Regularized Ordinal Regression and the ordinalNet R Package

Regularized Ordinal Regression and the ordinalNet R Package

ordinal regression, multinomial regression, variable selection, lasso, elastic net

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, that can be used to model either ordered or unordered
categorical response data. We call this the elementwise link multinomial-ordinal class,
and it includes widely used models such as multinomial logistic regression (which also has
an ordinal form) and ordinal logistic regression (which also has an unordered multinomial
form). We introduce an elastic net penalty class that applies to either model form, and
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.

Michael J. Wurm

https://www.jstatsoft.org/article/view/v099i06

University of
Wisconsin–Madison

August 2021

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