I have a pretty good grasp of the pros and cons of different methods of variable selection: LASSO and LARS, AIC, stepwise procedures, etc. But my question is: when modeling, should you conduct variable selection differently if you are using the model for the estimation of fixed effects compared with finding a model that has the best prediction?
I've never used the change-in-estimate variable selection. Is that the best way to do variable selection when you're just looking to estimate fixed effects?