All three solutions seem to be biased and/or circular to me. In your initial models or contrasts you detect region A based on a sig. relationship with variable 1 and region B based on a sig. relationship with variable 2. Then you look at these regions in another analysis to test whether they are associated with the cluster-defining variable (that's why the analysis is biased) plus the other variable. The second issue is that you switch between voxel-by-voxel analyses (initial analysis) and ROI or SVC analyses, thus looking at a composite score like average response or first eigenvariate in case of a ROI (which should be more sensitive as noise should be reduced) or possibly, at a restricted volume with a less conservative threshold in case of SVC).
There are three variables, V, S and some GM value, sounds like a multiple linear regression with predictor variables V and S, and response variable GM value. Now, what would you do outside SPM? Maybe a multiple linear regression with the two predictors included, look at the obtained T values and p values for each of the predictors? In that case people often are happy with e.g. one variable reaching sig. (~ V has a sig. influence on GM value) and another failing significance (~ S has no sig. influence on GM value). This could also be conducted with SPM, instead of just two p or T values you would of course obtain two statistical parametric maps (probably you would start with an initial F test to test whether *the model* based on the two predictors does explain any variance at all, and then focus on those voxels for which this is the case). In contrast to the other three solutions you would receive statistical values on a voxel-by-voxel basis, there would be no bias towards this or that predictor.
It might not be straightforward with SPM as you don't get outputs for e.g. coefficient of (multiple) determination R^2, adjusted R^2. But in principle you should be able to conduct all those analyses you would do in case of e.g. behavioral data.
Best
Helmut
|