# Low E-BFMI for Bayesian correlation model

**URL:** <https://discourse.mc-stan.org/t/low-e-bfmi-for-bayesian-correlation-model/32528>\
**Category:** Modeling\
**Tags:** fitting-issues\
**Created:** [August 23, 2023, 3:24pm UTC](https://discourse.mc-stan.org/t/low-e-bfmi-for-bayesian-correlation-model/32528 "2023-08-23T15:24:54Z")\
**Posts on this page:** 1\
**Page:** 1

<div class="post-metadata">

**Author:** ![hallerp](https://avatars.discourse-cdn.com/v4/letter/h/919ad9/32.png) [@hallerp](https://discourse.mc-stan.org/u/hallerp)\
**Post date:** [August 23, 2023, 3:24pm UTC](https://discourse.mc-stan.org/t/low-e-bfmi-for-bayesian-correlation-model/32528/1 "2023-08-23T15:24:54Z")

</div>

Hi everyone,

I’m currently trying to fit the following Bayesian correlation model, similar to [this one](https://online.ucpress.edu/collabra/article/3/1/25/112377/Bayesian-Inference-for-Correlations-in-the).

```stan
data {
    int<lower=1> N; // number of observations
    matrix[N, 2] xi_ind_obs_mu; // mean of observed effect in exp. 1/2
    matrix[N, 2] xi_ind_obs_sigma; // sd of observed effect in exp. 1/2
}

parameters {
    vector<lower=0>[2] xi_group_sigma; 
    vector[2] eta[N]; // true (unobserved) distribution for effect in exp. 1/2
    cholesky_factor_corr[2] L_Omega;
}

transformed parameters {
    matrix[2, 2] L_Sigma = diag_pre_multiply(xi_group_sigma, L_Omega);
}

model {
  xi_group_sigma ~ cauchy(0, 5); 
  L_Omega ~ lkj_corr_cholesky(2); 
  for (i in 1:N) {
    // loop through subjects
    eta[i] ~ normal(0, 10);
    target += multi_normal_cholesky_lpdf(eta[i] | [0, 0], L_Sigma); //
    for (j in 1:2){
      target += normal_lpdf(xi_ind_obs_mu[i, j] | eta[i, j], xi_ind_obs_sigma[i, j]);
    }
  }
}

generated quantities {
  matrix[2,2] Omega;
  matrix[2,2] Sigma;
  Omega = multiply_lower_tri_self_transpose(L_Omega);
  Sigma = quad_form_diag(Omega, xi_group_sigma); 
}

```

I’m correlating several (standardized: mean=0, sd=1) measures for a group of participants. For some of the measure pairs, the model fits well, but for most of the pairs, E-BFMI values are very low. There are no issues of convergence, though. For the correlation pairs with low E-BFMI, the 95% credible intervals for the correlation coefficients extracted from Omega are very wide (ranging from around -0.6 to 0.6).  
I got the warning message that E-BFMI below 0.2 indicates you may need to reparameterize your model. Does anybody have a suggestion how this could be done?

Thanks a lot in advance!