I’m trying to understand the case for including fixed effects in your model if you already have random effects in your model. Particularly if you’re using non-centred parametization for your random effects, it strikes me that having a fixed effect too is unnecessary.

For example, if you already have this:

```
model {
for (g in 1:NumGroups) {
alpha_grp[g] = alpha_bar + alpha_raw[g] * alpha_sigma
beta_grp[g] = beta_bar + beta_raw[g] * beta_sigma
}
vector[N] mu = alpha_grp[grpID] + beta_grp[grpID] * x;
y ~ normal(mu, sigma);
}
```

is there any point in adding in the fixed effects?:

```
model {
for (g in 1:NumGroups) {
alpha_grp[g] = alpha_bar + alpha_raw[g] * alpha_sigma;
beta_grp[g] = beta_bar + beta_raw[g] * beta_sigma;
}
vector[N] mu = alpha_grp[grpID] + beta_grp[grpID] * x + alpha + beta * x;
y ~ normal(mu, sigma);
}
```

It appears to me that the fixed effects will be make no difference as `alpha_bar`

and `beta_bar`

are already ‘doing the job’ that `alpha`

and `beta`

would do.

Any guidance would be much appreciated.