Fixed Effects Regression Methods for Longitudinal Data Using SAS

6.3. Fixed Effects as a Latent Variable Model

As noted in chapter 2, the basic random effects model is actually a special case of the fixed effects model (Mundlak 1978). The random effects model assumes that α_i is uncorrelated with x_it, the vector of time-varying covariates. The fixed effects model allows for any correlations between α_i and the elements of x_it. Figure 6.2 shows a path diagram for a simplified fixed effects model with a single time-varying predictor. The only difference between this diagram and the one in Figure 6.1 is the addition of the curved arrows representing correlations between α and the x variables.

Figure 6.2. Figure 6.2 Path Diagram of a Fixed Effects Model for Three Points in Time

These additional correlations ...