Fixed Effects Regression Methods for Longitudinal Data Using SAS

6.2. Random Effects as a Latent Variable Model

In chapter 2, the random effects model was specified as

where y_it is the value of the response variable for individual i at time t, x_it is a vector of time-varying covariates, z_i is a vector of time-invariant covariates, α_i denotes the random effects, and ε_it is a random disturbance term. We assume that α_i and ε_it represent independent normally distributed variables, each with a mean of 0 and a constant variance. We also assume, at least for now, that these random components are independent of both x_it and z_i.

It is now well known (Muthén 1994) that a random effects models such as the one in equation ...