Dear SPM list,
I'm analysing a study in which I'd like to do some
parametric contrasts, and I was wondering about an
issue that I'd like to hear SPM-people's opinion on.
The issue is general, but a specific example will
probably help: my conditions are audio-visual stimuli,
with each condition being a different SOA between
the auditory stimulus and the visual stimulus,
one column in the design matrix for each SOA-type.
Suppose I'm doing a contrast to find areas whose activity
increases with increasing SOA.
Then the contrast has, say,
-2 for the 0ms-SOA cols
-1 for the 50ms-SOA cols
0 for the 100ms-SOA cols
1 for the 150ms-SOA cols
2 for the 200ms-SOA cols
etc.
The problem is that this contrast doesn't only find areas
whose activity scales linearly with SOA. It finds any area
that is more active on average for the cols that have positive
coefficients than for the cols that have negative coefficients.
e.g. if the beta scores in a given voxel
for the conditions [ 0ms 50ms 100ms 150ms 200ms ]
are [ 1 2 3 4 5 ], i.e. if neural activity really does scale
linearly with increasing SOA, as is desired, then
that voxel will give a good contrast score.
However, we'll get an equally big contrast score
if the activity doesn't match the linear-increasing
form of the contrast vector, e.g. if the beta scores
for the conditions [ 0ms 50ms 100ms 150ms 200ms ] are [ 0 0 0 0 5 ].
sum( [ -2 -1 0 1 2 ] .* [ 1 2 3 4 5 ] ) = 10 but also
sum( [ -2 -1 0 1 2 ] .* [ 0 0 0 0 5 ] ) = 10,
so both show up as equally significant, even though the first
one is the better match to our parametric contrast,
coming from a voxel whose activity really does increase
with increasing SOA, whereas the second voxel example
just gives a big kick of activity for the longest SOA only.
What we really want is a way of finding the voxels
whose beta score vectors are *parallel* to a given
contrast vector. And that's just the sort of thing
that multiple regression would do, if the "data vector"
were made out of beta images, rather than the time-series
of BOLD images. So, I was wondering whether a way of finding
voxels that more precisely fit the contrast vector might be this:
1. Take all the beta images and stack them up in a column
to be fit by a multiple regression, analogous to the
way in which the actual time-series of acquisition images
gets fit by the design matrix regressors
2. Specify the parametric contrast vector as a regressor
3. Fit the regression
Then the voxels that give the best fit will be the ones
that are most parallel to the contrast vector, whereas
in the above example using a regular contrast a non-parallel
vector ended up fitting just as well.
If this is right, then we'd end up with an image made out
of "meta-beta" scores, indexing how well the activity
at each voxel matches the parametric contrast vector.
The problem is, I have absolutely no idea what the
correct statistical way of handling such an image
would be. Could it be made into a T-image, like a
standard contrast image? Could it be passed into a
random effects analysis?
It seems to me that another type of question that this approach
could be used for would be to ask questions such as
"which voxels are equally as active for condition A as they
are for condition B". As far as I know, this type
of A=B question is hard to ask with a regular contrast,
but could be answered by using a contrast vector as a
regressor on the beta-images, where the contrast vector
is 1 for all A columns, 1 for all B columns, and zero
everywhere else.
Apologies if the above isn't very clear.
It's just an issue that I'm wondering about.
Any feedback from the gurus of the SPM list
would be greatly appreciated!
Many thanks,
Raj
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Rajeev Raizada
Postdoctoral Research Fellow
MGH-NMR Center / Harvard Medical School
Building 149, 13th Street,
Charlestown, MA 02129
E.mail: [log in to unmask]
Tel: 617 726 8790
Fax: 617 726 7422
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