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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?

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since change-X is a [linear] function of pre-X and post-X they three cannot be linear predictors simultaneously. Remove one of them as a redundant term. – ttnphns Jul 13 '12 at 6:42
+1: I think you can use pre-X to predict the outcome, use pre-X and change-X to study the effect on the outcome variable or else you can cross-sectionally examine post-X on the outcome at post- time – BGreene Jul 13 '12 at 10:00
There is a big literature on using change scores, some excellent references given in this question, Best practice when analysing pre-post treatment-control designs. Also besides just the model being identified, when the independent variables are just different linear combinations it makes it difficult to interpret (as you can just arbitrarily re-write them). I give an example for this question with change scores and levels simultaneously on the right hand side. – Andy W Jul 13 '12 at 12:09

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