Econometric analysis Discrete Choice Modeling参考.ppt

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * A Random Effects Approach Allenby and Rossi, “Marketing Models of Consumer Heterogeneity” Discrete Choice Model – Brand Choice “Hierarchical Bayes” Multinomial Probit Panel Data: Purchases of 4 brands of Ketchup Structure Bayesian Priors Bayesian Estimator Joint Posterior= Integral does not exist in closed form. Estimate by random samples from the joint posterior. Full joint posterior is not known, so not possible to sample from the joint posterior. Gibbs Sampling: Target: Sample from f(x1, x2) = joint distribution Joint distribution is unknown or it is not possible to sample from the joint distribution. Assumed: f(x1|x2) and f(x2|x1) both known and samples can be drawn from both. Gibbs sampling: Obtain one draw from x1,x2 by many cycles between x1|x2 and x2|x1. Start x1,0 anywhere in the right range. Draw x2,0 from x2|x1,0. Return to x1,1 from x1|x2,0 and so on. Several thousand cycles produces a draw Repeat several thousand times to produce a sample Average the draws to estimate the marginal means. Gibbs Cycles for the MNP Model Samples from the marginal posteriors Results Individual parameter vectors and disturbance variances Individual estimates of choice probabilities The same as the “random parameters model” with slightly different weights. Allenby and Rossi call the classical method an “approximate Bayesian” approach. (Greene calls the Bayesian estimator an “approximate random parameters model”) Who’s right? Bayesian layers on implausible priors and calls the results “exact.” Classical is strongly parametric. Neither is right – Both are right. Comparison of Maximum Simulated Likelihood and Hierarchical Bayes Ken Train: “A Comparison of Hierarchical Bayes and Maximum Simulated Likelihood for Mixed Logit” Mixed Logit Stochastic Structure – Conditional Likelihood Note individual specific parameter v