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A multivariate Poisson mixture model for marketing applications
Author(s) -
Brijs Tom,
Karlis Dimitris,
Swinnen Gilbert,
Vanhoof Koen,
Wets Geert,
Manchanda Puneet
Publication year - 2004
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/j.1467-9574.2004.00125.x
Subject(s) - multivariate statistics , covariance , poisson distribution , multivariate analysis of variance , cluster analysis , econometrics , multivariate analysis , product (mathematics) , computer science , variance (accounting) , set (abstract data type) , mathematics , statistics , economics , accounting , geometry , programming language
This paper describes a multivariate Poisson mixture model for clustering supermarket shoppers based on their purchase frequency in a set of product categories. The multivariate nature of the model accounts for cross‐selling effects between the purchases made in different product categories. However, for computational reasons, most multivariate approaches limit the covariance structure by including just one common interaction term, or by not including any covariance at all. Although this reduces the number of parameters significantly, it is often too simplistic as typically multiple interactions exist on different levels. This paper proposes a theoretically more complete variance/covariance structure of the multivariate Poisson model, based on domain knowledge or preliminary statistical analysis of significant purchase interaction effects in the data. Consequently, the model does not contain more parameters than necessary, whilst still accounting for the existing covariance in the data. Practically, retail category managers can use the model to devise customized merchandising strategies.