Thank you for the response, Rik.
This is very helpful and my approach knowing this is to likely take the HRF
and time derivative to the 2nd level analyses. However, now that the 2nd
level analyses are constrained to a F-contrast, directionality is lost. Is
there a way around this with a F-contrast with multiple basis functions?
I thank others on this thread, as well, for their input. It's clear I
touched off a debate that apparently is still hotly contested.
Regards,
Jeff
-----Original Message-----
From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On
Behalf Of Rik Henson
Sent: Tuesday, October 24, 2006 4:39 AM
To: [log in to unmask]
Subject: Re: [SPM] Time & Dispersion Derivatives
Just to add to Alle's comments:
>In situations where the HRF is a bad fit, it may be a good idea to use
>derivatives. But this does come at a cost, because you have three times as
many
>regressors that, in general, are not orthogonal.
Actually, the canonical HRF and its first-order partial derivatives
functions
are nearly orthogonal by definition, and in fact all basis functions are
explicitly orthogonalised to be sure (see spm_get_bf). However, Alle is
correct
that correlation can be induced into the resulting regressors (ie, after
convolution) owing to 1) non-random ordering of different event-types (e.g,
for
two event-types close together in time, the *difference* in their canonical
HRFs
will be correlated with the temporal derivative for either one), and 2)
undersampling by the TR.
However, such correlation is not always a problem. Yes, it will affect
T-contrasts on one basis function alone (e.g, the canonical HRF). But
generally
when one uses multiple basis functions, one should perform F- rather than
T-contrasts over all basis functions, for which intercorrelation does not
matter
(ie., shared variance will be captured).
In the absence of correlation, the inclusion of extra basis functions can
reduce
the residual error in 1st-level models, and hence improve T-contrasts on one
basis function alone (eg the canonical HRF). However, the inclusion of such
extra basis functions will not affect 2nd-level analyses on only one basis
function in SPM99, or only minimally so in SPM2/5, because this
orthogonality
means that the parameter estimates are not affected under OLS, and only
minimally under WLS. Thus it is a common misapprehension that including, eg
the
temporal derivative of the canonical HRF in 1st-level models somehow allows
for
latency differences in 2nd-level analyses on the canonical HRF alone. It
does
not. The answer is to take (contrasts of) all basis functions to 2nd-level
analyses, and again perform F-contrasts.
>In the case of a consistent mismatch of the HRF, it may be better to
>- look for a different HRF (ths may sound a bit drastic)
>- use AR modelling to get rid of autocorrelations in the noise
>The second option is available in SPM. Kalina Christoff made a tool to do
the
>first option (http://www-psych.stanford.edu/~kalina/SPM99/Tools/eHRF.html).
>It's a very simple tool, but it does the job.
Using an empirically-defined, subject-specific HRF may help if you want to
use
only one basis function. However, it is not a perfect solution, since 1)
there
may be different-shaped HRFs in other brain regions within the same subject,
2)
there will always be estimation error associated with the
empricially-defined
HRF. The use of multiple basis functions is a more elegant solution, IMHO.
Rik
Jeff Browndyke, Ph.D. wrote:
> A few questions about the use of time and dispersion derivatives:
>
> If one uses time and dispersion derivatives in a model, does this mean
that
> error variance associated with the canonical HRF is "soaked up" in the
> model? If this is the case, then why wouldn't these be included as a
matter
> of routine when employing the standard HRF? I understand there are
> waveforms that are devoid of some of the canonical HRF constraints, but
> wouldn't using one of these mean that you are just incorporating into your
> model what would otherwise be error variance in the canonical HRF
situation?
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