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Multinomial Probit Model for Panel Data


In this thesis we applied the multinomial probit model to a panel dataset to study the brand preference for a consumer product that various households purchased over multiple purchase occasions by 100 households. There are four brands avail- able for the consumer product. The dataset comprises information regarding the brand of item purchased by a household given their annual income, household size, and purchase quantity along with the price for each brand of the product. We analyzed the effect of the three individual specific covariates, namely, annual income, household size, and quantity purchased, and the choice specific co- variate of price of each unit of the product for every brand. We used the MNP package in R by Imai and van Dyk for our analysis. The package does not have any function for model selection. Hence, we introduced a new approach to per- form model selection for multinomial probit model by applying Kullback-Leibler divergence to evaluate the mean divergence of the average posterior predictive probabilities in the presence and absence of each of the three individual specific covariates. Finally, we obtain insights regarding how consumer preference across brands changes with the covariate values in terms of the posterior predictive probabilities of purchasing a brand.

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