Dear Mike, dear Donald,
> Seeing the effect with one regressor in the model and not the other regressor does not mean that the relationship is different between the two regressors
Yes. But it depends on the hypotheses. In the first message Mike stated "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." If this is the hypothesis there's no need to contrast the different regressors and/or the different regions. You would just run a regression model, report sig. clusters showing relationship with V and sig. clusters showing relationship with S. Based on the findings there's indeed a qualitative difference between the two regions (sig. vs. non-sig.), and the statement "activity in different portions of MCC is [significantly] predicted by V1 and V2." is correct. The problem is that people tend to misinterpret the statement, but this is their fault ;-) Whether the finding is that informative is another issue, as p values for correlations between A and V might indeed be e.g. .0009 = sig., and .0011 = non-sig. for A and S. That's why I used the terms "often" and "maybe". Often people just run linear regressions concluding that some predictors are relevant (the significant ones) and others are not (the non-sig. ones).
> 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
Just in case, no. The slopes might be significantly different, but both predictors might nonetheless differ significantly from zero / significantly predict activation (in the current data set it doesn't seem to be the case though).
> I would skip right to step 3. This isn't circular
But the selection of the clusters seems to be biased, as we already know there's a sig. non-zero effect for V within region A, while the effect for S could be anything, and clusters identified via the V contrast not just represent the true effect, as some truely activated voxels will fail to reach significance due to inherent noise in the data and other voxels reach sig. although there was no true effect. This seems to correspond to the example in Fig. 3 of Kriegeskorte et al. (2009, Nat Neurosci). Instead of the contrast A-D to define clusters for another analysis A-B it would be contrast V (or V-Baseline) to infer something about contrast V-S. Accordingly, it should be more likely to find false effects V-S due to the biased voxel selection via V.
In any case, I think it would be important to exactly specify the hypotheses with regard to regions (if there are any a-priori hypotheses) and statistical procedures.
Concerning the latter (without knowing what V and S represent), often the predictors are correlated to some extent. Thus it might be interesting to see how much of the variance within the fMRI data can uniquely be explained by V and by S, and how much of the variance is shared by V and S. Or it might be something like "does adding S to the model improve quality of the model for region A".
Concerning the former, maybe you had no a-priori hypotheses about different patterns at all. Any analysis going into this direction would thus be driven by your initial results and be of exploratory nature, for a proper analysis another data set would be required. But maybe you had a-priori hypotheses about different patterns for different cingulate subregions. Maybe it was not just two different subregions (like in turns out in the whole-brain results), but rather 3 or 5. In that case go with
1) a simple one-sample t-test for average activations. Then conduct ROI analyses (defined anatomically / cytoarchitectonically / functionally via e.g. previously reported coordinates or different resting state labels) and extract a summary score (average beta estimate, percent signal change, first eigenvariate) and forward this into a linear regression model outside SPM and calculate whatever you like depending on exact hypotheses (see above).
2) possibly set up an additional SPM multiple regression model for confirmatory/illustrative/explorative purpose, e.g. "these cingulate regions survive correction on whole-brain level", "our hypothesis was about coordinates x y z based on study ..., our peaks agree (not so) well", "actually it looks as if this previously reported effect is not just restricted to subregion A but also extends into region B", and also to look at other brain regions that might have not been a-priori but possibly also show sig. effects.
Best
Helmut
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