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Consider survey data from surgeries. $Y$ represents observed surgical quality and is measured post-surgery; $X$ represents perceived surgical difficulty level and is measured pre and post surgery.

It is desired to assess the relationship between $Y$ and $X_{pre}$ and also $Y$ on $X_{\delta} = X_{post} - X_{pre}$. However, since $X_\delta$ is derived from $X_{pre}$, we know that $X_{pre}$ and $X_{\delta}$ will be highly correlated. One option is to attempt to reduce such multicollinearity via centering.
Any thoughts on alternative strategies and pros/cons? This scenario sounds similar to the commonly discussed scenario of how to handle change scores via ANCOVA (e.g., Senn 2009, Stat Med) when we have change scores with respect to $Y$, but it is different since here we have no baseline $Y$ and a change score for $X$.

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  • $\begingroup$ Are you sure of the high correlation? It is not necessarily the case that X.pre and X.delta will be correlated at all. Also, is it necessary for X.pre and X.delta to appear within the same analysis? $\endgroup$ – whuber Nov 14 '11 at 17:39

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