Hello,
I am interested in mapping partial correlations between signal and 2
variables. Basically, I want to identify voxels at which my signal
contains variance which can be explained by variable A after accounting
for variance explained by variable B, and vice versa.
I have done this by setting
EV1=variable A raw score (i.e., not demeaned) and
EV2=variable B raw score (i.e., not demeaned).
To look at voxels where variable A is positivly correlated with signal
after variance due to B is controlled, I set a contrast, [1 0]. To look
at corresponding negative correlation, I set a contrast [-1 0]. To
identify voxels where B is positively correlated with signal after A is
controlled, [0 1], and [0 -1] for negative correlation. If this is
correct, what is the interpretation of my resulting maps? Am I looking at
voxels with significant semipartial correlation between signal and EV
(i.e., variance contributed by B has been removed from error variance, vs.
partial correlation, where variance contributed by B has been removed from
both explained variance and error variance)?
I also repeated the above and orthogonized A wrt B. Resulting contrast
maps corresponding to A ([1 0] and [-1 0]) look exactly the same as
without orthogonalizing. Maps corresponding to B ([0 1] and [0 -1]) are
slightly different although the pattern is similar. Is this because the
joint variance between A & B have now all gone into B? Is it true that as
maps corresponding to B now also contain variance that overlapped with A,
it is inappropriate to interprete this map as voxels whose signal varied
with B with effects of A controlled?
To look at voxels whose signal varied with B with effects of A controlled,
I think I would need to orthogonize B wrt A. Theoretically, when I do
this, the resulting maps for B should look exactly like the results of the
original, unorthogonalized analysis. I am testing this now, but would
really like the experts' input regarding whether I have done the previous
steps correctly, and if my interpretation are accurate.
Thanks so much!
Lisa
Lisa Lu, Ph.D.
Postdoctoral Fellow
Laboratory of Neuro Imaging
UCLA Dept of Neurology - #1 in NIH Funding
David Geffen School of Medicine
Neuroscience Research Building 1, Suite 225
635 Charles Young Drive South
Los Angeles, CA 90095-7334
(310) 267-5555
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