The following random coefficient multinomial logit regression model is an extension of Equation (11.11). It is assumed that, in addition to the random effects on intercepts, the regression coefficients of time vary significantly over subjects, thereby specifying an extra random slope term. For analytic simplicity, the effects of time × time are assumed to remain fixed. Consequently, we have
Given the above specifications, SAS Program 11.2 is adapted for the creation of a random coefficient multinomial logit model by including two additional random terms. The following is the revised SAS program.
With the AHEAD longitudinal data, SAS Program D1 derives the following output:
In the above output, the analytic results for the fixed effects are analogous to those from the corresponding random intercept multinomial logit model, and the two additional random terms are not statistically significant. Therefore, in this analysis, the application of the random coefficient approach is not necessary.