Semi- and nonparametric 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 by a linear form of covariates. In this article the parametric models are extended to include smooth components in a semiparametric or partially parametric fashion. Parts of the covariates are thereby modeled linearly while other covariates 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. Two data examples demonstrate the applicability of the models.