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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?

kjetil b halvorsen
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Glen
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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 06:42
  • +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
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    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](http://stats.stackexchange.com/q/3466/1036). 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](http://stats.stackexchange.com/a/21781/1036) with change scores and levels simultaneously on the right hand side. – Andy W Jul 13 '12 at 12:09

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