Hi
>
> Therefore, any signal change detected under condition A is equal
> to a+b (that's the total 'height' modelled).
>
> Ok, so this is the logic step I find hard to understand.
>
during model fitting, both EV1 and EV2 contribute to the overall fit
and the parameter estimates are found so that a*EV1+b*PE2 best fits
into the data in the least-squares sense, i.e. so that the residuals
are minimised.
Now assume we have estimated the two parameters a and b and keep them
fixed. Now a*EV1+b*EV2 is what we have modelled at every voxel
(forgetting about EV3-EV7 now, because we've already established that
they are orthogonal to EV1 and EV2). Imagine a particular point in
the brain and start plotting the effect sizes in the correct order so
that the first 5 vals correspond to condition A, the next 5 points
corresponds to B and so on. Now image how the fitted model (a*EV1
+b*EV2) gives you a partial model fit, i.e. a vector that somewhat
follows the vector of effect sizes.
The first 5 values in this partial model fit vector correspond to
condition A and the amplitude of the first 5 values in the partial
model fit vector is a*EV1_(1-5) + b*EV2_(1-5). Both EV1 and EV2 are
set to 1 for the first 5 values, therefore the modelled height in the
partial model fit is a+b, assuming that we have normalised EV1 and
EV2 to unit amplitude prior to model fitting. During condition B the
modelled amplitude is a*EV1_(6-10) + b*EV2_(6-10) and therefore the
amplitude we estimated during the model fitting is -a etc.
hope this helps
christian
____
Christian F. Beckmann
University Research Lecturer
Oxford University Centre for Functional MRI of the Brain (FMRIB)
John Radcliffe Hospital, Headington, Oxford OX3 9DU, UK.
[log in to unmask] http://www.fmrib.ox.ac.uk/~beckmann
tel: +44 1865 222551 fax: +44 1865 222717
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