Global cross-ratio models for bivariate, discrete, ordered responses.
A family of statistical models is presented for bivariate, discrete response to a regressor when both components of the response have ordered categories. Association between components is expressed in terms of global cross-ratios, cross-product ratios of quadrant probabilities, for each double dichotomy of the response table of probabilities into quadrants (Pearson and Heron, 1913, Biometrika 9, 159-315). These models are extensions to the work of Plackett (1965, Journal of the American Statistical Association 60, 516-522) and Mantel and Brown (1973, Biometrics 29, 649-665). The marginal cumulative probabilities may satisfy linear logistic or other generalized linear models (McCullagh, 1980, Journal of the Royal Statistical Society, Series B 42, 109-142). An analysis of patients' postoperative pain level and medication frequency illustrates these methods.
D000704:Analysis of Variance; D001699:Biometry / Q000379:methods; D002986:Clinical Trials as Topic; D004381:Duodenal Ulcer / Q000601:surgery; D006801:Humans; D008962:Models, Theoretical; D010149:Postoperative Pain / Q000188:drug therapy / Q000503:physiopathology; D012107:Research Design