Proportional Odds Models with High‐Dimensional Data Structure. (24th October 2013)

• Record Type: Journal Article
• Authors: Zahid, Faisal Maqbool; Tutz, Gerhard
• Is Part Of: International statistical review. Volume 81:Number 3(2013:Dec.)
• Page Start: 388
• Page End: 406
• Publication Date: 2013-10-24
• Subjects: Logistic regression -- proportional odds model -- variable selection -- likelihood‐based boosting -- penalization -- hit rate -- false alarm rate; Statistics -- Periodicals; Statistics -- Bibliography -- Periodicals; Statistics -- Bibliography; Statistics -- Periodicals; Statistique; Statistique -- Périodiques; Statistique -- Bibliographie -- Périodiques; Statistique -- Étude et enseignement -- Périodiques; Statistique -- Étude et enseignement -- Bibliographie -- Périodiques; Ressource Internet (Descripteur de forme); Périodique électronique (Descripteur de forme); 519.2
• DOI: 10.1111/insr.12032
• Languages: English
• ISSNs: 0306-7734

Abstract

Summary: The proportional odds model is the most widely used model when the response has ordered categories. In the case of high‐dimensional predictor structure, the common maximum likelihood approach typically fails when all predictors are included. A boosting technique pomBoost is proposed to fit the model by implicitly selecting the influential predictors. The approach distinguishes between metric and categorical predictors. In the case of categorical predictors, where each predictor relates to a set of parameters, the objective is to select simultaneously all the associated parameters. In addition, the approach distinguishes between nominal and ordinal predictors. In the case of ordinal predictors, the proposed technique uses the ordering of the ordinal predictors by penalizing the difference between the parameters of adjacent categories. The technique has also a provision to consider some mandatory predictors (if any) that must be part of the final sparse model. The performance of the proposed boosting algorithm is evaluated in a simulation study and applications with respect to mean squared error and prediction error. Hit rates and false alarm rates are used to judge the performance of pomBoost for selection of the relevant predictors.