A General Framework for the Selection of Effect Type in Ordinal Regression

Pößnecker, Wolfgang und Tutz, Gerhard (18. Januar 2016): A General Framework for the Selection of Effect Type in Ordinal Regression. Department of Statistics: Technical Reports, Nr. 186

Abstract

In regression models for ordinal response, each covariate can be equipped with either a simple, global effect or a more flexible and complex effect which is specific to the response categories. Instead of a priori assuming one of these effect types, as is done in the majority of the literature, we argue in this paper that effect type selection shall be data-based. For this purpose, we propose a novel and general penalty framework that allows for an automatic, data-driven selection between global and category-specific effects in all types of ordinal regression models. Optimality conditions and an estimation algorithm for the resulting penalized estimator are given. We show that our approach is asymptotically consistent in both effect type and variable selection and possesses the oracle property. A detailed application further illustrates the workings of our method and demonstrates the advantages of effect type selection on real data.

• Dokumententyp: Paper
• Keywords: Effect Type Selection, Effect Type Lasso, Proportional Odds Model, Partial Proportional Odds Model, Ordinal Regression, Regularization, Penalization.
• Fakultät: Mathematik, Informatik und Statistik ; Mathematik, Informatik und Statistik > Statistik ; Mathematik, Informatik und Statistik > Statistik > Technische Reports
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• Sprache: Englisch