Semiparametric Modeling of Ordinal Data

Parametric models for categorical ordinal response variables, like
the proportional odds model or the continuation ratio model, assume
that the predictor is given as a linear form of covariates. In this
paper the parametric models are extended to a semiparametric or
partially parametric form where parts of the covariates are modeled
linearly and parts are modeled as unspecified but smooth functions.
Estimation is based on a combination of local likelihood and
profile likelihood and asymptotic properties of the estimates are
derived. In a simulation study it is demonstrated that the profile
likelihood approach is to be preferred over a backfitting
procedure. A data example shows the applicability of the models.