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I am currently conducting analyses where I wish to investigate how one variable (M) mediates the association between SES (3-level categorical variable) and a measure of health (continuous variable). The association between M and health is curvilinear, meaning that both low and high levels of M is associated with increased health problems.

Any suggestions on how to go about achieving this? I have studied the literature on mediation, but haven't been able to find an approach which seems suitable.

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This is not a purist's answer, but it would probably make things easier on you and your audience if you categorized M into 3 or 5 levels. Then it would be a straightforward anova task to show how different combinations of M and SES are linked with different health scores.

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I am not 100% sure, but I think the mediation package for R can do what you want as it covers a wide range of models that can act as the mediator (I am not totally sure how it works with the categorial variable, but you will find out).

Have a look at the nice vignette or the homepage of Kosuke Imai for some papers on the package.

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    $\begingroup$ Thanks for the suggestion, however, as you hint at, there are problems with categorical variables when the relationship with the outcome is not linear. It only analyzes the 0 and 1 level of the predictor variable, and when there is a different association at different values of predictor, it will not work. $\endgroup$
    – Tormod
    Sep 19, 2011 at 17:08

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