Modelling count data via copulas

Abstract

Copula models have been widely used to model the dependence between continuous random variables, but modelling count data via copulas has recently become popular in the statistics literature. Spearman's rho is an appropriate and effective tool to measure the degree of dependence between two random variables. In this paper, we derive the population version of Spearman's rho via copulas when both random variables are discrete. The closed-form expressions of the Spearman correlation are obtained for some copulas with different marginal distributions. We derive the upper and lower bounds of Spearman's rho for Bernoulli marginals. The proposed Spearman's rho correlations are compared with their corresponding Kendall's tau values and their functional relationships are characterized in some special cases. An extensive simulation study is conducted to demonstrate the validity of our theoretical results. Finally, we propose a bivariate copula regression model to analyse the count data of a cervical cancer dataset.

Keywords:

• Spearman's rho
• copula
• bivariate measure of association
• concordance discordance dependence

2010 Mathematics Subject Classifications:

• 60E15
• 62P10

Acknowledgments

We would like to thank the Editor in Chief, the Associate Editor, and two referees for their helpful and constructive comments which led to a significant improvement of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

Note: ${}^{\mathrm{a}}$Reference level.