Post-selection inference in generalized linear models via parametric programming

TL;DR

This paper introduces a unified framework for post-selection inference in generalized linear models using parametric programming, improving inference accuracy after variable selection.

Contribution

It adapts a parametric programming approach to non-Gaussian GLMs, enabling effective post-selection inference that corrects naive methods and enhances efficiency.

Findings

Effective correction of naive inference ignoring variable selection

Greater efficiency compared to polyhedral-based methods

Validated on synthetic data with various non-Gaussian responses

Abstract

We propose a unified framework to draw inferences for regression coefficients in a generalized linear model (GLM) following Lasso-based variable selection. We adapt to non-Gaussian GLMs a recently developed parametric programming strategy for post-selection inference in the linear model with a Gaussian response by drawing parallels between maximum likelihood estimation in GLMs and least squares estimation in linear models. We then conduct post-selection inference based on a linearized model for pseudo response and covariate data strategically created based on the raw data. Using synthetic data generated from regression models for three different types of non-Gaussian responses in simulation experiments, we demonstrate that the proposed method effectively corrects the naive inference that ignores variable selection while achieving greater efficiency than a polyhedral-based post-selection adjustment.