Range of correlation matrices for dependent Bernoulli random variables

• 成果类型: Article
• 署名作者: Chaganty, NR; Joe, H
• 署名单位: Old Dominion University; University of British Columbia
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/93.1.197
• 发表日期: 2006
• 页码: 197206
• 关键词: binary variables; distributions

摘要

We say that a pair (p, R) is compatible if there exists a multivariate binary distribution with mean vector p and correlation matrix R. In this paper we study necessary and sufficient conditions for compatibility for structured and unstructured correlation matrices. We give examples of correlation matrices that are incompatible with any p. Using our results we show that the parametric binary models of Emrich & Piedmonte (1991) and Qaqish (2003) allow a good range of correlations between the binary variables. We also obtain necessary and sufficient conditions for a matrix of odds ratios to be compatible with a given p. Our findings support the popular belief that the odds ratios are less constrained and more flexible than the correlations.