Regularization in Partially Ordinal Regression Models

Andreas Groll, TU Dortmund University

Co-authors: Maria Iannario, University of Naples Federico II; Thomas Kneib, Georg-August-Universität Göttingen; Nikolaus Umlauf, Universität Innsbruck

Abstract: We develop an extension of generalized additive models for location, scale and shape (GAMLSS) for analyzing regression data where the dependent variable follows a partially ordered Likert scale resulting from questionnaire responses on an ordinal scale combined with a “don’t know” option. The model is build on the basis of a latent bivariate continuous response vector, such that regression effects can be placed on the expectations of these latent variables (and possibly other parameters of their distribution). To encourage sparsity of the estimated models, we consider regularization penalties such as Lasso. We present the model specification and evaluate it in a simulation study, as well as an empirical analysis of data gathered through a COST project on Fintech and Artificial Intelligence in Finance.