Hello everybody,

I am fitting a multiple outcome mixed effects model where the correlation between the outcomes are going to capture by the random effects (random intercept).

The random intercept follows `N~(0,sigma_u)`

I am having a hard time of selecting an appropriate prior for the sigma_u.

I tried with half-cauchy , inv-gamma priors but so far getting the same warning as follows :

```
There were 4 chains where the estimated Bayesian Fraction of Missing Information was low. See
http://mc-stan.org/misc/warnings.html#bfmi-low
3: Examine the pairs() plot to diagnose sampling problems
```

My summary results are as follows :

This is based on 4 chains ,10000 iterations on each and `cauchy(0,4)`

prior on sigma_u

It can be observed that the results are reasonably okay with all parameters except with the `sigma_u`

. For sigma_u the n_eff is very low and the `Rhat`

is close to 1.01.

The pairs plot looks like this for chain1. And it is pretty much same for other chains also.

You can see that the energy parameter is highly correlated with the sigma_u.

Can you suggest anything to improve the results ?

Also based on low n_eff , will this can be improved if I increase the number of iterations.

I am new to Bayesian and Stan. So any advice will be highly appreciate.

Thank you.

##############Update######

My model with following Specifications: two outcomes, separate predictors for each outcome and common random intercepts which will share by each subject across different outcomes

```
data {
int<lower=1> N;
int<lower=1> K1;
int<lower=1> K2;
int<lower=0,upper=1> y1[N];
int<lower=0,upper=1> y2[N];
row_vector[K1] x1[N];
row_vector[K2] x2[N];
}
parameters {
real alpha1;
real alpha2;
vector[K1] beta1;
vector[K2] beta2;
real<lower=0> sigma_u;
real u[N];
}
model {
u ~ normal(0, sigma_u);
beta1 ~ normal(0, 100);
beta2 ~ normal(0, 100);
alpha1 ~ normal(0, 100);
alpha2 ~ normal(0, 100);
sigma_u ~ cauchy(0, 4);
for(i in 1:N){
y1[i] ~ bernoulli(inv_logit(alpha1 + u[i] + x1[i]*beta1 ));
y2[i] ~ bernoulli(inv_logit(alpha2 + u[i] + x2[i]*beta2 ));
}
}
```