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Kauermann, Göran and Tutz, Gerhard (2000): Semiparametric Modeling of Ordinal Data. Collaborative Research Center 386, Discussion Paper 193
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Abstract

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.