Dear Giancarlo,
I have seen this one go unanswered for a while, so I will have a go.
However, I am a wee bit uncertain about it, so if anyone has a better
suggestion, please. I have attached a couple of sample design matrices
for Giancarlo, but since I know the nuisance of large attachments those
wont go on the mailbase.
>
> Dear All,
>
> We have an experiment with the following factorial design
>
> Factor A, 3 levels
> Factor B, 4 levels
>
> We have identified significant activations for both main factors, and
> when we inspect the data, we have reason to believe that there exist
> significant interactions between the two main factors in certain
> brain areas. However, we are a bit stumped about how to develop the
> design matrix for a factorial design greater than 2x2 (for which, we
> have no problem investigating interactions). Further, would there be
> suggestions about how to inspect the location of the putative
> interactions in this 3x4 design?
>
I will here assume you have an epoch related fMRI study, and that both
your factors are categorical (i.e. that you dont consider e.g. the four
levels of factor B as a parameter (e.g. word presentation rate). I will
also assume that you have scanned every level of factor B at each level
of factor A.
Now, the way you would normally set this up (without interactions) is by
specifying three regressors (i.e. three trial types) for factor A, and
four for factor B. This would give you 7 regressors in total. When you
look at the design matrix you will notice that each level of factor B is
modelled as one single effect, regardles of that level of A under which
it was scanned. This is beacause there are no interactions in there (I
attach a design matrix called without_interaction.mat which you can
check).
Now, what you want is to model each level of B under each level of A
separately. One way in which you can do this is to specify that you want
"Interactions among trials (Volterra)". This will effectively give you
another set of columns which model the inteactions you want, AND some
that you dont want. SPM cannot know that the first three columns are
just three levels of the same factor, and will give you the interactions
among those as well. These really should be zero, but because of the
convolution with the HRF won't quite be (see with_volterra.mat). I guess
those extra columns won't do you to much harm, and if you are happy with
that you can check for interactions with an F-contrast encompassing all
the columns that specify interactions between your factors (there will
be 3*4 of them).
Another way in which you may do this is by considering e.g. each level
of factor A under each level of factor B as a distinct trial type and
specify that you have 3+4+3*4 trial types and then enter them
appropriately. Again, you can check for interactions with an F-contrast
across the last 3*4 columns (see with_interaction.mat). You can also
check specifik interactions within this set using t-contrats. Just watch
out for deep sea fishing, you have an awful lot ot columns.
>
> Thanks in advance.
>
> Giancarlo Zito
>
Good luck
Jesper
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