A note on dependence modeling for Bernoulli variables |
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Authors: | Engin A Sungur Jessica M Orth |
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Institution: | 1. Statistics Discipline, University of Minnesota, Morris, Minnesota, USA;2. Master of Public Health Program, University of North Dakota, School of Medicine and Health Sciences, Grand Forks, North Dakota, USA |
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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. |
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Keywords: | Bernoulli variables Cochran-Mantel-Haenszel statistics Conditional Ratio Dependence Directional dependence Odds ratio Risk Ratio |
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