A closer look at fixed effects regression in SEM
This article provides an in-depth look at the method of fixed-effects regression in the structural equation modeling (SEM) framework. It is meant for those who are less familiar with SEM but interested in panel data analysis as well as those familiar with SEM but new to fixed-effects regression. It demonstrates the decomposition of observed variables into within- and between-unit variance components using latent variables and gives an intuitive least squares-based explanation of latent variable estimation. The estimation of the substantive effect coefficients is shown analytically. The procedure is demonstrated on simulated as well as real-world data using the German Family Panel Survey (pairfam). The example analyses show the SEM results are identical to the conventional methods of pooled ordinary least squares on demeaned data. The supplementary materials provide the model code for use in replication and further study.