Dear Fsl experts,

I know this is not a new topic but I’ve carefully read about the previous discussions on this list (like https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind1503&L=fsl&P=R12676&1=fsl&9=A&J=on&d=No+Match%3BMatch%3BMatches&z=4
 and 
https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind1509&L=fsl&P=R41875&1=fsl&9=A&I=-3&J=on&X=DE4931DB92C803DC2B&Y=Kai.Wang-1%40colorado.edu&d=No+Match%3BMatch%3BMatches&z=4 ) and still believe that this my question deserves to be posted... By presenting some of our attempts and tests of two versions of mixed effect models as well as our confusion, we want to raise the question again, what is the right way to do so? 

We are trying to conduct a 2 by 2 mixed effect ANOVA at the higher level. Here’s a brief description of our fMRI study. We are doing a twin study using the nback task. There were monozygotic (MZ) twins and dizygotic (DZ) twins. Therefore we have a between-subject factor of zygosity dividing the subjects into two groups (MZ vs. DZ). Within each twin pairs, we identified one co-twin as high performance and the other as low performance co-twin according to their scores on several questionnaires. So we have a repeated/within subject factor of performance. We were doing mixed effect anvoa at the high level on interested 2-back vs. 0-back contrast.

I would like to talk about three sets of things we’ve done and the confusions.

1.	Models following instructions from this email list
Following instructions in previous discussions in the email list (see the two links above). We first conducted tried two models.

The first one was a "within-subject design" model (see tab “Within_Design_Contrasts” in attachment 1 for its design matrix and contrast matrix). H = high performance co-twins. L = high performance co-twins. In the contrast matrix, we modeled the simple effects of high vs. low and the interaction effect of the two factors. The second was a between subject model which could test the main effect of the between subject factor (see tab “Between_Design_Contrasts” in attachment 1for its design matrix and contrast matrix).

But the results looked weird. All the simple effect results (obtain from analyses in 1.1) of “high vs. low” looked exactly the same as the main effect of 2-back vs. 0-back (obtained from another one sample t test at the higher level). We thought this could not be the truth.

Therefore we want to test the correctness of this modelling by comparing its results of simple effects to standard paired t test which should be more liberal.

2.	Testing the “high vs. low” contrast through paired T test

We did two paired T tests for MZ and DZ twins respectively (see tab “T_Mz_Design_Contrast” in attachment 1 for the design and contrast matrix for the MZ model).
For both MZ and DZ tests, c3 and c4 generated the same results as the mixed model (see part 1), which we believe cannot be ture... But c1 and c2 yielded results which seemed to be more reasonable to us.

I think the fsl wiki (http://fsl.fmrib.ox.ac.uk/fsl/fslwiki/GLM#Single-Group_Paired_Difference_.28Paired_T-Test.29 ) suggested the style of c1 and c2 while the answers from FSL email list’s previous discussion (like those two links above) suggested c3 and c4. Also I think some online materials suggested the later (sorry for the absence of the link).

Could any experts give some comments on the math?

3.	Our version of mixed effect model
Since we are not quite sure about the mathematic mechanism of the model in part 1, we tried a model that we think was logically straight forward. It was a three level model. The lower level was the same as previous versions. In the second level, for each pair of twins, we used a fixed effect model to do a “High (performance) – Low” subtraction. So 61 second-level models was run. Then in the third level, we contracted an un-paired t test style model (see attachment 2).

Through this model, we abstained a result similar to c1 and c2 in part 2, which we think was reasonable. 

We also did “High + Low” and “Low - High” in the second level, and their correspondent third level analyses. We kind of believe this is the right thing to do for publication...



So, here’s our question, given these attempts/evidence, what should be the correct way and why?


Thank you so much,

Kai Wang
Postdoc in University of Colorado Boulder