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+
+A*B*C*D+covariate
+(1|Subject),
REML=TRUE,na.action=na.omit,data=MyData)

However, the 3-way interaction (A*B*C) 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.

lmer(Betaestimates~1+
+A*B*C+covariate
+(1|Subject),
REML=TRUE,na.action=na.omit,data=MyData)

I’d appreciate any suggestion.

Thanks in advance,
Irene