Thomas G. Stewart | Searcharxiv

arXiv2021

Variable Selection in GLM and Cox Models with Second-Generation P-Values

Variable selection has become a pivotal choice in data analyses that impacts subsequent inference and prediction. In linear models, variable selection using Second-Generation P-Values (SGPV) has been shown to be as good as any other algorithm available to researchers. Here we extend the idea of Penalized Regression with Second-Generation P-Values (ProSGPV) to the generalized linear model (GLM) and Cox regression settings. The proposed ProSGPV extension is largely free of tuning parameters, adaptable to various regularization schemes and null bound specifications, and is computationally fast. Like in the linear case, it excels in support recovery and parameter estimation while maintaining strong prediction performance. The algorithm also preforms as well as its competitors in the high dimensional setting (n>p). Slight modifications of the algorithm improve its performance when data are highly correlated or when signals are dense. This work significantly strengthens the case for the ProSGPV approach to variable selection.

stat.ME↗

arXiv2021

Variable Selection with Second-Generation P-Values

Many statistical methods have been proposed for variable selection in the past century, but few balance inference and prediction tasks well. Here we report on a novel variable selection approach called Penalized regression with Second-Generation P-Values (ProSGPV). It captures the true model at the best rate achieved by current standards, is easy to implement in practice, and often yields the smallest parameter estimation error. The idea is to use an l0 penalization scheme with second-generation p-values (SGPV), instead of traditional ones, to determine which variables remain in a model. The approach yields tangible advantages for balancing support recovery, parameter estimation, and prediction tasks. The ProSGPV algorithm can maintain its good performance even when there is strong collinearity among features or when a high dimensional feature space with p > n is considered. We present extensive simulations and a real-world application comparing the ProSGPV approach with smoothly clipped absolute deviation (SCAD), adaptive lasso (AL), and mini-max concave penalty with penalized linear unbiased selection (MC+). While the last three algorithms are among the current standards for variable selection, ProSGPV has superior inference performance and comparable prediction performance in certain scenarios. Supplementary materials are available online.

stat.ME↗