Dear Gang,

I have a modelling question about 3dLME. The help page mostly describes between-subjects designs, but I was wondering about cases with within-subjects design. My main interest is on a correlation analysis between brain and behavioral data in respect to within-subjects conditions.

I have a 2 x 2 design -- both factors are within-subjects contrasts (i.e., 2 treatments and 2 cue conditions).
- There are several covariates of no interests that I would like to control (e.g., between-subjects and within-subjects covariates of no interest, such as body mass and session order; all centered at grand average).
- Because both the behavioral and brain data would be affected by these covariates of no interests, I first residualized the behavioral data using lme framework: RT ~ body mass + session order + (1|subj) — including all data points from 2 x 2 conditions (i.e., 4 data points / subject).

Constructing 3dLME, my full model is y (brain) ~ treatment * cue * RT (residual) + body mass + session order + (1|subj).
I also added GLTs to observe how within-subjects factor/level interacts/correlates with RTs. For instance, given a specific treatment condition, I tested the effect of RT, or tested treatment * RT:
-gltLabel 1 ‘DD_RT’ -gltCode 1 ‘treatment : 1*DD RT : ’ \
-gltLabel 2 ‘PC_RT’ -gltCode 2 ‘treatment : 1*PC RT : ’ \
-gltLabel 3 ‘treatment_x_RT’ -gltCode 3 ‘treatment : 1*DD -1*PC RT : ’ \
…

The part that I am uncertain is that the correlation analyses (GLTs) are between-subjects (across participants). But the actual data points in brain and RT are now centered at each subject’s mean (b/c of random intercept of subjects), such that the actual variation across subjects are removed. So my GLTs are testing the relationship between subject-wise relative changes of RTs and brain/voxels in a specific condition across subjects. I am not sure if this is the right approach to test the correlation with quantitative data.

I am using 3dLME because I have to control covariates of no interest (covs that are both between-subjects and within-subjects). And behavioral data is collected during scanning, so I wanted to control these covariates from both behavior and brain.

Your feedback would be greatly appreciated. Thank you!
Best, Michelle