Investigation of the stochastic utility maximization process of consumer brand choice by semiparametric modeling

The use of nonparametric methods, which posit fewer assumptions and greater model flexibility than parametric methods, could provide useful insights when studying brand choice. It was found, however, that the data requirement for a fully nonparametric brand choice model is so great that obtaining such large data sets is difficult even in marketing. Semiparametric methods balance model flexibility and data requirement by imposing some parametric structure on components that are not sensitive to such assumptions while leaving the essential component nonparametric. In this paper, the authors compare two semiparametric brand choice models that are based on the generalized additive models (GAM). One model is specified as a nonparametric logistic regression of GAM (Hastie and Tibshirani 1986) with one equation for each brand. The other model is a multinomial logit (MNL) formulation with a nonparametric utility function, which is derived by extending the GAM framework (Abe 1999). Both models assume a parametric distribution for the random component, but capture the response of covariates nonparametrically. The competitive structure of the logistic regression formulation is specified by data through nonparametric response functions of the attributes for the competitive brands, whereas that of the MNL formulation is guided by the choice theory of stochastic utility maximization (SUM). Simulation study and application to actual scanner panel data seem to support the behavioral assumption of SUM. In addition, if we relax the SUM assumption by letting data specify the competitive structure, a substantially larger amount of data, perhaps an order of magnitude more, would be required. Therefore, if alternative brands are chosen carefully, nonparametric relaxation to capture cross effect (i.e., nonparametrization of the MNL structure) may not be warranted unless the size of database becomes substantially larger than the one currently used.