In a random intercept model with a binomial outcome should the predicted probabilities be normally distributed?

Question

I have fit a random intercept model in glmer and stan_glmer with the following model formula where my event is 0/1 and x1 and x2 are continuous covariates:

     model <- stan_glmer(binary event ~ x1 + x2 +(1 | group), family="binomial"

The predicted probabilities (i.e. the fitted values from the model) are not normally distributed. Does this mean the model is wrong?

Answer 1

No, for a variety of different reasons. I can't think of any situation where I would expect the predictions to be Normally distributed. There might be cases where I'd expect the residuals to be Normally distributed, but even this is not expected in the Bernoulli (0/1) response case. For example, see this question ...