I want to collect experimental data with 3 between subject levels and 2 within-subject levels to observe main effects as well as interaction effects on a binomial outcome. I had firstly defined the model as

F−1(πij)= β00 + β01Uj + β02Vj + β10Xij + β11Xij * Uj + β12Xij * Vj + Xije1j + e0j + rij

Here V and U represent Deviance Coded Levels of the Between-Subject Variable, j represents the person and i represents the level of the within-subject variable.

But with only a single observation for each level of the within-subject factor, the random slope would be completely confounded with the trial level error (Barr et al., 2013), so that was removed and the following remained

F−1(πij)= β00 + β01Uj + β02Vj + β10Xij + β11Xij * Uj + β12Xij * Vj + e0j + rij

I subsequently simulated data with random intercepts and tried to fit a mixed model with glmer in lme4, with the following code:

model