> From [log in to unmask] Fri Apr 14 03:22:23 2000
> Date: Thu, 13 Apr 2000 21:19:31 -0500
> Subject: psychophysiological interactions (in reverse)
Dear Darren,
> I have a question about psychophysiological interactions. In it's
> initial formulation the interaction is defined as
>
> Xi = Xk x Gp * Bi + [Xk Gp G] * BG + e
>
> This is a good model if one wants to see how activity in one area
> results in responses in another. But what if one wants the inverse,
> i.e. one wants to know what areas contributed to the modulation, i.e.
> one has the interaction and wants to work backwards. So if I see
> activity in area A, I want to know what areas contributed to this
> activity under the influence of the psychological variable. (Rather
> than finding the area whose response is influenced by A)
>
> Would it be valid instead to put in the model
>
> Xi = Xk/Gp * Bi + [Xk Gp G] * BG + e. ???
>
> and would this give the area (or set of areas) that contributed to
> the psychophysiological interaction in Xk?
This is an interesting question and in theory your approach might work
but may lead to odd results. The problem reduces to finding a
regressor that acts as a modulator of Gp to explain variance in the
target region. i.e.
Xi = Xk*Gp + e ..........(1
where Xk has to be estimated subject to suitable contraints (i.e. Kk
cannot be infinity when Gp = 0, in other words dividing Eq(1) by Gp may
not be the best way to estimate Xk). This estimation can be done by
treating Gp as the explanatory variable and expanding it in terms of
temporal basis function to estimate Xk (hard constraints). Soft
contraints could be imposed using penalized regression.
Perhaps this problem could be the focus of work during your next visit?
With very best wishes - Karl
PS The bug in conjunctions, as you appear to worked out, lies in the
fact that the t threshold is negative. Given that a conjunction should
be framed in terms of conjoint activations one would normaly like to
see t > 0 in all subjects and, consequently, we have not worried too
much about this particular 'bug'.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
|