An Analysis of Multi-Category/Brand Purchase Behavior with Hierarchical Bayes Multivariate Poisson Autoregressive Models
Kei Miyazaki
Graduate School of Economics, Nagoya University, Furo-cho, Chikusa-ku, Nagoya-shi, Aichi Pref., Japan

This study proposes a model that can explore time series variation of purchase quantities of multiple product categories or brands for each consumer segment. I assumed that purchase quantities are modeled by poisson distributions.

In economic time series analysis, vector autoregressive models are used frequently for understanding the interrelated influences among several times series. In this study, by introducing latent classes I developed the model that could search the interaction of time series variations of several products' purchase quantities. The proposed model makes it possible to infer appropriate promotional activities for each segment that differs in consumer demographics.

Finite mixture versions of autoregressive Poisson regression models have been proposed by Bockenholt (1999), but this model can deal with only one product category. Andrews and Currim (2009), Song and Chintagunta (2007) and Mehta (2007) estimate a simultaneous model of the three purchase outcomes-incidence, brand choice and quantity-in several product categories. However, these studies do not consider either time series variation of purchase behavior or consumer's demographic variables.

The proposed model can deal with times series variation of multiple categories simultaneously and makes it possible to understand latent switching of purchase behavior or loyalty in case that any promotional activities are not conducted. In parameter estimation, I used a Bayesian estimation method using Markov Chain Monte Carlo algorithm. I applied the proposed method to scanner panel data and meaningful results were obtained.


Andrews, R.L., & Currim, I.S. (2009). Multi-stage purchase decision models: Accommodating response heterogeneity, common demand shocks, and endogeneity using disaggregate data. International Journal of Research in Marketing, 26, 197-206.

Bockenholt, U. (1999). Mixed INAR(1) Poisson regression models: Analyzing heterogeneity and serial dependencies in longitudinal count data. Journal of Econometrics, 89, 317-338.

Mehta, N. (2007). Investigating consumers' purchase incidence and brand choice decisions across multiple product categories: A theoretical and empirical analysis. Marketing Science, 26(2), 196-217.

Song, I., & Chintagunta, P.K. (2007). A discrete-continuous model for multicategory purchase behavior of households. Journal of Marketing Research, 44(4), 595-612.

Keywords: scanner panel data; latent class analysis; vector autoregressive models; Markov Chain Monte Carlo algorithm

Biography: 2010 March The University of Tokyo. Doctor of Philosophy. Current: Research Fellow of the Japan Society for the Promotion of Science