We have a variable, X, measured at pre-study and post-study and are studying the effects of X across changes of several outcome variables (post-pre).
Currently we are using regression models to investigate the change in X (post-pre) effect while including pre-study X to control for the initial level of X.
We are also interested in if the relationship between change in X and the outcome variable differs by post-X level. Thus I am considering adding post-X level and the interaction between change in X and post-X level to the model.
Therefore the model would include pre-X, post-X, change-X, and change-X*post-X as predictors. This seems like a problem to me, especially since change-X is a function of pre-X and post-X. However we would still like to control for pre-X level. Is there a better model to address the question of if the change-X effect differs by post-X level?