Hi,

I would like to translate a relatively simple Lavaan model to Stan. I’m aware of the `blavaan`

package, but I plan to augment this model in the future with some specifications that are not available in `blavaan`

, so it’s important that I learn how to code this model directly in Stan.

This is the model depicted in a path diagram:

Based on previous studies, I constrain the variances of the error terms E_1, E_2, and E_3 to be equal for identifiability.

Here’s the Lavaan model, which I run with the `lavaan()`

and `blavaan()`

functions’ default specifications:

```
model.lavaan <- '
cs08 =~ 1 * cs08a247
cs10 =~ 1 * cs10c247
cs11 =~ 1 * cs11d247
cs10 ~ beta21 * cs08
cs11 ~ beta32 * cs10
cs08a247 ~~ vare * cs08a247
cs10c247 ~~ vare * cs10c247
cs11d247 ~~ vare * cs11d247
cs08 ~~ resvart08 * cs08
cs10 ~~ resvart10 * cs10
cs11 ~~ resvart11 * cs11
'
```

And here’s my current Stan code:

```
data {
int<lower=1> N; // Number of observations
vector[N] cs08a247; // Observed variable for cs08
vector[N] cs10c247; // Observed variable for cs10
vector[N] cs11d247; // Observed variable for cs11
}
parameters {
real beta21; // Effect of cs08 on cs10
real beta32; // Effect of cs10 on cs11
real<lower=0> sde; // Error variance for observed variables
real<lower=0> ressd08; // Residual variance of cs08
real<lower=0> ressd10; // Residual variance of cs10
real<lower=0> ressd11; // Residual variance of cs11
vector[N] cs08_std; // Standard normal for cs08 latent variable
vector[N] cs10_std; // Standard normal for cs10 latent variable
vector[N] cs11_std; // Standard normal for cs11 latent variable
}
transformed parameters {
vector[N] cs08 = ressd08 * cs08_std; // Apply non-centered parametrization
vector[N] cs10 = beta21 * cs08 + ressd10 * cs10_std; // Apply non-centered parametrization
vector[N] cs11 = beta32 * cs10 + ressd11 * cs11_std; // Apply non-centered parametrization
}
model {
// Priors for beta coefficients
beta21 ~ normal(0, 10);
beta32 ~ normal(0, 10);
// Prior for variance parameters
sde ~ gamma(1,.5);
ressd08 ~ gamma(1,.5);
ressd10 ~ gamma(1,.5);
ressd11 ~ gamma(1,.5);
// Priors for standard normal parameters
cs08_std ~ normal(0, 1);
cs10_std ~ normal(0, 1);
cs11_std ~ normal(0, 1);
// Measurement model
cs08a247 ~ normal(cs08, sde);
cs10c247 ~ normal(cs10, sde);
cs11d247 ~ normal(cs11, sde);
}
```

My estimates are similar to those yielded by `lavaan()`

and `blavaan()`

, but I’m getting a low E-BFMI.

Could someone please assist me? I appreciate your time and help.