A Heterogeneous Bayesian Regression Model for Cross-Sectional Data Involving a Single Observation Per Response Unit

Abstract

Multiple regression is frequently used across the various social sciences to analyze cross-sectional data. However, it can often times be challenging to justify the assumption of common regression coefficients across all respondents. This manuscript presents a heterogeneous Bayesian regression model that enables the estimation of individual level regression coefficients in cross sectional data involving a single observation per response unit. A Gibbs sampling algorithm is developed to implement the proposed Bayesian methodology. A Monte Carlo simulation study is constructed to assess the performance of the proposed methodology across a number of experimental factors. We then apply the proposed method to analyze data collected from a consumer psychology study that examines the differential importance of price and quality in determining perceived value evaluations.

Keywords: Bayesian estimation, cross-sectional analysis, heterogeneity, consumer psychology, inequality sign constraints

JEL Classification: C1, C11, C21, C5, M30