Fixed Effects Regression Methods for Longitudinal Data Using SAS

4.3. Poisson Models for Data with More Than Two Observations Per Individual

When there are more than two observations per individual, estimation of a fixed effects Poisson model in SAS is not so straightforward. Let's extend the example of the last section by analyzing annual patent counts from 1975 through 1979, with each count denoted by y_it. As before, we assume that y_it has a Poisson distribution given by equation (4.1) with parameter λ_it, and we let λ_it be the log-linear function of the predictor variables given in equation (4.3).

We'll consider two approaches to estimation—conditional maximum likelihood and unconditional maximum likelihood. In conditional maximum likelihood, the likelihood function is conditioned on the total count for ...