I have a fairly large dataset ($\approx 3 \bar{M}$ observations for a dozen candidate predictors) and I would like to perform a logistic regression on that dataset. I have a problem of separation in that dataset so usual model can't converge. That's why I am using Firth penalization (logistf package for R) to have my model to adjust.
I would like to select the best subset of variables for my final model but I can't find the proper way to do that. I know that stepwise selection is out of question and I usually would use L1 or L2 penalized regression so that some coefficients are reduced to 0.
My problem is : the function I am using to adjust my model doesn't handle extra penalization so no Elasticnet-Firth regression.
Is there, apart from stepwise selection, another way to select my variables?