Generalized Semiparametrically Structured Ordinal Models

Semiparametrically structured models are defined as a class of models for which the predictors may contain parametric parts, additive parts of covariates with an unspecified functional form, and interactions which are described as varying coefficients. In the case of an ordinal response the complexity of the predictor is determined by different sorts of effects. Global effects and category-specific effects are distinguished; the latter allow the effect to vary across response categories. A general framework is developed in which global as well as category-specific effects may have unspecified functional form. The framework extends various existing methods of modeling ordinal responses. The Wilkinson-Rogers notation is extended to incorporate smooth model parts and varying coefficient terms, the latter being important for the smooth specification of category-specific effects.