Weak signal identification and inference in penalized likelihood models for categorical responses

TL;DR

This paper introduces a unified method for identifying weak signals and making valid inferences in penalized likelihood models, especially for categorical responses, improving variable selection and estimation accuracy.

Contribution

It develops a novel approach using selection probabilities for weak signal detection and a two-step inference procedure, enhancing existing methods.

Findings

Proposed method outperforms existing techniques in simulations.

Effective in identifying weak signals in categorical response models.

Validated on diabetes dataset with improved inference accuracy.

Abstract

Penalized likelihood models are widely used to simultaneously select variables and estimate model parameters. However, the existence of weak signals can lead to inaccurate variable selection, biased parameter estimation, and invalid inference. Thus, identifying weak signals accurately and making valid inferences are crucial in penalized likelihood models. We develop a unified approach to identify weak signals and make inferences in penalized likelihood models, including the special case when the responses are categorical. To identify weak signals, we use the estimated selection probability of each covariate as a measure of the signal strength and formulate a signal identification criterion. To construct confidence intervals, we propose a two-step inference procedure. Extensive simulation studies show that the proposed procedure outperforms several existing methods. We illustrate the proposed method by applying it to the Practice Fusion diabetes data set.