A note on dependence modeling for Bernoulli variables

ABSTRACT

Understanding and modeling multivariate dependence structures depending upon the direction are challenging but an interest of theoretical and applied researchers. In this paper, we propose a characterization of tables generated by Bernoulli variables through the uniformization of the marginals and refer to them as Q-type tables. The idea is similar to the copulas. This approach helps to see the dependence structure clearly by eliminating the effect of the marginals that have nothing to do with the dependence structure. We define and study conditional and unconditional Q-type tables and provide various applications for them. The limitations of existing approaches such as Cochran-Mantel-Haenszel pooled odds ratio are discussed, and a new one that stems naturally from our approach is introduced.

KEYWORDS:

• Bernoulli variables
• Cochran-Mantel-Haenszel statistics
• Conditional Ratio
• Dependence
• Directional dependence
• Odds ratio
• Risk Ratio.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E02
• 62H20

Acknowledgments

The authors gratefully acknowledge the insightful and generous comments and suggestions of the referees on the previous version of the manuscript.