Dear Daniel,

That is perfectly fine. You are right that in the context of an ABAB task design without an explicit baseline the individual AxROI or BxROI interaction effects from gPPI are not meaningful/estimable yet the difference effect "AxROI - BxROI" is perfectly estimable and meaningful. 

To clarify, this is the same issue of "non-estimable" contrasts that appears in standard second-level analyses, for example, if you have two subject groups (dummy coded as Group1 and Group2 covariates) and you define a second-level model that includes 'AllSubjects' (containing 1's for all subjects), 'Group1' (containing 1's for group1 subjects and 0's for group2), and 'Group2' (containing 1's for group2 subjects and 0's for group1). When doing this the design matrix contains three regressors, yet the rank of this matrix is only two, because the first regressor (AllSubjects) is simply a linear combination of the other two (Group1 + Group2). In this case none of the individual contrasts [1 0 0], [0 1 0], or [0 0 1] are estimable, yet the contrasts [0 1 -1] (looking at between-group differences) is perfectly fine/estimable from this design. In the context of gPPI analyses this issue arises because the gPPI model explicitly includes a baseline connectivity regressor (the "main physiological" effect), which acts as the "AllSubjects" term in the example above, which is going to be very close to a simple linear combination of your two connectivity-by-task interaction regressors (the "physiological*taskA + physiological*taskB" effects), which act as the "Group1 + Group2" terms in the example above. 

All of this means that, in your analyses, if you select simply the "taskA" condition in the second-level results window, then those results are not going to be particularly meaningful (they represent the difference in connectivity between taskA and an arbitrary/non-existing baseline condition). Yet, if you instead select the "taskA" and "taskB" conditions and enter a [1 -1] between-conditions contrast, then those results are perfectly valid/meaningful (they represent the difference in connectivity between taskA and taskB)

As an addition comment, I should probably point out that in the case of block designs both weighted-GLM and gPPI analyses will typically result in very similar results (almost identical for relativley long blocks), so in those cases I typically recommend using weighted-GLM just because it results in a simpler-to-use interpretation of those results (e.g. you can look at the individual condition effects and they will represent the connectivity "during" the blocks associated with that individual condition). Also as yet another additional comment, I should also probably point out that, in the same way that in the 'AllSubjects/Group1/Group2" example above it is actually possible to still get the average effect within the Group1 subjects from this design using a perfectly-estimable contrast [1 1 0] -or [1 0 1] for group2-, in gPPI analyses it is perfectly possible to still get the same "connectivity during taskA" effect-sizes from the original gPPI parameter estimates by using a contrast that combines the main physiological effect with the task-specific task interaction effects, instead of porting directly the interaction terms to the second-level analyses, but unfortunately the option to do so is not easily accessible in the CONN toolbox without some code-editing (so strictly speaking this limitation about non-estimable task-specific effects is just a limitation of the CONN software itself, not a limitation of gPPI analyses per se) 
 
Hope this helps
Alfonso 

Originally posted by Daniel Yang: