That must be it... we were using OLS. I'll try re-running the models with
FLAME, and the varcopes will hopefully make sense then.
--Greg
On Thu, 3 May 2007 10:20:07 +0100, Mark Woolrich <[log in to unmask]>
wrote:
>Hi Greg,
>
>Is it possible that you are doing OLS and not FLAME? OLS does not
>implement different group variance estimation, and so if the group
>size is identical then your result makes sense. Failing that, please
>upload the necessary files in a single compressed tarfile to:
>http://www.fmrib.ox.ac.uk/cgi-bin/upload.cgi
>
>and then email me the upload ID, and we'll take a look.
>
>Cheers, Mark.
>
>----
>Dr Mark Woolrich
>EPSRC Advanced Research Fellow University Research Lecturer
>
>Oxford University Centre for Functional MRI of the Brain (FMRIB),
>John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
>
>Tel: (+44)1865-222782 Homepage: http://www.fmrib.ox.ac.uk/~woolrich
>
>
>
>
>On 2 May 2007, at 23:31, Greg Burgess wrote:
>
>> Hi Mark,
>>
>> Thanks for you're detailed explanation. I'll need to sit with my
>> GLM and
>> matrix algebra books for a while to absorb it fully, but I've
>> understood
>> most of it. In the meantime, I wanted to move things down to a
>> practical
>> level for a bit.
>>
>> You said that the varcopes might be the same for the two groups if the
>> number of subjects was similar in the two groups. We have the same
>> number of
>> Ss in each group, so similar varcopes might be expected. However, our
>> varcopes for the two groups are identical. I don't think that is
>> expected
>> unless the groups are precisely identical, which they aren't.
>>
>> Also, you stated that the varcopes depend on whether we modelled
>> variances
>> for each group separately. It wasn't clear from your original
>> reply, but I
>> assume that if we modelled each group variance separately, that the
>> varcopes
>> should differ for each group. The website states that modelling
>> separate
>> variances for each group "is simply a case of specifying in the GUI
>> what
>> group each subject belongs to." We've done that, but I still don't see
>> differences in the varcopes for the two groups, and the varcopes
>> for the
>> individual group contrasts in the unpaired t-test model are
>> different from
>> the varcopes in a single-group average (one-sample t-test) model, even
>> though the COPEs are identical for those two models. How do I know
>> whether
>> the variances were modelled for each group separately other than
>> specifying
>> different group membership in the GUI?
>>
>> Thanks in advance,
>> Greg
>>
>>
>> On Sat, 28 Apr 2007 00:02:36 +0100, Mark Jenkinson
>> <[log in to unmask]> wrote:
>>
>>> Hi Greg,
>>>
>>> The varcope is the expected variance of the estimated contrast of
>>> parameter
>>> estimates (cope). This is not the same as the residual variance
>>> which is
>>> the variance of the data after having all the regressors removed.
>>>
>>> In maths this can be derived from the GLM starting with the basic
>>> equation:
>>> Y = X*beta + e
>>> where Y is the voxel timeseries data, X is the design matrix, beta is
>>> the
>>> true parameter vector and e is the residual noise. Thus the expected
>>> value of the data is: E(Y) = X*beta and the variance of the residual,
>>> Var(e) = sigma^2, which is the same as the variance of the data, Y,
>>> about
>>> its expected value E(Y). So, by getting the best unbiased
>>> estimate for
>>> beta as: betahat = (X'*X)^{-1} * X'*Y
>>> then X*betahat can be removed from the data, leaving the
>>> residuals, from
>>> which sigma is estimated.
>>> Then, if a contrast vector, C, is specified, the cope is given by:
>>> cope = C * (X'*X)^{-1} * (X'*Y)
>>> and the expected variance of the cope is:
>>> Var(cope) = Var(C*(X'*X)^{-1}*(X'*Y))
>>> = C*(X'*X)^{-1}*(X'*Var(Y)*X)*(X'*X)^{-1}*C'
>>> = C*(X'*X)^{-1}*(sigma^2)*(X'*I*X)*(X'*X)^{-1}*C'
>>> = (sigma^2)*C*(X'*X)^{-1}*C'
>>>
>>> In words, the residual variance tells you about the variance of e,
>>> while
>>> the varcope tells you about the variance of the cope, which is
>>> related to
>>> Y (and hence e) by the matrix expressions for the estimate of the
>>> cope.
>>>
>>> Typically, simple means of parameters are more robust to noise
>>> (and have
>>> lower varcopes) than differences between parameters. You can use the
>>> estimability feature of FEAT to get a feeling for this.
>>>
>>> As for your unpaired t-test, I think it is reasonable for the
>>> varcopes to
>>> be the same if the number of individuals in each group is similar,
>>> although
>>> it would depend on whether you've modelled a different variance
>>> for each
>>> group or not. There should be no problems with running any of the
>>> sort of
>>> tests you are talking about. All the relevant corrections are taken
>>> care of
>>> within the code, and you can ask any sort of contrast you like -
>>> especially
>>> single group means, as that is quite standard.
>>>
>>> Hope this helps.
>>> All the best,
>>> Mark
>>>
>>>
>>>
>>>
>>> On 27 Apr 2007, at 23:35, Greg Burgess wrote:
>>>
>>>> Hi FSL list,
>>>>
>>>> I'm a bit confused about the difference between the sigmasquareds
>>>> and
>>>> varcope maps. Specifically, why is it necessary to have a different
>>>> error
>>>> variance (varcope) for each contrast, as opposed to using the
>>>> overall
>>>> residual (sigmasquareds)? How are the individual varcopes estimated
>>>> (i.e.,
>>>> what makes error variance specific to one contrast and not another)?
>>>>
>>>> Lastly, I'm comparing two groups in an unpaired t-test
>>>> (http://www.fmrib.ox.ac.uk/fsl/feat5/
>>>> detail.html#UnpairedTwoGroupDifference)
>>>> with different values for the group membership variable, and two
>>>> additional
>>>> contrasts to test each individual group mean (C3: 1 0 ; C4: 0 1).
>>>> Shouldn't
>>>> the varcope for the contrast of each group mean (i.e., C3 and C4) be
>>>> different (they're not)? What is the best way to determine whether
>>>> the error
>>>> variance does indeed differ for the two groups? Are these tests
>>>> of the
>>>> individual group means valid when they're conducted within the
>>>> context of
>>>> the unpaired t-test model?
>>>>
>>>> Thanks,
>>>> Greg
>>>>
>>>> ____________________________________________________________________
>>>> __
>>>> _____
>>>> Greg Burgess, Ph.D.
>>>> Research Associate, Institute of Cognitive Science
>>>> University of Colorado - Boulder
>>>> Phone: 303-735-5802
>>>> Email: [log in to unmask]
>>>>
>>>> Department of Psychology
>>>> Muenzinger Hall
>>>> UCB 345
>>>> Boulder, CO 80309
>>> =====================================================================
>>> ====
>
>
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