Just to add to Rik's comments:
There's also another factor particularly if one is doing a between-group or
drug study.
Detecting one's signal is important as well as dealing with noise - and if
the canonical HRF 'mismatches' the signal, one still wants to detect
stimulus-correlated activity, even if this does not take a canonical form.
This is potentially of particular importance if one is comparing different
subject groups or drug conditions where the shape of the HRF may vary thus
spurious interactions could appear secondary to different timings/shapes.
Regarding multiple basis functions vs tailored HRFs - Rik's right of course
about F tests. But also, to deal with the slight collinearity one can in
principle orthogonalise one or more of the convolved stimulus trains with
respect to the other/s (e.g. temporal derivative w.r.t. canonical) although
this is not the default in SPM.
Alexa
> -----Original Message-----
> From: SPM (Statistical Parametric Mapping) [mailto:[log in to unmask]] On
> Behalf Of Rik Henson
> Sent: 24 October 2006 09:39
> 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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