Dear SPM colleagues
I'm attempting to scale regressors in a design matrix so that their sum of squares equals 1. The reason to do this is that I have subjects with different HRF timings in my task and I want to be able to calculate 'amplitude' images (or 'derivative boost') from canonical and temporal derivative images using the formula in Vince Calhoun's 2004 paper, but this formula makes assumptions about the scaling of canonical and derivative regressors.
The key in their methods is that the HRFs are scaled correctly. If you scale the design matrix, then you will be biased by the number trials in each condition.
I've looked at previous helpful postings by Donald McLaren
See http://www.jiscmail.ac.uk/cgi-bin/wa.exe?A2=SPM;fa723f27.0908 (Aug 17 2009)
..as well as the 2010 Neuroimage paper by Jason Steffener and others which highlights the scaling issue.
My first question is a check on some basic GLM maths. I thought that T values should not change with regressor scaling, even though beta values do, as the variance estimate changes too by the right amount. Can someone confirm whether this is correct, as I have different T results following my scaling operation. If this is correct, something is not right.
If you scale the HRF regressors (not DM), then the statistics shouldn't change. However, if you scale each column of the DM, then the T-statistics can change as you are changing the relationships between different columns.
IF something is not right, can someone advise on what is not working about normalising columns of SPM.xX.X so that sum of squares of each column = 1? This is how I understand the recommendations in Steffener et al 2010 and this is what I've done (followed by re-estimation of the model & contrasts, obviously). But I may well have misunderstood something in the method.
I'd email Jason about how to normalise the HRFs rather than the DM.
Thanks!
Alexa
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