title: The analysis of dependence in cross-classifications having ordered categories, using log-linear models for frequencies and log-linear models for odds.
abstract: To analyse the dependence of a qualitative (dichotomous or polytomous) response variable upon one or more qualitative explanatory variables, log-linear models for frequencies are compared with log-linear models for odds, when the categories of the response variable are ordered and the categories of each explanatory variable may be either ordered or unordered. The log-linear models for odds express the odds (or log odds) pertaining to adjacent response categories in terms of appropriate multiplicative (or additive) factors. These models include the 'null log-odds model', the 'uniform log-odds model', the 'parallel log-odds model', and other log-linear models for the odds. With these models, the dependence of the response variable (with ordered categories) can be analyzed in a manner analogous to the usual multiple regression analysis and related analysis of variance and analysis of covariance. Application of log-linear models for the odds sheds light on earlier applications of log-linear models for the frequencies in contingency tables with ordered categories.
mesh_terms: D001699:Biometry; D006801:Humans; D007902:Length of Stay; D008954:Models, Biological; D012107:Research Design; D012565:Schizophrenic Psychology; D014789:Visitors to Patients