Hi Tom,
Thanks for the quick reply.
In reality, the time intervals would be days, i.e. there are
differences between subjects, that's why I would like to regress out
the effects, I also include the age and gender as covariates.
Ping
On Fri, Apr 17, 2009 at 9:28 AM, Thomas Nichols <[log in to unmask]> wrote:
> Dear Ping-Hong,
>>
>> I have questions similar to this thread, if there are 3 subjects,
>> all scanned at 3 timepoints, say baseline, 3months and 5months; and to
>> test "3months vs baseline", "5months vs baseline" effects. Would the
>> design matrix set up be like
>>
>> A0 A1 A ---B---
>> 0 0 0 1 0 0
>> 0 0 0 0 1 0
>> 0 0 0 0 0 1
>> 1 0 3 1 0 0
>> 1 0 3 0 1 0
>> 1 0 3 0 0 1
>> 0 1 5 1 0 0
>> 0 1 5 0 1 0
>> 0 1 5 0 0 1
>>
>> A0 is "3months vs baseline", A1 for "5months vs baseline", and A1-A0
>> for "5months vs 3months" contrasts.
>
> Yes and no. Yes, this is the spirit of my previous answer, but, no, it
> doesn't make sense in your setting. In the previous question each
> individual was scanned at a slightly different time, there was interest in
> finding variation related to these small timing differences. In your
> example, everyone is scanned at exactly the same time, and thus predictor A
> is totally redundant (i.e. explains a subset of the variation that A0 and A1
> explain).
>
>>
>> If there are another 2-level factor , say "disease and control" and 3
>> subjects in each group, then
>>
>> A0 A1 A01 A11 A ---B---
>> 0 0 0 0 0 1 0 0 0 0 0
>> 0 0 0 0 0 0 1 0
>> 0 0 0 0 0 0 0 1
>> 0 0 0 0 0 0 0 0
>> 0 0 0 0 0 0 0 0
>> 0 0 0 0 0 0 0 1
>>
>>
>> 1 0 3 1 0 0
>> 1 0 3 0 1 0
>> 1 0 3 0 0 1
>> 0 1 5 1 0 0
>> 0 1 5 0 1 0
>> 0 1 5 0 0 1
>
>
> I think there's a formatting error in what you're trying to show, but I
> think the answer is no, you can't do this. The general set up with the
> block variables for subjects is only useful for within subject designs.
> I.e. the blocking variables soak up intersubject variability, but in a two
> group design you're specifically interested in the differences between
> groups of subjects.
> If you have some *covariate* driven by within subject effects, then, yes,
> you could split that by group and look for group differences in this
> setting.
> Hope this helps.
> -Tom
>
>>
>>
>>
>>
>>
>>
>>
>>
>>
>> On Mon, Nov 3, 2008 at 10:21 AM, Thomas Nichols <[log in to unmask]>
>> 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
>> >
>>
>
>
>
> --
> ____________________________________________
> Thomas Nichols, PhD
> Director, Modelling & Genetics
> GlaxoSmithKline Clinical Imaging Centre
>
> Senior Research Fellow
> Oxford University FMRIB Centre
>
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