Skip Navigation

Biometrika 2006 93(1):197-206; doi:10.1093/biomet/93.1.197
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Chaganty, N. R.
Right arrow Articles by Joe, H.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2006 Biometrika Trust

Range of correlation matrices for dependent Bernoulli random variables

N. Rao Chaganty1 and Harry Joe2

1 Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia 23529-0077, U.S.A. rchagant{at}odu.edu, 2 Department of Statistics, University of British Columbia, 6356 Agricultural Road, Vancouver, British Columbia, Canada V6T1Z2 harry{at}stat.ubc.ca

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.

Key Words: Fréchet bound; Generalised estimating equation; Multivariate binary; Odds ratio

Received June 2005. Revised October 2005.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer: Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.