Equation representing 3dMVM model

Dear AFNI Expert,

During the process of post-hoc analysis to probe 3 way interaction, I wanted to check the exact equation representing my model examined through 3dMVM.
Maybe knowledge of internal functions of the 3dMVM would help, but I end up asking for an expert’s help here.

In my 3dMVM script,
I have 4 independent variables.
(2 categorical, 2 continuous) and 1 covariate.

There was a significant 3-way interaction effect in several regions, A (categorical) x B (categorical) x C (continuous).

To probe the pattern of interaction,
After extracting the beta estimates of significant regions of 3-way interaction effect,
I decided to use R lme4 package for examining the same model that involves 4 way interaction and lower-order terms using lmer function with a random intercept for each subject. This is the first step I thought appropriate for probing interaction using emmeans/emtrends function or interact_plot function in R.

lmer(Betaestimates ~1+

However, the 3-way interaction (ABC) turned out to be not significant at p < 0.001, while it should have been significant if the equation I wrote above represents my 3dMVM model.

For reference, If I remove the 4way interaction term in the model like below, 3way interaction becomes significant at p < .001.


I’d appreciate any suggestion.

Thanks in advance,


Such a small difference in p-value is not surprising for two main reasons:

** The LME model you adopted using lmer() is close to, but not exactly the same as, the one with 3dMVM. The MVM model is elaborated in the following paper: https://www.sciencedirect.com/science/article/pii/S1053811914005047

** Extracting and the averaging the voxels within an ROI would change the data structure to some extent. In other words, the two processes of averaging and modeling are not commutative.

Thank you very much !!