Dear Aaron,
> > During an fMRI analysis in SPM99b, using a standard boxcar paradigm,
> > there are two occasions when the user must decide whether to convolve
> > with the hemodynamic response function. The first occurs during setup of
> > the design matrix, when the option to convolve the boxcar with the hrf
> > is offered. The second occurs during the estimation step, when the hrf
> > is offered as an alternative to a Gaussian kernel for temporal smoothing
> > of (I believe) the data as well as the entire design matrix, which I
> > understand to be necessary due to the nature of serially correlated
> > regression. If I select both of these options, does the boxcar get
> > convolved with the hrf twice? If so, this seems inappropriate, as once
> > should be enough.
>
> I can not answer your question regarding what the SPM program does, but
> indeed it is theoretically correct to convolve the boxcar with the HRF
> twice. This is because the underlying neural activity has been convolved
> twice (given the assumptions one makes): once by physiology (which
> one could heuristically associated with your "1st" HRF convolution)
> and once by the matrix operations peformed in the SPM program.
>
> Sincerely,
> Eric
Eric is absolutely right. The box-car convolution with the hrf emulates
the causes of the observed data (specifically the endogenous
convolution of changes in neuronal activity by the hrf) to provide a
better model of the responses. The second time the hrf can enter is in
terms of filtering (i.e. smoothing). This is unrelated to modeling the
causes but allows for a better model of the temporal correlations. A
critical point to note here is that the second convolution uses a
symmetric kernel that has the same frequency structure as the hrf but
is not the actual hrf. This means that filtering does not implement a
second 'delay'.
Best wishes - Karl
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