researcher can test whether a covariate's impact on the repeated measure stays the same across all waves of data; test whether the error variances should be allowed to vary over time; include lagged covariates or lagged dependent variables; estimate the covariance of the latent time-invariant variables with the observed time varying covariates; and include observed time-invariant variables in a fixed effects model. The paper explains how to take advantage of the estimation, testing, and fit assessment capabilities that are readily available for SEMs and how to reveal flaws not visible with typical assessment techniques. The paper is oriented towards applied researchers with most technical details given in the appendix and footnotes