Regularization and Model Selection for Ordinal-on-Ordinal Regression with Applications to Food Products' Testing and Survey Data

TL;DR

This paper introduces novel regularization techniques for ordinal-on-ordinal regression, specifically tailored for applications like food testing and survey analysis, enhancing predictor selection and smoothing in cumulative logit models.

Contribution

It develops modified group lasso and fused lasso penalties that incorporate the ordinal structure of predictors, advancing model selection methods for ordinal-on-ordinal regression.

Findings

Modified group lasso improves predictor selection with ordinal data

Fused lasso effectively fuses predictor categories and selects relevant factors

Methods perform well in simulations and real-world applications

Abstract

Ordinal data are quite common in applied statistics. Although some model selection and regularization techniques for categorical predictors and ordinal response models have been developed over the past few years, less work has been done concerning ordinal-on-ordinal regression. Motivated by a consumer test and a survey on the willingness to pay for luxury food products consisting of Likert-type items, we propose a strategy for smoothing and selecting ordinally scaled predictors in the cumulative logit model. First, the group lasso is modified by the use of difference penalties on neighboring dummy coefficients, thus taking into account the predictors' ordinal structure. Second, a fused lasso-type penalty is presented for the fusion of predictor categories and factor selection. The performance of both approaches is evaluated in simulation studies and on real-world data.