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We have a metric dependent variable (impairment, scale 0-40), and a larger number of symptoms of a mental disorder, each on a scale of 0 (nonexistant) - 3 (very severe).

We try to find out whether symptoms are associated with different levels of impairment. We test this in two steps. First, we use a linear regression, predicting impairment by individual symptoms, in which symptoms explain about 45% of the variance of impairment. Second, we use the LMG metric of the R package RELAIMPO (Grömping, 2006; "relative importance") to allocate unique R^2 shares to each symptom. The result is that individual symptoms vary drastically in their explained variance of impairment. The estimate range between 1% and 20% explained.

This fits nicely with our hypothesis:

Some symptoms are more impairing than others, because they are different things (and not simply interchangeable indicators of the same latent). Impairment depends on the nature of symptoms (thus, sum-scores of symptoms might obfuscate information).

However, a reviewer put forward an alternative hypothesis:

Impairment depends on the severity of the symptoms, irrespective of the nature of symptoms. This hypothesis would state that all symptoms that explain a lot of variance are symptoms that have a high mean, and that symptoms that explain moderate amounts of variance are average severe symptoms, and that symptoms that explain only little variance are only slightly debilitating.

I don't quite know how to test this idea, and would very much appreciate input.

(EDIT: A colleague of mine suggested to test a null hypothesis model that uses the score sum only (i.e. forcing all betas to be identical) against the model with individual betas (13 degree of freedom test), but frankly, I don't understand what that would do and how it would help).

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Maybe I am missing something but why not just look at the relationship between importance (from your previous output) and average severity of each symptom? You could do a regression with DV = importance and IV = average score.

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  • $\begingroup$ Peter, I used a correlation instead of a regression, but I guess the idea is basically the same: find shared variance. However, the data matrix is tiny (14 symptoms x 2 rows, 1 for importance, 1 for average score), I hope that is no problem? The correlation is .45, and I am not sure about the interpretation: "the importance of a symptom on impairment is positively associated to the mean, but the mean does not entirely explain importance?" Would you recommend a regression over a correlation? $\endgroup$
    – Torvon
    Mar 28 '13 at 16:28
  • $\begingroup$ They will give similar meanings; I thought of regression because you clearly have one dependent variable. $\endgroup$
    – Peter Flom
    Mar 28 '13 at 16:31

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