Non- and semiparametric marginal regression models for ordinal response

Abstract

We present a class of multivariate regression models for ordinal response variables in which the coefficients of the explanatory variables are allowed to vary as smooth functions of other variables. In the first part of the paper we consider a semiparametric cumulative regression model for a single ordinal outcome variable. A penalized maximum likelihood approach for estimating functions and parameters of interest is described. In the second part we explore a semiparametric marginal modeling framework appropriate for correlated ordinal responses. We model the marginal response probabilities and pairwise association structure by two semiparametric regressions. To estimate the model we derive an algorithm which is based on penalized generalized estimating equations. This nonparametric approach allows to estimate the marginal model without specifying the entire distribution of the correlated response. The methods are illustrated by two applications concerning the attitude toward smoking restrictions in the workplace and the state of damage in a Bavarian forest district.