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Semi- and Nonparametric Modeling of Ordinal Data
Abstract: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.
Keywords:Continuation ratio model  Cumulative model  Local likelihood  Profile likelihood  Proportional odds model  Semiparametric model  Sequential model  Smoothing  Varying coefficient model
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