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I can't agree more, better looking at efficiency than correlation ..
> Hi Cyril,
>
>>> Is there some way of interpreting the cosine similarity of
>>> non-centered vectors (with regards to design efficiency) that I'm not
>>> quite catching?
>
>> I don't uinderstand where is the problem cos(theta) is the angle
>> between regressors, so orthogonal regressors means > 90 degrees and
>> thus cos(theta) = 0 ; since you project the data onto that matrix it
>> is what matters ..
>
>
> Thanks for getting back to me. Perhaps I need to refresh my maths!
> I'll pop open a textbook and see if I can get this straight. I'm
> ashamed to say that I had forgotten that we already flogged this
> horse on the list a few years back:
> https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=spm;783b18e.1005
>
> Anyhow, to give you a sense of what I find confusing: Take an ABAB
> block design. To maximize efficiency of detecting a difference
> between A and B you want them to be anti-correlated. I have such a
> design handy. Correlation between A and B for centered and
> un-centered designs is -0.9 (so pretty good for [1 -1 0]). The
> cos-theta for the centered is also -0.9, but for the uncentered
> design it's 0.32. The confusion comes from wanting to use the
> orthogonality check prior to collecting data to evaluate design
> efficiency. Given a result of 0.32 I would keep tinkering, however
> had I centered the regressors, I would have seen that the design was
> already optimal. . I think it's not so much that the cos(theta) is
> incorrect (it does what it says on the tin) only that it strikes me
> as somewhat unhelpful in attempting to optimize design efficiency. Of
> course, as it's been mentioned before, what we really should be doing
> is evaluating the efficiency of the contrast we care about (which
> will span the constant column and thus it doesn't matter if
> regressors are centered or not) so in some sense I admit this is all
> a moot point.
>
>
>
>
>
--
Dr Cyril Pernet,
Academic Fellow
Brain Research Imaging Center
Division of Clinical Neurosciences
University of Edinburgh
Western General Hospital
Crewe Road
Edinburgh
EH4 2XU
Scotland, UK
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http://www.sinapse.ac.uk/
http://www.sbirc.ed.ac.uk/cyril
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