Hi Henk,
Please, see below:
Am 25.02.14 16:02, schrieb H van Steenbergen:
> Dear FSL-ers,
>
> I would like to use a GLM model in randomise that, among other factors and interactions involves
> a multiple groups x continuous covariate interaction.
>
> I am using the "factor effects" template because I have a couple of categorial predictors in my model.
>
> If I understood the GLM (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM) examples correctly, it is possible to model "Two Groups with continuous covariate interaction" like this: (please note that I use -1 en +1 for the categorical factor A, because the real model is more complicated and also looks at interactions between A and other factors):
>
> Mean A COV COVxA1 COVxA2
> 1 -1 21.9 -21.9 00.0
> 1 1 14.9 00.0 14.9
> 1 -1 -10.1 10.1 00.0
> 1 1 -09.1 00.0 -09.1
> 1 -1 21.9 -21.9 00.0
> 1 1 30.9 00.0 30.9
> 1 -1 00.9 -00.9 00.0
> 1 1 -54.1 00.0 -54.1
> 1 -1 -09.1 09.1 00.0
> 1 1 -08.1 00.0 -08.1
This design is rank deficient I'm afraid, but the simplified version you
propose below is fine on this regard.
> With F-test of interaction effect involving the contrasts belonging to EVs COVxA1 and COVxA2.
>
> However, how does this work if my variable A has three levels? In that case, I might need something like this:
>
> Mean A2-Mn A3-Mn COV COVxA2 COVxA3
> 1 -1 -1 21.9 -21.9 -21.9
> 1 1 0 14.9 14.9 00.0
> 1 0 1 -10.1 00.0 -10.1
> 1 -1 -1 -09.1 09.1 09.1
> 1 1 0 21.9 21.9 00.0
> 1 0 1 30.9 00.0 30.9
> 1 -1 -1 00.9 -00.9 -00.9
> 1 1 0 -54.1 -54.1 00.0
> 1 0 1 -09.1 00.0 -09.1
> 1 -1 -1 -08.1 08.1 08.1
>
> With F-test of interaction effect involving the contrasts belonging to EVs COVxA2 and COVxA3.
>
> I have two questions
> 1. Is the proposed model for three levels of A correct?
I think that constructing the contrasts here would be complicated with
the factor effects model. If Jeanette is reading this perhaps she could
comment. I would go with the cell means model (even for the smaller
model with just 2 groups), and construct the interactions as usual. The
construction of the F-contrasts should be direct then:
[1 -1 0 0 0 0]' F1
[1 0 -1 0 0 0]' F1
[0 0 0 1 -1 0]' F2
[0 0 0 1 0 -1]' F2
Other simple t-tests could be added too (as well as the negatives):
[1 0 0 0 0 0]'
[0 1 0 0 0 0]'
[0 0 1 0 0 0]'
[0 0 0 1 0 0]'
[0 0 0 0 1 0]'
[0 0 0 0 0 1]'
To test the effects of the groups A1, A2 and A3, the COV should be mean
centered (and I'd further demean each interaction EV within group).
Hope this helps!
All the best,
Anderson
> 2. Could the first model for two levels of A not be simplied into. And if not, what is the reason for this?
>
> Mean A COV COVxA
> 1 -1 21.9 -21.9
> 1 1 14.9 14.9
> 1 -1 -10.1 10.1
> 1 1 -09.1 -09.1
> 1 -1 21.9 -21.9
> 1 1 30.9 30.9
> 1 -1 00.9 -00.9
> 1 1 -54.1 -54.1
> 1 -1 -09.1 09.1
> 1 1 -08.1 -08.1
>
> Thanks in advance for your help!
>
> Best,
>
> Henk van Steenbergen
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