Ian -

> i have a question with respect to the inclusion of the time derivative
> in event related and blocked fmri models.  in particular, i was under
> the impression that inclusion of this variable "simply"
> captured differences in the onset/fall off velocities of the
> response function across different conditions.  presumably this
> improves the solution by preventing this variance from ending
> up in the error term.  i did not think that inclusion of the time
> derivative changed the nature of the shape of the response
> function that is fitted to the data.  however when i use the
> plot function it is clear that when the time derviative is
> included in the model, two different conditions can yield
> best fit hrfs which are grossly different in shape.

All basis functions contribute to the shape of the fitted
response. Linear combination of an HRF and its temporal
derivative can shift the fitted response forward and backwards
in time. This can capture real responses that have a shape
resembling the HRF, but are simply shifted by up to ~+/-1s
relative to the HRF. Note however that if the HRF is a poor
fit to the real response, you can get spurious fits in which the
shape of the fitted response might look more like the derivative
(eg more bimodal) - eg when, due to random noise, the parameter
estimate for the HRF is small, but that for the derivative is large.

You are correct that ihe inclusion of a temporal derivative can
improve the T-values in a Fixed Effects model by accommodating
additional residual error. (Note however that its inclusion does not
change the parameter estimate for the HRF, because it is orthogonal
to the HRF).


> my question relates to the interpretation of condition contrasts with
> hrfs that clearly differ in overall shape.  without the time
> derivative i thought that the contrast represented a difference
> in the average height estimate (beta) between two or more
> conditions.  however, if the shape of the theoretical hrfs for
> conditions is grossly different when the time derivative
> is included, what does the beta that is being contrasted
> across conditions represent? is it now an estimate of area?
> thanks in advance.

This is a general point - one can only really interpret the
parameter estimate for an HRF as the "magnitude" of
the response if that HRF is a good fit to the response.
If the response differs markedly in shape from the HRF,
the parameter estimate for the HRF is not meaningful.
For example, if a response is delayed by >2s relative to
the HRF, you will get a small parameter estimate for the HRF.
Thus two event-types, one resembling the HRF and one
delayed by 2s, might have significantly different parameter
estimates for the HRF, even though the peak height of the
two responses might be identical. It is always worth plotting
the adjusted data to see whether the fitted responses are
a good fit to the data.

Rik

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DR R HENSON
Institute of Cognitive Neuroscience &
Wellcome Department of Cognitive Neurology
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