Hierarchical Bayes Regression Model with Multiple Heterogeneity Coefficients for a Single Explanatory Variable

Abstract

This study proposes a hierarchical Bayes regression model designed to distinguish and estimate the multiple heterogeneous regression coefficients for a single explanatory variable, such as the heterogeneity in product offerings and time. We examine the effectiveness of the proposed model by both numerical experiments and analysis using actual POS data. In the numerical experiment, the proposed estimation algorithm's effectiveness is shown in that the estimated model based on the simulated data can reproduce the original model with high accuracy. Besides, this paper reports POS data analysis to show how the proposed framework works in actual data well by distinguishing products and time heterogeneities in the market responses. The proposed framework achieves the factor decomposition of a single market response explicitly and can be effectively utilized in modeling various social science phenomena and decision making based on the models.