Regularized Ordinal Regression and the ordinalNet R Package.

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 (ELMO) 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.

Semiparametric Generalized Linear Models with the gldrm Package.

This paper introduces a new algorithm to estimate and perform inferences on a recently proposed and developed semiparametric generalized linear model (glm). Rather than selecting a particular parametric exponential family model, such as the Poisson distribution, this semiparametric glm assumes that the response is drawn from the more general exponential tilt family. The regression coefficients and unspecified reference distribution are estimated by maximizing a semiparametric likelihood. The new algorithm incorporates several computational stability and efficiency improvements over the algorithm originally proposed. In particular, the new algorithm performs well for either small or large support for the nonparametric response distribution. The algorithm is implemented in a new R package called gldrm.