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I am centering variables that enter interaction terms in my linear regression. To check the robustness of my results, I exclude certain cases from the original sample, and re-run the regression analysis in that modified sample.

Which of the following approaches to centering of the variables is more appropriate to compare the results of the regression analysis between the modified and original sample?

  1. use the means from the original sample for centering in both regression analysis; or
  2. use the means from the original sample for centering for the regression in the original sample, and use the means from the
    modified sample for centering for the regression in the modified sample.

In the methods books I have consulted, notably Cohen, Cohen, Aiken & West (2003) and Tabachnick & Fidell (2007), as well as on the web, I have not been able to find a recommendation. I only found the following consideration:

If you do center, be consistent throughout, i.e. different sample selections could produce different means, so comparing results produced by different centerings could be deceptive. see Interpreting Interaction Effects; Interaction Effects and Centering

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I would typically center on "some meaningful value somewhere in the middle of the data". For example, I would center years of schooling in the US educational system at 12 years (finish high school), occupational status at the occupational status of a high school teacher or a nurse, number of hours a week spent working at 40, etc. This makes it much easier and less abstract to talk about the coefficients, and it does not suffer from the problem you have found.

If you really cannot avoid using the mean, I would stick to one mean, which would probabily be the mean in the original sample.

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