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Solution 1 would be the better approach. Solution 2 runs into the same issue as the two separate models -- you are using the absence of an effect to conclude there is a difference. For a discussion on this issue, please read:
Erroneous analyses of interactions in neuroscience: a problem of significance. Sander Nieuwenhuis, Birte U Forstmann, and Eric-Jan Wagenmakers Nature Neuroscience 14, 1105 (2011). doi:10.1038/nn.2886 Nature Publishing Group, 2011 vol. 14 (9) pp. 1105-1109 http://ezp-prod1.hul.harvard.edu/login?url=http://dx.doi.org/10.1038/nn.2886

If you tested the contrast [1 -1] in solution 2, then this contrast would tell if the relationship in region A and B are different for the two behavioral measures.

One other caveat to both solution #1 and my proposed solution #2, both behavioral covariates need to be on the same scale. For example, height and weight would be bad covariates to compare because they differ by an order of magnitude, but Z-scored height and weight would be acceptable because they are both on the same order of magnitude.


Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Postdoctoral Research Fellow, GRECC, Bedford VA
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Sun, May 24, 2015 at 6:00 AM, Mike <[log in to unmask]> wrote:
Hi,

I encounter an analysis question and hope someone could help. In my group analysis, I first do a linear regression analysis using a Visual (V) behavioral parameter of each subject as a covariate, and I found that the brain region A is correlated with V. I also do a second group analysis in another model using a Spatial (S) behavioral parameter of each subject as a covariate, and I found that brain region B is correlated with S.

Since I've separately identified brain regions associated with V and S, my question is how can I make a direct statistical assessment of this difference? In other words, I want to prove that activity in region A is associated with / predicted by V, whereas that in B is associated with / predicted by S.

I have two ideas to solve this issue but not sure if my thinking is correct.

Solution (1).
Extract the BOLD signal changes in region A, plot the data with V and S parameters respectively. Prove that BOLD signals in A is correlated with V and not correlated with S. Compare the slopes of the two lines and, if both slopes are significantly different, I can say that activity in region A is associated with / predicted by V. Repeat the same process for region B.

Solution (2).
Construct another linear regression model (actually a multiple linear regression one) and enter V and S as the two covariates. Perform small-volume correction (SVC) analyses in regions A and B. Considering SVC in region A, if the contrast (1 0) shows that region A is significantly predicted by V after regressing out the effect of S, and contrast (0 1) shows that it is not correlated with S after regressing out the effect of V, I can conclude that activity in region A is associated with V. On the other hand, considering SVC in region B, if the contrast (0 1) shows that its activity is significantly predicted by S after regressing out the effect of V, and contrast (1 0) shows that it is not significantly predicted by V after regressing out the effect of S, I can conclude that activity in region B is associated with / predicted by S.

Can I use either one of them? Thanks a lot.

Mike