I have 40 treatment variables, and I am interested to find out which ones are related to my dependent variable. I want to do this in an entirely data-driven way. I also have two variables that I would like to control for. One of these control variables is significantly correlated with several of my predictors.
My approach at the moment is to run an adaptive LASSO, forcing in the two control variables (by setting lambda to 0 at both steps of the adaptive LASSO).
- Does using Adaptive LASSO make sense? If not, what approach would be better?
- Does my way of dealing with the control variables make sense? If not, how should I do it?