Assessing Heterogeneity in Discrete Choice Models Using a Dirichlet Process Prior

Abstract

The finite normal mixture model has emerged as a dominant methodology for assessing heterogeneity in choice models. Although it extends the classic mixture models by allowing within component variablility, it requires that a relatively large number of models be separately estimated and fairly difficult test procedures to determine the "correct" number of mixing components. We present a very general formulation, based on Dirichlet Process Piror, which yields the number and composition of mixing components a posteriori, obviating the need for post hoc test procedures and is capable of approximating any target heterogeneity distribution. Adapting Stephens' (2000) algorithm allows the determination of 'substantively' different clusters, as well as a way to sidestep problems arising from label-switching and overlapping mixtures. These methods are illustrated both on simulated data and A.C. Nielsen scanner panel data for liquid detergents. We find that the large number of mixing components required to adequately represent the heterogeneity distribution can be reduced in practice to a far smaller number of segments of managerial relevance.

Modeling the “Pseudodeductible” in Insurance Claims Decisions

“…In our case, we use the common kernel choice of the bivariate normal distribution. The advantage of using an MDP is that any distribution can be approximated by incorporating a sufficient number of these kernels without resorting to a specific parametric form (Kim et al 2004). Furthermore, an MDP can be used as a proxy for latent class models without a need to specify the number of classes up front (Escobar and West 1995), and can relax restrictions that are often imposed by parametric priors, such as unimodality (Draper 1999).…”

“…Additionally, the MDP model allows for within-class heterogeneity, unlike standard latent class approaches. Examples of the use of MDP in a variety of settings are available in Congdon (2001) and an application of the MDP to discrete choice models is developed by Kim et al (2004).…”

Estimation of Residual Equity in Hierarchical Branding Structures: A Nonparametric Approach on Aggregate Beer Category Data

“…But these alternatives suffer from a host of problems (see, e.g., Kim, Menzefricke and Feinberg, 2004).…”

“…DP mixture models are finding use in Marketing (Braun et al, 2004;Kim et al, 2004), Statistics (Ghosh, Basu and Tiwari, 2009) and the Social networking literatures (e.g., Ghosh et al, 2009;Braun and Bonfrer, 2009). In Marketing in particular, Braun et al (2004) use a DP prior to model the latent threshold above which insurance losses are claimed.…”

“…In Marketing in particular, Braun et al (2004) use a DP prior to model the latent threshold above which insurance losses are claimed. Kim, Menzefricke and Feinberg (2004) implement a DP prior in a discrete choice model setting and demonstrate the DP mixtures' advantages over alternative finite mixture methods. In this paper, we extend the Marketing application of DP mixture models to an equity estimation setting.…”