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Dear Dorian, Dorian P. wrote: > Dear Will, > > I have a question on the topic. Is there a risk that the > orthogonalization A<-B produces a vector C1, which is not uncorrelated > with the vector C2 produced by the reverse orthogonalization B<-A? Is > it possible that we're still measuring correlated activity if we use 2 > GLMs with inverted pmods? > > Otherwise why not getting the orth values from A<-B and B<-A and use > them in one GLM? > > If you do this then you get back the original regressors A and B. The transformations are perhaps best visualised using Venn Diagrams. See eg. Slide 26 onwards of the Statistical Inferece PPT from http://www.fil.ion.ucl.ac.uk/spm/course/slides09-zurich/ These are really to show the difference between F and t-tests (F-test for overall, t for unique contributions). The orthogonalsisation gives the shared variance to the regressors that are not orthogonalised. Best, Will. > > Best regards. > Dorian > > > 2010/2/18 Will Penny <[log in to unmask]>: >> Dear Bruno, >> >> The standard way of thinking about correlated regressors is as follows. >> >> Because A and B are correlated what they can explain about a third >> variable C (eg. BOLD activity) comprises 3 parts >> >> 1. That uniquely attributable to A >> 2. That uniquely attributable to B >> 3. Shared variance - that which could be explained by either A or B >> >> In the orthogonalisation of parametric regressors the second variable is >> orthogonalised wrt the first. So for AB the shared variance is 'given' to >> the A regressor (of course it also has component 1). For BA the shared >> variance is given to the B regressor. >> >> So, in your language, its the second variable thats "cleaned" from the >> first. The one that is *not* orthogonalised gets all the shared variance. >> >> Best, >> >> Will. >> >> Bruno Oertel wrote: >>> Dear SPM users, >>> >>> >>> I know the topic has been discussed in length in this forum and I tried to >>> figure out a solution to my problem by searching the archives, but I am >>> still not 100 percent sure whether or not I am getting it right. >>> >>> >>> I have a first level design where I defined a single condition (stimulus) >>> with two parametric modulators (A and B, both 1st order). I tried both >>> parameter sequences (A-B and B-A) and got different results looking at the >>> simple contrasts for A and B, respectively, depending on the sequence order. >>> Since I am mainly interested in the effects of the parameters, I was a bit >>> confused about this. By searching the archives, I found out that the order >>> of the parameters matters because the 2nd regressor is orthogonalized to the >>> 1st regressor. This would explain, why I got different results for both >>> parameters depending on the sequence order. >>> >>> >>> My question now is, is it right to say that by looking at the simple >>> contrast for A (0 1 0) in the parameter sequence A-B, I am looking at the >>> effects of A "cleaned" from B and vice versa for B (0 1 0) in parameter >>> sequence (B-A)? If that is so, can I go on and do a one sample t-test for A >>> (from sequence A-B) and B (from sequence B-A), respectively, on the >>> second-level to get my group results? Is this a valid approach? >>> >>> >>> Thanks in advance for any insights. >>> >>> Best, >>> >>> Bruno >>> >>> >>> >>> >>> >>> >>> >>> >> -- >> William D. Penny >> Wellcome Trust Centre for Neuroimaging >> University College London >> 12 Queen Square >> London WC1N 3BG >> >> Tel: 020 7833 7475 >> FAX: 020 7813 1420 >> Email: [log in to unmask] >> URL: http://www.fil.ion.ucl.ac.uk/~wpenny/ >> > > -- William D. Penny Wellcome Trust Centre for Neuroimaging University College London 12 Queen Square London WC1N 3BG Tel: 020 7833 7475 FAX: 020 7813 1420 Email: [log in to unmask] URL: http://www.fil.ion.ucl.ac.uk/~wpenny/