Help with bfmi issues

Modeling
1

Hello, I could use some help in understanding why I am hitting energy issues in the model below

data{
    int N;
    vector[111] se;
    vector[111] effect_size;
    int outcome_id[111];
    int study_id[111];
}
parameters{
    vector[N] effect_size_true;
    vector[76] a;
    real alpha_bar;
    vector[17] b;
    real<lower=0> sigma_a;
    real<lower=0> sigma;
}
model{
    vector[111] mu;
    sigma ~ exponential( 10 );
    sigma_a ~ exponential( 10 );
    b ~ normal( 0 , 1 );
    alpha_bar ~ normal( 0 , 1 );
    a ~ normal( alpha_bar , sigma_a );
    for ( i in 1:111 ) {
        mu[i] = a[study_id[i]] + b[outcome_id[i]];
    }
    effect_size_true ~ normal( mu , sigma );
    effect_size ~ normal( effect_size_true , se );
}


E-BFMI indicated possible pathological behavior:
  Chain 1: E-BFMI = 0.161
  Chain 3: E-BFMI = 0.161
  Chain 4: E-BFMI = 0.171
E-BFMI below 0.2 indicates you may need to reparameterize your model.

The model is a meta-analysis of 111 studies, each reported with an effect size and a standard error. I include a varying effect for study and a fixed effect for the type of outcome the study was analyzing.

Thanks for your help!

2

For these meta-analysis things, it is usually worthwhile to integrate out the study-specific parameters, which are unlikely to be of much interest anyway. I don’t know the formulas off the top of my head for your case, but basically you want to use the likelihood function that frequentists would use.