Dear all,

I am trying to use non-centred parameterisation on a hierarchical model. My problem is that I’m not sure how to deal with boundaries for the parameter of the individual subject that is drawn from the group level. Let’s assume I want the parameter for my individual subject to be larger than 0. In the centered parameterisation I would code:

```
parameters{
real<lower=0> p_group_mu; // group level parameter in my model that only makes sense >0
real<lower=0> p_group_sd; // group level standard deviation
real<lower=0> p_sub[nsub]; //individual subject parameter
}
model{
p_sub ~ normal(p_group_mu,p_group_sd);
}
```

In the non-centred parameterisation, I am stuck with what boundaries to set for p_sub_raw or how otherwise to have the boundaries on p_sub as before:

```
parameters{
real<lower=0> p_group_mu;
real<lower=0> p_group_sd;
real<lower=0> p_sub_raw[nsub]; // ?? what boundaries to choose here??
}
transformed parameters{
real<lower=0> p_sub[nsub];
p_sub = p_group_mu + p_group_sd*p_sub_raw;
}
model{
p_sub_raw ~ normal(0,1);
}
```

One solution that I see is to have an extra transformation that has p_sub_raw without boundaries and in the transformed parameters I then use

```
p_sub = exp(p_group_mu + p_group_sd*p_sub_raw)
```

It does change the meaning of the hiearchy somewhat. Is this the only way?

Many thanks

Jacquie