Regression in a copula model for bivariate count data

Abstract

In many cases of modeling bivariate count data, the interest lies on studying the association rather than the marginal properties. We form a flexible regression copula-based model where covariates are used not only for the marginal but also for the copula parameters. Since copula measures the association, the use of covariates in its parameters allow for direct modeling of association. A real-data application related to transaction market basket data is used. Our goal is to refine and understand whether the association between the number of purchases of certain product categories depends on particular demographic customers’ characteristics. Such information is important for decision making for marketing purposes.

Keywords:

• dependence modeling
• Kendall's tau
• covariate function
• negative binomial distribution

Acknowledgements

This work is part of first author's Ph.D. thesis under the supervision of the second author at the Athens University of Economics and Business. The first author would like to thank the National Scholarship Foundation of Greece for financial support. The authors would like to thank the referees and Professor Harry Joe, University of British Columbia, for comments that led to an improvement of the presentation of the paper.