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Subject:

How do regressors compete for variance if not orthogonalized?

From:

Dorian P.

Date:

Wed, 4 Mar 2009 10:55:34 +0100

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 ```Dear all, I was discussing this in private with another member of the list but we cannot fully understand it. 1. When we bypass orthogonalization the variance of the model is explained by all regressors in a kind of *competition*. I don't understand how this competition works statistically but actually I need the regressors to compete as much as possible with each other. This way I can compare them in a paired t-test at the 2nd level in order to find areas where one explains more variance than the other (independently of the order I put them in SPM). Does this make sense to you? 2. Also discussing with my friend, I thought having one model with 5 non-orthogonalized (i.e. independent) parametric modulations is like having 5 GLMs. Apparently this is not true because in the first case we have X variance exlpained by 5 modulations, while in the second case we have X variance explained by 1 modulation each time. But wouldn't the comparison in a paired t-test produce the same *winner* ? It make sense logically: if two collinear regressors A and B explain 50% variance, with regressor A 30%, and regressor B 40%, their variance overlaps but regressor B will result with higher T values, no matter of measured in the same GLM or in two separate GLMs. So is it better to keep them in the same GLM or split them up? Would the result be the same? 3. Somebody advised to orthogonalize modulations (not with each-other but) with the main condition . Does this produce any benefit? Help is highly appreciated from experts or non-experts. :) Dorian Ruhr University Bochum ```