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Biometrika 1984 71(3):507-514; doi:10.1093/biomet/71.3.507
© 1984 by Biometrika Trust
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Local versus global association for bivariate ordered responses

JOCELYN R. DALE

Applied Mathematics Division, D.S.I.R. Auckland, New Zealand

Local and global parameters modelling association are examined for contingency tables with both margins ordered responses. Local association parameters are cross-ratios of 2 x 2 subtables of adjacent cell probabilities: global association parameters are cross-ratios of quadrant probabilities. The interpretation and various properties of these measures of association are compared and illustrated.

Key Words: Discretized bivariate normal • Cross-ratio • Global cross-ratio • Ill-defined cutpoint • Likelihood ratio dependence • Odds ratio • Ordered margin • Positive quadrant dependence


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