Kauermann, Göran and Tutz, Gerhard
Semiparametric Modeling of Ordinal Data.
Collaborative Research Center 386, Discussion Paper 193
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.