I have forty candidate predictors. They are no colinear. I want to know which ones are related to the DV. Prediction isn't important to me. I want to do this in an exploratory and data-driven way.
What's my best option? I've looked at: multiple regression, stepwise regression (AIC,BIC), best subsets regression, and Adaptive LASSO.
Is one of those better than the others? And if not, what is a better option?
There is a battery of problems with stepwise regression, which also includes best subset regression. Multiple regression is fine if $n\gg p$, otherwise you may be better off using regularization.
Namely, a regularized model (like the LASSO you mentioned), restricts the total size of the parameter estimates. Perhaps somewhat surprisingly, introducing this bias can yield better estimates, especially for small $\frac{n}{p}$ ratios.
hdmpackage of R. – runr Sep 14 '20 at 22:09