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. It is distinguished
between global effects and category-specific effects where the
latter allow that the effect varies 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 Wilcoxon-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.