$\ell_1$-penalized Multinomial Regression: Estimation, inference, and prediction, with an application to risk factor identification for different dementia subtypes

TL;DR

This paper develops a robust $ ext{L}_1$-penalized multinomial regression framework that enables accurate estimation, inference, and prediction, with an application to identifying risk factors for dementia subtypes.

Contribution

It extends debiasing techniques to multinomial models, providing valid confidence intervals and $p$-values, and demonstrates robustness under model misspecification and non-i.i.d. data.

Findings

Debiasing method outperforms existing inference methods in simulations.

The approach successfully identifies key predictors for dementia subtypes.

Method remains robust under violations of model assumptions.

Abstract

High-dimensional multinomial regression models are very useful in practice but have received less research attention than logistic regression models, especially from the perspective of statistical inference. In this work, we analyze the estimation and prediction error of the contrast-based $\ell_1$-penalized multinomial regression model and extend the debiasing method to the multinomial case, providing a valid confidence interval for each coefficient and $p$-value of the individual hypothesis test. We also examine cases of model misspecification and non-identically distributed data to demonstrate the robustness of our method when some assumptions are violated. We apply the debiasing method to identify important predictors in the progression into dementia of different subtypes. Results from extensive simulations show the superiority of the debiasing method compared to other inference methods.