Hi there. I have finished fitting a multilevel regression model (binomial response, categorical predictors). The issue I am having is understanding whether to be concerned with the apparent spread of the posterior distribution of the intercept parameter when I plot the posterior model (using mcmc_areas). I have attached the output:

It seems like the posterior distribution over the intercept is spread far too widely across parameter values (ranging from ~-10 to ~6). But, I am not sure; is this something to be concerned about? As far as I can tell, the posterior model parameter values do not look abnormal (below), and the tails of the other parameter estimates do not appear abnormal. On the other hand, if this is something I should be concerned about, how might I go about fixing this?

Here is the code I used to specify the model:

comp_glmm2 ā brm(values_anna_bernoulli ~ age_group * speaker + order_comp_prod + (speaker|participant_id) + (1|comp_trial),

data = wepc_comp,

family = bernoulli,

chains = 4,

iter = 10000,

warmup = 2000,

control = list(adapt_delta = 0.9999),

save_pars = save_pars(all = TRUE),

cores = 4,

seed = 31)

Here is the model output:

Family: bernoulli

Links: mu = logit

Formula: values_anna_bernoulli ~ age_group * speaker + order_comp_prod + (speaker | participant_id) + (1 | comp_trial)

Data: wepc_comp (Number of observations: 236)

Samples: 4 chains, each with iter = 10000; warmup = 2000; thin = 1;

total post-warmup samples = 32000

Group-Level Effects:

~comp_trial (Number of levels: 2)

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

sd(Intercept) 0.89 1.08 0.02 3.80 1.00 9377 14010

~participant_id (Number of levels: 61)

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

sd(Intercept) 1.59 0.45 0.80 2.59 1.00 9772 14781

sd(speakerp1p2) 0.94 0.65 0.05 2.44 1.00 4707 10475

cor(Intercept,speakerp1p2) 0.14 0.52 -0.89 0.95 1.00 13363 14528

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

Intercept -0.73 0.93 -2.59 1.18 1.00 11518 11729

age_group4 1.19 0.65 -0.01 2.53 1.00 13916 16754

speakerp1p2 0.06 0.56 -1.07 1.15 1.00 19916 20618

order_comp_prodComprehension2nd 0.07 0.57 -1.03 1.20 1.00 13526 18799

age_group4:speakerp1p2 -1.11 0.75 -2.61 0.38 1.00 19241 20712

OS: Mac (Catalina, 10.15.7)

brms: 2.15.0

I apologize if I have excluded pertinent information or have formatted the code or output unconventionally for this post, this is my first time posting on this forum. Thank you.