  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.
