Dear Stuart,
>I have the following study design consisting of two conditions and a
>covariate in the presence of each condition:
>
>Condition: drug on or off
>Covariate: Stimulation during drug on and off
OK, so presumably it's a 2x2 factorial design.
>I have chosen "single subject: conditions and covariates" for my
>first level analysis and entered the drug scans as conditions giving
>me the first two columns in my design matrix and then two covariates
>of interest giving me the next two columns.
>
>I believe the following to be true:
>
>[1 -1 0 0] ---> rCBF decreases due to drug (condition 1 is pre-drug)
>[-1 1 0 0] ---> rCBF increases due to drug (condition 2 is on drug)
>[0 0 1 1] ----> Main effect of stimulus rating (covariate)
>[0 0 1 0] ----> Effect of stimulus rating during condition 1 (no drug)
>[0 0 0 1] ----> Effect of stimulus rating during condition 2 (drug)
Sure. Obviously the effect of the drug is confounded by time if the
'no-drug' condition is always 'pre-drug', ie. always comes before the
'drug' condition. Perhaps this is unavoidable though.
>What I am wondering is where I get my covariate by condition
>interactions from. Intuitively I think it is some combination of
>condition and covariate contrasts [1 -1 1 0] but logically I think it
>is simply the contrast of my two covariates [0 0 -1 1].
You are right. The reason why it is a bit of a brainteaser is that
your model is not specified in the way that factorial designs
habitually are (although the model is strictly speaking the same).
One would normally have four covariates, one for each of the cells in
your factorial design:
1. drug off, stimulus off;
2. drug off, stimulus on;
3. drug on, stimulus off;
4. drug on, stimulus on.
In this case, an interaction would look something like 1 -1 -1 1,
which is much more familiar.
However, the interaction is just one simple main effect minus the
other simple main effect, and as you stated above, in your
specification this is the difference between 0 0 0 1 and 0 0 1 0,
which is 0 0 -1 1. The results should be the same whichever way you
specify the model.
When you come to write your stuff up, I would be inclined to write
out your design specification in the more traditional way, so that
referees don't have to sweat over the contrasts!
Best of luck,
Richard.
--
from: Dr Richard Perry,
Clinical Lecturer, Wellcome Department of Cognitive Neurology,
Institute of Neurology, Darwin Building, University College London,
Gower Street, London WC1E 6BT.
Tel: 0207 679 2187; e mail: [log in to unmask]
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