The BCHOICE Procedure

The underlying structure of PROC BCHOICE is similar to the structure of PROC MCMC in that both procedures obtain samples from the posterior distributions and produce summary and diagnostic statistics when you specify the model or the priors or both. However, they differ in that PROC MCMC is a general-purpose Markov chain Monte Carlo (MCMC) simulation procedure that is designed to fit a wide range of Bayesian models, whereas PROC BCHOICE is designed specifically for discrete choice models. You can call PROC MCMC to analyze data that have any likelihood, prior, or hyperprior, as long as these functions can be programmed by using the SAS DATA step functions. For example, you can fit choice logit and nested logit models in PROC MCMC by using some SAS coding to specify the likelihood. PROC BCHOICE works only with choice models, but it is customized to fit special characteristics and features in a choice model. The syntax is quite different from PROC MCMC’s syntax. PROC BCHOICE provides a CLASS statement to handle categorical variables, and it requires less complicated SAS coding for choice models. The default sampling method for choice logit models when direct sampling is not available is the Metropolis-Hastings method, which is based on the Gamerman approach, which in turn has proved to be often more efficient than the random walk Metropolis algorithm that PROC MCMC uses. In addition, it is difficult to fit choice probit models in PROC MCMC.

For a standard logit choice model, you can use the TIES=BRESLOW option in the PHREG procedure. The approach has the same likelihood as PROC BCHOICE of fitting the data. You use the STRATA statement in PROC PHREG to specify how to define the choice set. However, this is a frequentist approach, and it does not work for a choice model with random effects.