JDS Journal of Data Science 1683-86021680-743X1680-743X School of Statistics, Renmin University of China JDS1188 10.6339/25-JDS1188 Statistical Data Science Exploring Massive Risk Factors of Categorical Outcomes via Supervised Dimension Reduction LiYan1 AlemdjrodoKangni2 LinYanzhu3 ZhangMin1 ZhangDabaodabao.zhang@uci.edu1∗ Department of Epidemiology and Biostatistics, University of California, Irvine, CA 92617, United States Department of Mathematics and Statistics, Georgia State University, Atlanta, GA 30303, United States Eli Lilly and Company, Indianapolis, IN 46285, United States Corresponding author. Email: dabao.zhang@uci.edu. 20252752025234607623 Supplementary Material

The MATLAB code for gPOCRE is available on the journal’s website. The ISOLET data by Fanty and Cole (1990) can be downloaded from https://www.openml.org/search?type=data&sort=version&status=any&order=asc&exact_name=isolet&id=41966, and the breast cancer data can be found in the R package mixOmics (https://mixomics.org/).

2992024252025 2025 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2025 Open access article under the CC BY license.

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.

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