MPBART - Multinomial Probit Bayesian Additive Regression Trees

Multinomial probit (MNP) model for discrete choice modeling is often used in economics, market research, political sciences and transportation. It models the choices made by agents given their demographic characteristics and/or the features of the K 2 available choice alternatives. Examples include the study of consumer's purchasing behavior (e.g., McCulloch et al. (2000); Imai and van Dyk (2005)); voting behavior in multi-party elections (e.g., Quinn et al. (1999)); and choice of different modes of transportation (e.g., Bolduc (1999)). Details of the MNP model in which choices depend on predictors in a linear fashion is studied in McFadden et al.(1973); McFadden(1989); Keane(1992); McCulloch and Rossi (1994); Nobile (1998); McCulloch et al. (2000); Imai and van Dyk (2005); Train (2009); Burgette and Nordheim (2012) among others. Among widely used multinomial choice modeling procedures are the multinomial logit model (e.g., McFadden et al. (1973); Train (2009)) and multinomial probit model (e.g., McFadden (1989); McCulloch and Rossi (1994); Imai and van Dyk (2005)). The former relies on an assumption that a choice outcome is independent of removal (or introduction) of an irrelevant choice alternative while the latter including MPBART does not make this restrictive assumption.