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On Mon, Sep 9, 2013 at 2:54 PM, Annchen Knodt <[log in to unmask]> wrote:
Dear Dr. McLaren (and anyone else experienced with gPPI),

I apologize in advance for the long, and hopefully not too confusing email, but any advice or feedback would be appreciated.

We have been conducting analyses using your gPPI toolbox and have found some interesting results. Specifically we conducted 3-way psycho-physio-physiological interaction, testing if the time series from the seed region is differentially correlated with the rest of the brain as a function of our experimental task (condition A vs. condition B) and a time series from another ROI. After specifying this model on an individual level, we enter the beta images from the 3-way interaction term into a one sample t test and see significant results at the group level.

The three-way interaction would need to be formed from the beta of the 3-way elements as you should be using the conditional approach.
tc1*tc2*A,tc1*tc2*B,tc1*tc2,tc1*A,tc1*B,tc2*A,tc2*B,tc1,tc2 are the regressors in the model
 

We were interested in probing the interaction to further understand the results. Although we are not aware of a standard method for probing any type of PPI results, we have ideas for how to do so but had a couple concerns we wanted to get your thoughts on. Basically, we know from the GLM that when you have a significant interaction, the beta coefficient for a continuous variable in the model describes the slope for that independent variable when the other variables in the equation are zero. (If stress interacts with gender to predict depression, and gender is coded (male = 0, and female = 1) the beta for stress in the model containing stress, gender, and stress X gender would represent the relationship between stress and depression in males). Further, you can deduce the slope for females by adding the beta for the interaction term to the slope for males. We were interested applying this principle to data generated with your gPPI toolbox.

Yes. This principle works with any GLM. However, significance testing will be effected differently in different models.
 

Along with beta images for the 3-way interaction term, your toolbox generates beta images for all repressors in the model. We thought that it may be possible to extract parameters for the cluster identified with our one sample t test from the beta images for the time series in our seed region, which would give us the slope for the relationship between our seed and our identified cluster when the experimental task and time series from the second ROI are zero. Then we would extract parameters from the same cluster for the beta images associated with the interaction terms to determine how this slope changes as a function of experimental condition and BOLD signal in the second ROI.

Yes. The tc1 regressor would give you the slope of the relationship; however, this is only the partial correlation. In the regression model, you've removed the variance associated with tc2. The relationship of tc1 and the second ROI - which could be positive - could show up as negative in the model when you include tc2. So while you are right in that you are interpreting tc1 slopes as the value when tc2 is 0, it could still have a very different relationship.

Thus, I don't think you want to follow your approach as the initial starting point is possibly not where you want to start.

If you found a 3-way interaction, you should report the 3-way interaction. If you want to say more about this, then you could say condition A had a greater 2-way interaction than condition B. I think you want to simplify your analysis and not try and divide up the two-way interaction because of the concerns on interpreting the direction of the smaller effects.

A good comparison is resting state data. If you compare the effects of your seed region (tc1) with and without global signal regression (tc2), you will find very different patterns. Thus, gPPI with 2 tc that have shared variance might skew the relationship of one of the tc1 and make it difficult to interpret. In essence, looking at the separate pieces only makes sense in some cases.
 

Our concerns are threefold. First, would this method be feasible, and would extracting parameters from the beta images associated with the other regressors in the model be giving us values that would be representative of the betas derived from a GLM with a significant interaction produced by SPSS or other statistical software.

Yes. It's the same principle.
 
Second, with regard to the experimental task (condition A vs. condition B) although at the single subject level one condition is modeled as more positive and the other is modeled as less positive, the task is modeled continuously from (-0.14426) to (1.44326) (which are generated by the toolbox). Do you think it would be meaningful to probe the effects at experimental condition = 1 and experimental condition = 0?

I think you should model each condition separately using the 'cond' option. Then you the two-way interaction of A and B, which would be relative to the implicit baseline.
 
Finally, we were interested to know if there may be some sort of between subjects vs within subjects effects going on in SPM during the group level models that we are not aware of that may complicate interpretations of this type.

If you have a between-subjects group model, then the effects are between-subjects. The only time it gets complicated is when you add multiple observations per subject into the same model, then you have a mixture of effects.

Your between-subject effect could be the 3-way interaction from the first-level models though.
 

Any advice or feedback would be appreciated. Thanks for your time.

Adam Gorka & Annchen Knodt
Laboratory of NeuroGenetics
Duke University

Hope this helps.