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#### Options  Subscribe or Unsubscribe   Log In   Get Password Subject: Re: computing normalized beta weights

From:  Date: Mon, 23 Aug 2004 21:34:28 +0100

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 ```hi, sorry to regurgitate an old thread, but i don't quite understand the last post. for the case of multiple PE's (and COPE's), the dimensions in the formula sqrt(c'*b*X*X'*b'*c) do not match up; in my case, i have 320 time points and 8 PE's (4 EV's +temporal derivatives). Therefore, the design matrix is 320x8; if b is a vector, it would have to be 1x320 - how can that be? i tried transposing the design matrix, to make it 8x320 - then, the multiplication becomes (1x1)(1x8)(8x320)(320x8)(8x1)(1x1), for each voxel. However, when the result was divided by the standard deviation of the filtered_func_data, the values were not normalized between -1 and 1. normally, we would divide the betas of the PE's by the beta of the constant column; however, since there is not a constant column, the aforementioned approached seems suitable. Thanks in advance, Ram ------------------------------------- Brain Behavior Laboratory University of Pennsylvania Philadelphia, Pennsylvania, USA On Tue, 12 Aug 2003 14:39:47 +0100, Tim Behrens <[log in to unmask]> wrote: >Ok - there are various levels to this answer. > >It seems to be a sensible thing to do - effectively you want to know the >amount amount of the data's standard deviation which is explained by a >single COPE. > >1) If you've only got one PE, then this is relatively trivial. >the std of the design can be computed easily from design.mat (ascii file >containing design timeseries). Call this sx. The std of the data is > >avwmaths filtered_func_data -Tstd sy > >then the fractional deviation explained by your PE is just > >avwmaths PE -mul sx -div sy Beta_norm > >I think, in this case, you can do this with the unwhitened data as the >whitening matrix is normalised. > >2) If you've got more than 1 PE, life is more complicated (and I don't >think you can compute what you want with simple FSL commands ). > >You need to project the variance explained by all of your EVs onto a >single COPE. > >if you assume the data is white and demeaned then and your Design is >demeaned.. > >the std explained by your cope is: > >sqrt(c'*b*X*X'*b'*c)/dof > >c is cour contrast, b is your vector of PEs, X is your design, dof is your >degrees of freedom > >if it's not white then > >sqrt(c'*b*k*X*X'*k'*b'*c)/dof > >k is the whitening matrix. >(The whitening will change the projection) > >and the standard deviation of the whitened data is just std(k*Y) > >Dividing one by the other should give you what you want. > >Hate to say it, but you might need matlab!! > >cheers >T > > >------------------------------------------------------------------------------- >Tim Behrens >Centre for Functional MRI of the Brain >The John Radcliffe Hospital >Headley Way Oxford OX3 9DU >Oxford University >Work 01865 222782 >Mobile 07980 884537 >------------------------------------------------------------------------------- > >On Tue, 12 Aug 2003, Edward Vessel wrote: > >> Ok, well, here is something that might give you a feeling for the difference. >> In a regression with only a single independent variable, the standardized >> beta equals r (the Pearson's correlation). This would also be true (I think) >> if all the variables were totally uncorrelated in a multiple regression. >> >> The analysis I have done is one in which I want to look at a correlation as my >> statistic, and the standardized Beta coefficient is one way to report a >> factor loading which takes into account that factor's covariance w/ other >> factors. It would be 1 if the activity of a voxel were perfectly predictable >> from that factor, and 0 if that factor had no power to predict it. So, the >> reason for having it is in the _interpretation_ of the statistic. >> >> Typically, it is computed as: >> >> Beta = b * (sx / sy) >> >> where >> >> Beta: standardized regression coefficient (-1 to 1) >> >> b: the unstandardized regression coefficient (can take any value), which is >> the 'regulular' weight, sometimes confusingly referred to as beta but isn't >> standardized) - probably a pe, which is equivalent to one of my copes in this >> case >> >> sx: standard deviation of the EV >> xy: standard deviation of the data >> >> Does that make any sense? >> >> Ed >> >> ```