Fixed Effects Regression Methods for Longitudinal Data Using SAS

3.4. Fixed Effects versus Random Effects

As with the linear models in chapter 2, the most popular alternative to the fixed effects model is a random effects model. That model begins with an identical equation:

Solving for p_it, this can also be written as

Now, instead of assuming that α_i is a fixed constant, we assume that it is a random variable with the following properties:

• E(α_i) = 0.

• Var(α_i) = τ².

• α_i is independent of x_it and z_i.

• α_i is normally distributed.

Models of this sort can be handled with PROC NLMIXED, which estimates a variety of nonlinear ...