Doh, yes Tom's right - that's the suggestion that we've made in the
past, since forgotten clearly :)
Cheers, Steve.
On 3 Nov 2008, at 14:21, Thomas Nichols wrote:
> Hi,
>
> I think the answer is simpler than Steve implies.
>
> Ideally, this would be an easy model to fit. Say you have just 3
> subjects, imaged 2, 5 and 3 months apart, the design matrix you'd
> like to fit would be...
>
> A ---B---
> 0 1 0 0
> 0 0 1 0
> 0 0 0 1
> 2 1 0 0
> 5 0 1 0
> 3 0 0 1
>
> which consists of the linear effect of time relative to the 1st scan
> (A), and the 3 subject-pairing/blocking variables (which also model
> the grand mean) (B). This is presumably not satisfying, since it
> measures the linear time effect as a whole (i.e. significance of A
> will be determined by both an over-all time effect and the
> individual differences in the time effect).
>
> BTW, due to the orthogonalizing magic of the GLM, the model above
> will have the same fit if you had replaced column A with
> [ -1 -2.5 -1.5 1 2.5 1.5 ].
>
> If you would like to dissociate the average Time1-vs-Time2 effect
> from the additional variation explained by exact scanning times,
> then you'd use the model
>
> A0 A ---B---
> 0 0 1 0 0
> 0 0 0 1 0
> 0 0 0 0 1
> 1 2 1 0 0
> 1 5 0 1 0
> 1 3 0 0 1
>
> Where A0 is the Time1-vs-Time2 effect, and A is the exact scanning
> time variable. I frankly can't see how A0 would ever be
> significant, but, crucially, A will be significant whenever there is
> appreciable inter-individual variation in FA explained by the
> precise scanning intervals *discounting* any variation explained by
> the average Time1-vs-Time2 effect.
>
> Again, due to GLM magic, A0 and A can be specified as A0 = [-1 -1
> -1 1 1 1 ] and A as above, though I find the way I have set it up
> to be clearer.
>
> Hope this helps!
>
> -Tom
>
> __________________________________________________
> Thomas Nichols, PhD
> Director, Modelling & Genetics
> GlaxoSmithKline Clinical Imaging Centre
>
> Senior Research Fellow
> Oxford University FMRIB Centre
---------------------------------------------------------------------------
Stephen M. Smith, Professor of Biomedical Engineering
Associate Director, Oxford University FMRIB Centre
FMRIB, JR Hospital, Headington, Oxford OX3 9DU, UK
+44 (0) 1865 222726 (fax 222717)
[log in to unmask] http://www.fmrib.ox.ac.uk/~steve
---------------------------------------------------------------------------
|