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Proportional Odds Models with High‐Dimensional Data Structure
Author(s) -
Zahid Faisal Maqbool,
Tutz Gerhard
Publication year - 2013
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12032
Subject(s) - categorical variable , ordinal regression , boosting (machine learning) , ordinal data , odds , statistics , mathematics , mean squared error , ordered logit , feature selection , metric (unit) , model selection , econometrics , computer science , data mining , artificial intelligence , logistic regression , operations management , economics
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.