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Hi Dorian > Dear all, > I was discussing this in private with another member of the list but > we cannot fully understand it. > ok I'll try then .. > 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? > Without orthogonalization (the usual stuff) each regressors fits the data but you are only looking at the 'unique part of variance' for each of them -- with orthogonalization, the order matters because you attribute the maximum of variance to the 1st then 2nd etc ...(it's like performing a simple linear regression with the 1st regressor then another simple linear regression with the 2nd regressor on the residuals of the 1st fit etc .. ) The way I think of this is using a diagram: think you have 3 conditions represented by 3 circles. Case 1, the 3 circles do not overlap - easy each condition got its own part of variance explained. Case 2, the circles overlap - well that's where you have several options (that also relates to the different sum of squares options in the statisitcal packages) ; the unique part of variance like in SPM is that you estimate the effect of each circle removing the overlapping part ; now if you orthogonalize you give to the 1st regressor its full variance (full circle) then to the 2nd the full variance minus the overlap with the 1st circle etc ... (hope that makes sens to you :-\ ) Note that in all cases (orthogonalization or not) you can perform a 2nd level analysis. > 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? > didn't quite understand this -- the sum square of the effect is computed via a single design matrix no matter you orthogonalize or not .. regarding the T value it depends on the error; if orthogonalized A=30% and B=40% they make up 70% of the variance but if not orthogonalized they may make up more (the overlapping bit) so T values will vary > 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. :) > well orthogonalization is a matter of theory more than stats; it all depends how you are thinking of your data .. say you use a standard regressor and a some orthogonalized modulation then you mean to model the BOLD response the standard way and the remaining variance by the modulation .. now if you do not, well, as you said above, they 'compete' and one voxel will have some variance explained by the standard model and some other part of variance explained by the modulator ; the problem is that they are extremely correlated (large overlap) and thus the unique part of variance will be small .. i.e. it is likely (I think) that you end up having nothing significant .. Hope this helps Cyril -- The University of Edinburgh is a charitable body, registered in Scotland, with registration number SC005336.