Exploring Massive Risk Factors of Categorical Outcomes via Supervised Dimension Reduction

We propose to explore high-dimensional data with categorical outcomes by generalizing the penalized orthogonal-components regression method (POCRE), a supervised dimension reduction method initially proposed for high-dimensional linear regression. This generalized POCRE, i.e., gPOCRE, sequentially builds up orthogonal components by selecting predictors which maximally explain the variation of the response variables. Therefore, gPOCRE simultaneously selects significant predictors and reduces dimensions by constructing linear components of these selected predictors for a high-dimensional generalized linear model. For multiple categorical outcomes, gPOCRE can also construct common components shared by all outcomes to improve the power of selecting variables shared by multiple outcomes. Both simulation studies and real data analysis are carried out to illustrate the performance of gPOCRE.