# Binomial GLMM model that fails to converge: which random effect to remove?

I am trying to use a binomial generalized linear mixed model to analyze binary data of an experiment. Just few details on the experiment that could be useful:

• The dependent variable is Score: 0 (incorrect); 1 (correct)
• The two predictors are CongRec: -1 (Congruent); +1 (Incongruent) and TempsExp: 6 levels (33ms,50ms,67ms,..117ms), used as a categorical predictor.

For each combination of the levels of the two predictors, we have 40 observations for 29 participants.

The issue: When I try to fit a model with only the main effects of the predictors (+intercept) and by-subject random slope for both Congruency and ExposureTime, the model fails to converge.

In such cases, I have been told to remove the random effect with the smallest variance. However depending on the way I define the predictor Congruence, i.e., as a categorical predictor with 2 levels (Congruence) or as continuous variable (CongRec), the random effect with the smallest variance differs.

Here is the R command for the (second) model:

Model4_Categbis = glmer(formula = Score~1+CongRec+TempsExp+(1+CongRec+TempsExp|Sujet),
data=donneestestCN, family="binomial", REML=F)


Here are the random effects for both cases:

1. Congruency as categorical predictor

2. Congruency as continuous predictor

So basically, in the first case, I should remove the random slope for CongRec while, in the second case, I should remove the random intercept by subject. Normally, I think the way I define the predictor Congruence should not have any influence on model main characteristics but, here, it does because of the non-convergence.

So, which random effects should I remove in your opinion and, that being done, which type of variable should I use for Congruency?