Dear Tom, Rik, Jesper, and Ian,
> So, to summarize, you can either orthogonalize or not, though it will
> have no impact on the F-images. You can test for additional
> variability explained by set of regressors in the presence of another.
> Hopefully you will find one model is clearly superior to the other,
> though it is feasible that [X_1] will fit better in some areas and
> [X_2] will fit better in others.
Thanks so much for you comments and advice on this. But if I could, let me
further ask for your opinion on the following related questions --
First, can we safely assume that in this case, testing if X_2 accounts for
significant additional variability is identical to testing if X_2
by itself provides a regression function with a significantly better line
fit than the regression function in X_1 alone? In other words,
for voxels where the reduced F-test [0 1] is significant, have we
demonstrated a lack of fit for the first model (the first model is [X_1]
alone)?
Also, if this assumption is true (seems likely to me, but please correct
me on it) for voxels where the reverse [1 0] F-test is significant, we
would have demonstrated a lack of fit for the second model (the second
model is based on [X_2] alone).
The second question is a bit more conceptual and assumes that the above
assumtion is correct.
Suppose now after comparing the two models' fits, we go back to the
original models to make inferences about the parameter estimates (I think
the consensus was that's not possible from the [Y = X_1 X_2] model).
Let's say we have two types of regions:
type A, for which we have found a lack of fit for model_1 [Y=X_1]
through a significant partial F-test [0 1], and
type B, for which we have found a lack of fit for model_2 [Y=X_2]
through a significant partial F-test [1 0]
Strictly speaking, we cannot draw conlusions from a model for which we
have demonstrated a significant lack of it. Would that imply that the
proper thing to do would be to use model_1 to draw conclusiong about the
parameter estimates for regions of type A, and to use model_2 to draw
conclusions about regions of type B? (keeping in mind the different
interpretation that the parameter estimates would have in the two
models, e.g., in my case, model_1 models what can be described as
transient responses at the onset of each trial, while model_2 models
sustained responses lasting throughout the working cycle).
Thanks again for you comments so far and for any future ones.
-k.
_____________________________________________________________________________
Kalina Christoff Email: [log in to unmask]
Office: Rm.478; (650) 725-0797
Department of Psychology Home: (650) 497-7170
Jordan Hall, Main Quad Fax: (650) 725-5699
Stanford, CA 94305-2130 http://www-psych.stanford.edu/~kalina/
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