Modeling Multivariate Count Data Using Copulas

Abstract

Multivariate count data occur in several different disciplines. However, existing models do not offer great flexibility for dependence modeling. Models based on copulas nowadays are widely used for continuous data dependence modeling. Modeling count data via copulas is still in its infancy; see the recent article of Genest and Nešlehová (2007). A series of different copula models providing various residual dependence structures are considered for vectors of count response variables whose marginal distributions depend on covariates through negative binomial regressions. A real data application related to the number of purchases of different products is provided.

Keywords:

• Archimedean copulas
• Kendall's tau
• Market basket count data
• Mixtures of max-id copulas
• Partially symmetric copulas

Mathematics Subject Classification:

• 62H20
• 62P10

Acknowledgments

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 want to thank a referee for his constructive comments.