A General Framework for the Selection of Effect Type in Ordinal Regression 2/2

In regression models for ordinal response, each covariate can be
equipped with either a simple, global effect or a more flexible and
complex effect which is specific to the response categories.
Instead of a priori assuming one of these effect types, as is done
in the majority of the literature, we argue in this paper that
effect type selection shall be data-based. For this purpose, we
propose a novel and general penalty framework that allows for an
automatic, data-driven selection between global and
category-specific effects in all types of ordinal regression
models. Optimality conditions and an estimation algorithm for the
resulting penalized estimator are given. We show that our approach
is asymptotically consistent in both effect type and variable
selection and possesses the oracle property. A detailed application
further illustrates the workings of our method and demonstrates the
advantages of effect type selection on real data.