> Is it possible to do something similar in AFNI?
Model comparison is currently not implemented in 3dLME due to the complexity at the voxel level.
> Also, why it does not let me run the analysis without random effects specified (I have tried both: -ranEff NA and no ranEFF option at all)?
The current implementation in 3dLME requires a minimum setting with a random intercept. For voxel-wise analysis, it's hard, it not impossible, to vary the model or the random-effects components from voxel to voxel.
> How can I correctly report the betas that are taking the covariate in account?
How are you modeling the random effects? With a random intercept or both random intercept and slope? Does the average covariate value differ much between the two levels of the within-subject factor?