Quantitative factor in LME (within-subjects conditions)

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 : 1DD RT : ’
-gltLabel 2 ‘PC_RT’ -gltCode 2 ‘treatment : 1
PC RT : ’
-gltLabel 3 ‘treatment_x_RT’ -gltCode 3 ‘treatment : 1DD -1PC 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


Could you elaborate the reason for residualizing the RT values before feeding them into 3dLME? If possible, try incorporating the raw RT values into the 3dLME model. Also, compare the results with the 2 x 2 ANOVA without any covariates.

Hi Gang,

Thanks for your reply. The reason to residualize all data (even the RTs) is to control potential confounds (such as session order). For instance, the two different treatment conditions (DD and PC) were given in either session 1 or 2 (was counterbalanced across subjects). Because the same task was given in two sessions, participants’ RTs were generally lower in session 2 than 1 (irrespective of the treatment). So if RT somewhat differs across the sessions, I guess that would affect the distribution of RTs in each treatment condition (e.g., DD condition RT: generally high RTs from subjects had DD in session 1 but low RTs from subjects had DD in session 2). This is partly why I wanted to residualize RT as I would do for the brain data.

I also have tried with raw RT with and without covariates in the 3dLME, they look somewhat similar for some correlations that I checked.
But given the concern I have above, I thought I would have to control the factor somehow.

Best, Michelle


I would avoid residualizing if possible. The better approach is to incorporating everything in one model. If you believe that the average RT is lower during one session than the other, would centering RT within each session take care of your concern?

Dear Gang,

Sorry – I replied to the wrong post… I just attached the same post as a follow-up to your suggestion.

Thanks a lot for the suggestion. I see that centering would be a good option to remove the session effect (which is a within-ss covariate). I just have a few follow-up questions:

  1. But for between-ss covariates, it is ok to residualize it (e.g., body mass on RT in case if the covariate is related to the overall grand mean across subjects)? Since the between-ss covariates still preserve the subject-wise differences, I presume it might be something similar to centering across subjects?
  2. Would you still recommend using 3dLME framework after I center RTs or other ones like 3dMVM? My model specification for 3dLME is following:
    y (brain) ~ treatment * cue * RT (centered) + body mass + session order + (1|subj)
    -gltLabel 1 ‘DD_RT’ -gltCode 1 ‘treatment : 1DD RT : ’
    -gltLabel 2 ‘PC_RT’ -gltCode 2 ‘treatment : 1
    PC RT : ’
    -gltLabel 3 ‘treatment_x_RT’ -gltCode 3 ‘treatment : 1DD -1PC RT : ’ \

OR without any COVs:
y (brain) ~ treatment * cue * RT (centered) + (1|subj)…
and same GLTs as above.

Thank you so much for your help again. I really appreciate it.
Best, Michelle.


For between-subjects covariates, check out the discussion here: https://afni.nimh.nih.gov/pub/dist/doc/htmldoc/STATISTICS/center.html

For the model with RT, 3dLME is the way to go with a model like this:

y (brain) ~ treatment * cue * RT (centered) + (1+RT | subj)