Introduction

A powerful set of procedures for estimating discrete choice models has been developed within the Bayesian tradition. The breakthough concepts were introduced by Albert and Chib (1993) and McCulloch and Rossi (1994) in the context of probit, and by Allenby and Lenk (1994) and Allenby (1997) for mixed logits with normally distributed coefficients. These authors showed how the parameters of the model can be estimated without needing to calculate the choice probabilities. Their procedures provide an alternative to the classical estimation methods described in Chapter 10. Rossi et al. (1996), Allenby (1997), and Allenby and Rossi (1999) showed how the procedures can also be used to obtain information on individual-level parameters within a model with random taste variation. By this means, they provide a Bayesian analog to the classical procedures that we describe in Chapter 11. Variations of these procedures to accommodate other aspects of behavior have been numerous. For example, Arora et al. (1998) generalized the mixed logit procedure to take account of the quantity of purchases as well as brand choice in each purchase occasion. Bradlow and Fader (2001) showed how similar methods can be used to examine rankings data at an aggregate level rather than choice data at the individual level. Chib and Greenberg (1998) and Wang et al. (2002) developed methods for interrelated discrete responses. Chiang et al. (1999) examined situations where the choice set that the decision maker considers is unknown to the researcher.