Dear Kalina, and Tom and other proper statisticians,
I had an idea about this, and would like to know if people thinks it is
Lets say you have a regressor which is "peaks" at the onset times convolved
with the HRF, i.e. the "standard" regressor (Kalinas first model).
Then let us construct the regressor Kalina suggests for the second model
(i.e. variable length, short "epochs" convolved with the HRF). Now we
orthogonalise the second regressor with respect to the first and plug both
into the same design matrix.
Couldn't we now just test for the "necessity" of the orthogonalised second
regressor with an F-test, and wouldn't that answer Kalinas question? I.e.
"do I get a significantly better fit to my data if I take the variable
response time into account"?
I realise the question being answered with the suggested model is not
identical to Kalinas original question since the models will now have
different degrees of freedom (i.e. we put slightly harsher demands on the
second regressor than was originally intended) but would that be of any
consequence given the very high df?
It would be straightforward to extend to multiple event types and sessions.
Thomas Edgar Nichols wrote:
> Excerpts from SPM-help#: 13-Sep-100 comparing line fit across m.. by
> Kalina [log in to unmask]
> > for the first model:
> > Sum_ResMS_1 = (ResMS for Subj No1) + (ResMS for Subj No2) + ...
> > and for the second model:
> > Sum_ResMS_2 = (ResMS for Subj No1) + (ResMS for Subj No2) + ...
> > and then perform an F-test,
> > F = Sum_ResMS_1 / Sum_ResMS_2,
> > with df1 = df2 = the sum of the error df from the subjects' analyses
> The immediate problem that comes to mind is that the F test assumes
> that the numerator and denominator are independent... something that
> is satisfied when you are looking at nested models, but not here.
> The F images still have the qualitative interpretation, that of relative
> magnitude of variance explained, but the p-values and thresholds won't
> be right.
> It's an excellent question, because this is a perfect example of an
> interesting, but non-nested model selection problem. But I'm afraid I
> don't have any solutions off hand.
> -- Thomas Nichols -------------------- Department of Biostatistics
> http://www.sph.umich.edu/~nichols University of Michigan
> [log in to unmask] 1420 Washington Blvd
> -------------------------------------- Ann Arbor, MI 48109-2029