Hi Gang,
Thank you so much for your response!!
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I assume that you're not interested in things such as heritability among different twin types.
For the purposes of this specific analysis - that is, looking at whether the task worked as it was supposed to, and whether it's correlated to age, no. However, I did read your recent HBM paper on ICC (http://onlinelibrary.wiley.com/doi/10.1002/hbm.23909/abstract) and am definitely interested in looking into this later. I was actually planning to ask you at some point for some clarification on how to run ICC(1,1) using the best current available AFNI tools, haha. But for now, yes, it's ok to ignore that.
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So, I would just simplify the situation by treating/pretending each pair of twins as *one* subject and using their effect estimates as duplicates. You can use 3dMVM, and the effects from each twin pair are averaged by 3dMVM if each twin pair shares the same subject ID. Does this sound like a reasonable approach to you?
Thanks for the suggestion! I have a few questions though:
1. Do you imply that I should use 3dcalc or something like that to compute the average coefficient map for each twin pair, for each condition; and then feed these average coefficient maps into 3dMVM? So, for each pair, there would be 3 rows in the data table (one for each condition)? Or, do you mean that I can just leave the data table as it is, and 3dMVM will average the repeated observations automatically?
2. By averaging the twins, am I not losing degrees of freedom / power? That is, this approach would allow me the same degrees of freedom as splitting the sample in half (such that no twin pair is in the same group), and then running the same analyses on each cohort, correct?
A clarification is in order here. So, my incentive with looking into a LME approach here was to attempt to maximize power while accounting for non-independence in the data. One thing I did previously, for looking at the interaction and age specifically (Goal #2), was feeding the first-level contrasts (e.g., cue5-cue0) as the observed variables, such that each twin pair had two rows and the non-independence was accounted for by the random intercept (specified as ~1, i.e., by "subj" column). This approach models age as a main effect on the contrast, and is straightforward to specify since there's only one "level" to account for. Although, it seems like I'd have to do a test for significance of the intercept in this approach, which doesn't seem possible using 3dLME (at least from my knowledge).
3. I guess what I am wondering here then is, will I only be able to confirm that the task is "doing what it's supposed to" (Goal #1) using the 3dMVM/averaged approach, or if there is some sort of way to do it in a more sophisticated fashion using a LME model. Like, for example, specifying nested random effects like '(1|subj)+(1|subj:ID)' [[ i.e., '(1|twinpair)+(1+|twinpair:individual)' ]]
Thank you so, so much!!!