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What p value should I report here?

Can you show us summary(GCA_data) and
summary(model.frame(fitted_model)) please? It looks like for some reason
(maybe because of observations dropped due to NA values?) you have no
variation in your predictor variable (P_Diz_today).

  It's also potentially problematic that you have an observation-level
random effect for a Bernoulli outcome (i.e., you're fitting a binomial
model with a single-column value as the response and no weights=
argument, which implies you have a 0/1 outcome; you have the same number
of groups in your fully nested [ID:Scan:Side] random effect as
observations), but I don't think this would lead to the dropping of the
P_Diz_today predictor ...

  cheers
    Ben Bolker
On 2019-05-02 3:30 p.m., DESPINA MICHAILIDOU wrote: