Fixed Effects Regression Methods for Longitudinal Data Using SAS

3.7. Fixed Effects Methods for Multinomial Responses

So far, this chapter has dealt only with binary response variables. We now consider a categorical response variable y_it that can take on more than two values. Without loss of generality, let's suppose that those values are the integers ranging from 1 to J. Let p_ijt = Prob(y_it = j). We now want a model for the dependence of this probability on predictors x_it and z_i.

We begin with the simpler case in which we assume an ordering of the J categories. The most popular model for ordered categorical data is the cumulative logit model which, in its conventional form, is available in both PROC LOGISTIC and PROC GENMOD. A fixed effects version of the model can be written as

where is the "cumulative" ...