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Re: Can you trust your SPM orthogonality matrix (?)

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Fri, 7 May 2010 14:37:42 +0100

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 ```Dear Adrian, Dylan, Cyril, I might be kicking into touch but SPM99/2/5/8 have always been claiming to display the magnitude of the cosine of the angle between any two columns of the design matrix, see spm_DesRep.m help: % * Design orthogonality - Displays orthogonality matrix for this design % % The design matrix is displayed as in "Design Matrix" view above, % labelled with the parameter names. % % Under the design matrix the design orthogonality matrix is % displayed. For each pair of columns of the design matrix, the % orthogonality matrix depicts the magnitude of the cosine of the % angle between them, with the range 0 to 1 mapped to white to % black. Orthogonal vectors (shown in white), have cosine of zero. % Colinear vectors (shown in black), have cosine of 1 or -1. % % The cosine of the angle between two vectors a & b is obtained by % dividing the dot product of the two vectors by the product of % their lengths: % % a'*b % ------------------------ % sqrt(sum(a.^2)*sum(b.^2) % % If (and only if) both vectors have zero mean, i.e. % sum(a)==sum(b)==0, then the cosine of the angle between the % vectors is the same as the correlation between the two variates. and effectively there has been a change between SPM99 and SPM2 such that regressors were mean-centered in SPM99 but they are not any more (this is regressed out by the constant term anyway). That said, if you are looking at the correlation between your regressors for design efficiency, you'd better compute the efficiency explicitly for your contrast(s) of interest: (c'*inv(X'X)*c)^-1 http://imaging.mrc-cbu.cam.ac.uk/imaging/DesignEfficiency#head-0fb8e61618d58fcd6d29ca67fee6dd6b79f28e6d All the best, Guillaume. Dr Cyril Pernet wrote: > Hi Adrian > > I'm not SPM developper but it seems to me that mean centering and > orthogonality are kind of separate issues - if you use parametric > modulation, regresors are orthogonalized i.e. in geometrical term theta > = 90 and therefore the correlation which corresponds to the cos(theta) > is 0. Whatever centered or not the correlation is still 0. > > Hope this makes sense. > > Cyril > > >> Dear SPMers, >> >> While checking the design orthogonality matrix of my study, I've found > that >> the mean values of the regressors have a remarkable impact on the design >> orthogonality matrix in SPM8. SPM8 does not mean-center the regressors to >> zero (as SPM99 apparently did), and therefore, the values of the design >> orthogonality matrix do not correspond with the correlations between the >> regressors. So the exact same design leads to quite different > orthogonality >> matrices when comparing SPM8's regressors (attached image1.png) with >> mean-centered regressors (image2.png). >> >> So I'm not quite sure whether the design matrix given by SPM8 (image1) >> contains any meaningful information. Should I judge my design based on the >> orthogonality matrix design given by SPM8 or by the orthogonanlity matrix >> based on mean-centered regressors?. >> >> The following post nicely states the same problem and remained > unanswered on >> the SPM mailing-list: >> >> https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind04&L=SPM&a > mp;P=R98293&1=SPM&9=A&J=on&X=00793331D7D673CA9A&Y=wunibald%4 > 0gmx.ch&d=No+Match%3BMatch%3BMatches&z=4 > 9=A&J=on&X=00793331D7D673CA9A&Y=wunibald%40gmx.ch&d=No+Match%3BMatch%3BMatches&z > =4> >> >> Any clarifications are highly appreciated, >> >> Adrian >> > > > > -- > The University of Edinburgh is a charitable body, registered in > Scotland, with registration number SC005336. -- Guillaume Flandin, PhD Wellcome Trust Centre for Neuroimaging University College London 12 Queen Square London WC1N 3BG ```