Non- and semiparametric marginal regression models for ordinal response

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.