Hi Aaron,
Basically, including a temporal derivative as an additional
"covariate of no interest" (in SPM terms) allows a little slop in the
time-to-peak values of the HRF function. That is, assuming you're
using the double gamma HRF to correspond to SPM's canonical HRF,
there is a time to peak value around 6s. For any given brain region,
however, the actual ttp value may be somewhere in the 4.5-8.0s
range. Including the temporal derivative allows the model to better
fit this ttp difference on a voxel-wise basis. As a rule, that's
normally why people include temp derivs in their models.
There are a couple of points to add, though.
1. TDs are rarely included in contrasts because to do it properly
requires using F-tests -- not t-tests. So you don't want a mean of
the actual EV and it's TD -- eg a contrast like [1 1 -1 -1] for
animate > inanimate which includes TDs. Instead you would use
F-tests with something like
[1 0 -1 0]
[0 1 0 -1]
The problem comes with bringing these first level f-tests to higher
levels. As a result, the assumption is that nothing important is
encoded in the parameter estimates of the TDs -- all they do is
remove structured noise from the model, thereby improving
sensitivity. The contrasts typically just include the main EV (but
see pt 3 below).
2. If you want to include dispersion derivatives, the easiest method
is simply to choose the optimal basis set instead of the double gamma
when setting up the model. This set approximates the HRF, its
temporal derivative and its dispersion derivative. The advantage is
that together these basis functions model a wider range of HRF
shapes. Again, the problem is that they require F-tests at the first
level to be meaningful and these are difficult to bring to higher levels.
3. Finally, including TDs in blocked design may not be a good idea
because the TDs are likely to suck up variance that one would like to
leave in the parameter estimates of the main EV. There was a good
discussion of this on the SPM list a few years back -- perhaps Jesper
would care to remind us all?
Cheers,
Joe
|