hi Shaquanda
> What is a simple example for when it might be more appropriate to use FIR
> rather than the canonical HRF?
One reason to use an FIR model is that it does not make any shapes
about the shape or timing of the hemodynamic response. That is, if
you use a canonical HRF, what you are saying is that you predict a
response that looks a certain way (a certain time to peak, a certain
overall duration, etc.). If this is accurate, it's a parsimonious and
convenient way of characterizing the response. However, the less
accurate a model the canonical HRF is, the less accurate your results
will be.
So how accurate is a canonical HRF? A good demonstration of the
variability of the BOLD response is:
Aguirre et al. (1998) The variability of human, BOLD hemodynamic
responses. NeuroImage 8, 360-369.
http://dx.doi.org/10.1006/nimg.1998.0369
You could imagine that a canonical HRF would be similar to all of
these measured responses, but it couldn't fit them all perfectly due
to slight changes in the response shape or latency. With an FIR
model, you are more able to capture these variations, because each
time bin (typically whatever your TR is, so let's say every 2 seconds)
can be fit individually. This is in contrast to using just a
canonical HRF, in which the entire predicted response will scale up
and down together.
With sufficient degrees of freedom (which is generally not a problem),
I can't think of a time in which an FIR model would give you a *worse*
fit to your data. HOWEVER, this comes at a cost of interpretation.
With a canonical HRF, it's simple to do a t-test, and infer that if
this is significant, there was an increase in activity that
statistically matches the canonical HRF, which is generally what we're
interested in. With an FIR model you need to test whether any bin
differs from zero, and hence an F test---but a significant F test
could reflect any number of different response profiles, and it's
generally hard to characterize these parsimoniously for a whole-brain
analysis (because in theory you could have a different response
profile at every significant voxel). So maybe a good bottom line of
FIR models is: more flexible, but harder to interpret.
As you might have seen, there is also an example of a FIR analysis in
Chapter 30 of the SPM8 manual on the face dataset, which includes a
comparison to results obtained with a canonical HRF, and also a
comparison of an FIR model with an informed basis set (HRF + 2
derivatives).
Hope this helps!
Jonathan
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