Fitting Bayesian hierarchical multinomial logit models in PROC MCMC

The paper illustrates how to use the MCMC procedure to fit a hierarchical, multinomial logit model for a nominal response variable with correlated responses in a Bayesian framework. In particular, the paper illustrates how to perform three important parts of Bayesian model fitting. First, to make sure appropriate prior distributions are selected, the paper shows how to simulate draws directly from the prior distribution. Second, since the reference category and random effects may require special attention, the paper shows how to code the sampling model into PROC MCMC using the RANDOM statement, new to SAS ® 9.3. Finally, the paper demonstrates how to run two chains simultaneously on a multi-core processor, and how to use those two chains to check convergence of the MCMC chain using the Gelman-Rubin diagnostic test. By following these steps, many common pitfalls associated with fitting complicated models in PROC MCMC may be avoided. The target audience for this paper is people with some knowledge of Bayesian methods and a moderate level of SAS experience, but who may not be familiar with PROC MCMC or multinomial logit models.