Dear Sylvain,
>Therefore, I get 5 kind of task period ( (Aa), (Ab), (Ba), (Bb), (Bc)) that
>are presented 3 times each (random order).
>
>I can imagine 2 way of defining my design matrix :
>1) Tell SPM that there are 5 conditions with each condition being a kind of
>task period ( (Aa), (Ab), (Ba), (Bb), (Bc)). That gives me a matrix like
>that (if each cond are presented only once):
This would certainly be the normal way of building your design matrix.
However, I am not sure why you have included so many rows of five zeros in
your version of the design matrix. Imagining that you had presented each
condition once, in the order which you gave them (and just for simplicity
of writing out the design matrix, that there was only one scan per
condition), the usual design matrix would look like this:
>100001
>010001
>001001
>000101
>000011
In fact each of these columns would be mean-corrected. Note the column of
ones added on the right hand side automatically by SPM to model any
departure of the mean fMRI signal from zero.
Possibly the rows of zeros were there to represent a baseline condition
which you didn't mention (and which you modelled implicitly). If so, then
an alternative option is that you might wish to model the each 'baseline'
condition (following each task condition) explicitly and separately, if you
think that it is possible that any cognitive components of task Aa, for
example, may carry over into the baseline condition following it. If you
don't do this, then make sure that you use a high-pass filter.
>2) Tell SPM that there are 5 conditions but with 2 condition defining the
>levels of factor1 and 3 conditions defining the levels of factor2. I then
>get the following matrix:
>AABBB
>ababc
Again I've taken out the rows of zeros and added a column of ones for ease
of comparison.
>101001
>100101
>011001
>010101
>010011
This is not a good model. It assumes that there is no interaction between
factor AB and factor abc. Thus the difference between Aa and Ab is assumed
to be the same as the difference between Ba and Bb (both are modelled in
the 3rd and 4th columns). The reduced flexibility of the model, with the
same number of columns, is explained by the fact that there is now
redundancy in the design matrix: i.e. the sum of columns 1 and 2 is the
same as the sum of columns 3 to 5 (which is also the same as column 6, but
this is only because I haven't mean corrected the other columns, as SPM
does automatically). Thus columns 2 and 5, for example, could be removed
from the design matrix without any change to the model (e.g. the variance
previously modelled by column 2 would now be modelled by column 6 minus
column 1).
>The question I'd like to answer are :
>
>1) Does the 2 levels A & B of Factor1 Activate different regions ( I think
>that I have exclude the c level of factor2 to answer) ?
>2) Does the levels a & b of Factor2 activate different regions ?
>3) Does the levels b & c of Factor2 activate different regions (I think I
>have to exclude the A level of factor1) ?
>4) Are there interactions between the 2 factors. for example :"Does the
>difference of activation between a & b depend on the level of Factor 1?"
So, returning to your first model, you can think of your design as a 2 x 2
factorial design, plus an extra condition (Bc). Your question 1 is the
main effect of 'A' vs 'B' (contrast 1 1 -1 -1 0 0), and its converse
contrast 'B' vs 'A' (-1 -1 1 1 0 0). Question 2 is the main effect of 'a'
vs 'b' (contrast 1 -1 1 -1 0 0) and its converse. Question 4 is the
interaction of 'A-B' with 'a-b' (contrast 1 -1 -1 1 0 0) and its converse.
Question 3 is a question 'outside' the 2 x 2 factorial design, which is the
simple main effect of 'b' vs 'c' in the context of B (0 0 0 1 -1 0) and its
converse.
Best wishes,
Richard Perry.
from: Dr Richard Perry,
Clinical Research Fellow, Wellcome Department of Cognitive Neurology,
Darwin Building, University College London, Gower Street, London WC1E 6BT.
Tel: 0171 504 2187; e mail: [log in to unmask]
Pager: 04325 253 566.
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