A Bayesian Methodology for Simultaneously Detecting and Estimating Regime Change Points and Variable Selection in Multiple Regression Models for Marketing Research

Abstract

We present a Bayesian change point multiple regression methodology which simultaneously estimates the location of change points/regimes, the corresponding subset of independent variables per regime, as well as the associated regimes’ regression parameters. Unlike existing switching multiple regression models, our method does not require the presence of all independent variables in each regime to detect change points. This allows us to relax the minimum size constraint on each regime as fewer observations are needed to estimate the unknown regression coefficients. Thus our method provides a means to search for small regimes where only a few independent variables are significant. Note that accuracy of change points can drastically affect the identified models within each regime. As the number of change points in the data is typically unknown, we have provided a probability based model selection heuristic to determine its value. Both synthetic and real data sets are utilized to demonstrate that our procedure can yield better fitted models over aggregate OLS regression models and traditional MLE based regime switching models. Furthermore, an actual prescription drug data application involving a promotion response model is used to gainfully illustrate the methodology.

Keywords: Change point models, Variable selection, Bayesian analysis, Multiple regression models, Promotion response modeling