Dear Torben,
>
> Thank you very much for your reply, you seemed to have got my point. So now for
> the explanation of why would I like non-integer df's. I second level analyses
> one uses contrast images from different persons whom are likely to have
> different degrees of paradigm related motion. If one of the motion parameters
> have correlation with the paradigm of more than some threshold (say 0.4 ), I
> consider the contrast image belonging to the paradigm to uncertain, and exclude
> it from the second level analysis. If some correlation between one of the motion
> parameters are close to this threshold, I would like to let this information go
> into the second level analysis, as a covariate. Clearly the six motion
> parameters are not orthogonal, but in the current setup of df calculation they
> will take 6 degrees of freedom. If I were to include a single correlation
> coefficient in the second-level analysis I would need some apriori knowledge of
> how to weight the different parameters, and here my common sense is not good
> enough.
>
> Torben
If I understand you correctly you would like to extract some (single) parameter
from each subject that somehow indicates to what degree that data set has been
corrupted by movement. It doesn't sound easy. Spontaneously I would guess that a
pretty kosher way of doing that would be a canonical correlation analysis between
the (first few) eigenvariates (following an SVD) of your data, and your estimated
motion parameters. That would give you the linear combination of your (6) motion
parameters that best explains observed variance in your data, and I guess that the
corresponding correlation coefficient would be a good candidate parameter.
On a pragmatical note I guess you could pick any of the z-translation or the pitch
(x-rotation) since those are almost always the largest, and strongly correlated
with each other.
Finally, my choice would be to handle the motion induced task correlated variance
at the first level to as large an extent as possible. Including the motion
parameters in the first level model will ensure that you err on the conservative
side. Granted, there is an extra little complication in that a large degree of task
related motion -> a lot of "true" activation variance will be removed at the first
level -> variance of activations across subjects may increase AND in a
task_by_group interaction one might conclude that one group activates less, while
in reality they just moved more with the task.
Good luck Jesper
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