Manish -
As you can see from the equation for contrast variance there is a component
of error variance s^2 and a component of (contrast-specific) design
variance, but I suspect in comparing designs you are interested in the
latter.
Given similarly scaled designs with similar haemodynamic models etc you can
compare and attempt to maximise design efficiency. This means that by
making the assumption that the residual error is equivalent you don't need
to estimate your alternate models but can compare just the contrast &
design part of the equation:
Design variance is c'(X'X)^-1c which you want to minimise
Efficiency is proportional to trace(c'(X'X)^-1 c)^-1
An excellent resource on this and related issues is Rik Henson's info on
the CBU wiki - http://imaging.mrc-cbu.cam.ac.uk/imaging/DesignEfficiency.
An example of a study which looks at both variance factors is Mechelli
Price Henson & Friston, NeuroImage 2003
HTH, Alexa
On Sep 25 2006, Ged Ridgway wrote:
>Hi Manish,
>
>Hopefully someone with more stats knowledge has replied off
>list-already, but if not, I'll try to point you in the right direction
>as well as I can.
>
>I think you should be able to get all the variances you're interested
>in using contrasts, and with the formula
> var(c'*beta) = s^2*c'*pinv(X'*X)*c
>for some contrast c of the parameters beta. Where s^2 is the estimated
>variance or residual mean square, which I believe is what SPM stores
>in the file ResMS.img under your results directory.
>
>So if you define suitable contrasts for the subject and/or task
>regressors in your design matrix X then you should be able to recover
>your desired variances. It won't matter what order of A and I you
>have, so long as the design matrix correctly codes this.
>
>I hope this helps (and isn't wrong!), and to be honest, I hope someone
>else replies with a better answer...
>
>Best,
>Ged.
>
>
>Manish Dalwani wrote:
>> Hi SPM'ers,
>>
>> I have a conceptual question and would be grateful if someone could help
>> me understand it. Let's say I have rapid event task where I have 2
>> conditions Active and Inactive. I, originally, had the task designed as
>> Active Inactive Active Inactive....
>>
>> But have decided to add jitter and pseudorandomize the trials....so it
>> could be A I A A I A I I .....for optimization to get better estimation
>> efficiency (Dale, 1999).
>>
>> Now as I understand SPM2 uses a GLM model Y = X B + E
>>
>> For my experiment it would y = x1b1 + x2b2 + e.
>>
>> How can I calculate the intrasubject covariance using SPM2? (I think it
>> is equivalent to inverse of (XtVX) where V is the correlation matrix).
>> Also, lets say I change my design back to A I A I A I.... how can I
>> then measure the inter-trial (A-I) variance for the associated pairs? is
>> that possible?
>>
>>
>> Thanks,
>> Manish Dalwani
>> PRA
>> Dept. of Psychiatry
>> UCHSC
>>
>>
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--
Dr. Alexa Morcom
Department of Psychiatry
Downing Site
Downing Street
Cambridge CB2 3EB
Tel: 01223 764674
Fax: 01223 764675 (please contact first)
http://www-bmu.psychiatry.cam.ac.uk/people/amm96/
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