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Hi Mauricio,

Please, see below:

On 3 November 2016 at 01:29, Mauricio Delgado <[log in to unmask]> wrote:
Dear Anderson,

Again, many thanks for your time and effort!!

I have done what you said, that is, looking at the test statistic signs for the group-specific effects relating to Q1 and Q2. I have done this in FSLview, in which I load in uncorrected tstat or zstat images  (or should cope images be used?

Either. They have the same sign.
 
), and look at the test sign in regions that showed the group-level 3-way interaction (G x Q1 x Q2).

However, given that the cluster of regions in which the 3-way interaction emerged is rather large, it is quite difficult to compare the signs for Q1 and Q2 between groups, as there is no consistency in the direction of the signs. For instance, for Q1 in the patient group some voxels in the effect site show positive values while others show negative values, and the same holds for Q1 in the control group. For Q2 I find similar trends.

The 3-way interaction is a complex question that has a complex answer. From the description you have it's a cluster where, as one moves across space, the slopes of both Q1 and Q2 change together, keeping the same difference between them across groups, which leads to the significant interaction. How this can be meaningful? I don't know. You have to decide what the interaction means and why it would be useful to test it.
 

So what is the best way to check the direction of the test statistic sign (positive | negative) in such a situation? Should one extract mean z or t values from the group-specific Q1 and Q2 statistic images so that you get a general idea of the direction? Or do you suggest something else?

It's possible to take the average signal of that cluster and run again the model with just that data. It can be done in statistical packages as SPSS, or if you save as a .csv, using the same design and contrasts with PALM. However, this will not guarantee a simple answer, because the original test used the data at each voxel, which isn't quite the same as the average, and that spatial variability will be lost.
 

Also, the signs only tell you the direction of the effects, but how do I know whether they are significant. That is, we don’t fully know if the interaction occurs because of the opposing relations Q1 and Q2 may have with Y, or is due to the fact that only one of the predictors (Q1 or Q2) is significantly associated with Y while the other is not (despite an ostensible association with Y based on test statistic sign). Can this be formally tested in FSL, I think reviewers also want to know what drives the 3-way interaction (e.g., significant but opposing relations between Y and the two predictors (Q1 and Q2) in patients relative to controls, or lack of significant associations between one or both of the predictors and Y in patients relative to controls). We just like to be really sure about what we are planning to write down, and the fact that formal testing of the test statistic signs is seemingly lacking makes us a bit uncomfortable. I truly hope you can come up with a solution for this matter.

There is no need to test the significance if the objective is only to see what is driving the interaction. The main effects may be both/all significant, or neither significant, or just one significant. To see what goes on with the interaction, the p-values for the main effects are not helpful, only the signs. Of course the testing the main effects may be interesting on its own right, in which case the contrasts for the main effects can be tested, but the result of the test doesn't affect much the interpretation of the interaction term.

Consider making some scatter plots for voxels of significant interaction of Q1 vs. FA and Q2 vs FA for each group separately. This should elucidate things.

All the best,

Anderson

 

Thanks in advance.

Regards,
Mauricio