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Regularized Ordinal Regression and the ordinalNet R Package.

Michael J Wurm1, Paul J Rathouz2, Bret M Hanlon3

  • 1Department of Statistics, University of Wisconsin-Madison, wurm@uwalumni.com.

Journal of Statistical Software
|September 13, 2021
PubMed
Summary

We introduce a new algorithm for regularized ordinal regression, enhancing variable selection and prediction accuracy. The elementwise link multinomial-ordinal (ELMO) class and the ordinalNet R package are presented.

Keywords:
elastic netlassomultinomial regressionordinal regressionvariable selection

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Area of Science:

  • Statistics
  • Machine Learning
  • Biostatistics

Background:

  • Regularization techniques like lasso and elastic net improve regression models but are often unavailable for ordinal regression.
  • Ordinal regression models are crucial in many applications, yet lack integration with popular regularized regression software.

Purpose of the Study:

  • To develop a coordinate descent algorithm for fitting ordinal regression models with an elastic net penalty.
  • To generalize these models into the elementwise link multinomial-ordinal (ELMO) class, accommodating ordered and unordered categorical data.
  • To introduce an elastic net penalty applicable to both model forms and for shrinking non-ordinal models toward ordinal ones.

Main Methods:

  • A coordinate descent algorithm is proposed for fitting ordinal regression models with an elastic net penalty.
  • The elementwise link multinomial-ordinal (ELMO) class is defined, encompassing multinomial and ordinal logistic regression.
  • An elastic net penalty is introduced for the ELMO class, enabling shrinkage towards ordinality.

Main Results:

  • The proposed algorithm effectively fits a broad class of regularized ordinal regression models.
  • The ELMO class provides a flexible framework for modeling various categorical response types.
  • The elastic net penalty facilitates variable selection and coefficient shrinkage within this class.

Conclusions:

  • The developed methods extend regularized regression capabilities to ordinal and multinomial models.
  • The new ELMO class and its associated elastic net penalty offer enhanced flexibility and control.
  • The R package ordinalNet provides a practical implementation for researchers and practitioners.