Here is my situation. I have n predictors of interest, and two control variables.
If I put them all together in a multiple regression, I get issues with colinearity (i.e., VIFs are very high, and the coefficients don't make sense).
It seems that my control variables are causing the colinearity. If I run colineaity diagnositics on just my predictors of interest they seem fine. But when I run the diagnosticts on the predictors of interest AND the control variables, I get high VIF values.
I tried predicting my dependent variable with just my control variables and saving the residuals (in other words residualizing my dependent variable). If I then predict these with my predictors of interest, the results are very interpretable, and I don't have any colineaity issues.
Is this an acceptable way to deal with this?
I'm talking specifically about multiple regression and stepwise regression.
Now I am also conducting a LASSO, to compare results. Is there any harm in also doing the same there?
Long story short. I use my control variables to residualize my dependent variable. I then run a model predicting the residualized dependent variable with my variables of interest. Is that okay?