A Likelihood-Based Approach for Multivariate Categorical Response Regression in High Dimensions

• Published in: Journal of the American Statistical Association Vol. 118; no. 542; pp. 1402 - 1414
• Main Authors: Molstad, Aaron J., Rothman, Adam J.
• Format: Journal Article
• Language: English
• Published: Alexandria Taylor & Francis 03.04.2023; Taylor & Francis Ltd
• Subjects: Algorithms; Asymptotic methods; Bivariate analysis; Cancer; Categorical data analysis; Classification; Convex optimization; Generalizations; Multi-label classification; Multinomial logistic regression; Multivariate analysis; prediction; Regression analysis; Regression models; risk; Simulation; Statistical methods; Statistics; Usefulness
• ISSN: 0162-1459; 1537-274X; 1537-274X
• DOI: 10.1080/01621459.2021.1999819

We propose a penalized likelihood method to fit the bivariate categorical response regression model. Our method allows practitioners to estimate which predictors are irrelevant, which predictors only affect the marginal distributions of the bivariate response, and which predictors affect both the marginal distributions and log odds ratios. To compute our estimator, we propose an efficient algorithm which we extend to settings where some subjects have only one response variable measured, that is, a semi-supervised setting. We derive an asymptotic error bound which illustrates the performance of our estimator in high-dimensional settings. Generalizations to the multivariate categorical response regression model are proposed. Finally, simulation studies and an application in pan-cancer risk prediction demonstrate the usefulness of our method in terms of interpretability and prediction accuracy. Supplementary materials for this article are available online.