  Regularization techniques such as the lasso (Tibshirani 1996) and elastic net
(Zou and Hastie 2005) can be used to improve regression model coefficient
estimation and prediction accuracy, as well as to perform variable selection.
Ordinal regression models are widely used in applications where the use of
regularization could be beneficial; however, these models are not included in
many popular software packages for regularized regression. We propose a
coordinate descent algorithm to fit a broad class of ordinal regression models
with an elastic net penalty. Furthermore, we demonstrate that each model in
this class generalizes to a more flexible form, for instance to accommodate
unordered categorical data. We introduce an elastic net penalty class that
applies to both model forms. Additionally, this penalty can be used to shrink a
non-ordinal model toward its ordinal counterpart. Finally, we introduce the R
package ordinalNet, which implements the algorithm for this model class.
