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).
