Bayesian Analysis of Hierarchical Effects

Abstract

The idea of hierarchical, sequential, or intermediate effects has long been posited in textbooks and academic literature. Hierarchical effects occur when relationships among variables are mediated through other variables. Despite the attractive theoretical properties of these models, their practical existence has been difficult to show in empirical studies. We propose an approach to studying hierarchical effects using sets of conditional relationships among affected variables while allowing for heterogeneous response segments, and using Bayesian variable selection to deal with the high dimensional parameter space often encountered in applied empirical studies. Cross-sectional data from a national brand-tracking study is used to illustrate our model, where we find empirical support for a hierarchical relationship among media recall, brand beliefs, and intended actions. We find these effects to be insignificant when measured with standard models and aggregate analyses. The proposed model is useful for understanding the influence of variables that lead to intermediate as opposed to direct effects on brand choice.

Keywords: Hierarchical Bayes, mediation analysis, structural heterogeneity, variable selection

JEL Classification: C11, M31, M37