Bayesian Semiparametric Regression: An Exposition and Application to Print Advertising Data

Abstract

A new regression-based approach is proposed for modeling marketing databases. The approach is Bayesian and provides a number of significant improvements over current methods. Independent variables can enter into the model in either a parametric or nonparametric manner, significant variables can be identified from a large number of potential regressors, and an appropriate transformation of the dependent variable can be automatically selected from a discrete set of prespecified candidate transformations. All these features are estimated simultaneously and automatically using a Bayesian hierarchical model coupled with a Gibbs sampling scheme. Being Bayesian, it is straightforward to introduce subjective information about the relative importance of each variable, or with regard to a suitable data transformation. The methodology is applied to print advertising Starch data collected from 13 issues of an Australian monthly magazine for women. The empirical results highlight the complex and detailed relationships that can be uncovered using the methodology. An Splus compatible package called “br” that implements the semiparametric approach in this article is currently available at the Statlib repository on the world wide web at http://www.stat.cmu.edu/S/.