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Train_Discrete Choice Methods with Simulation - Chapter 12

12 Bayesian Procedures 12.1 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) | P1 GEM IKJ CB495-12Drv P2 GEM IKJ QC GEM ABE CB495 Train KEY BOARDED T1 GEM August 20 2002 13 44 Char Count 0 12 Bayesian Procedures 12.1 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. 2001 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. Train 2001 extended the Bayesian procedure for mixed logit to nonnormal distributions of coefficients including lognormal uniform and triangular distributions. The Bayesian procedures avoid two of the most prominent difficulties associated with classical procedures. First the Bayesian procedures do not require maximization of any function.