Hi, I’m trying to implement this model from Morey et al. ( 2009) in `brms`

, to have more flexibility given that I am not an expert in raw STAN. I have read about `brms`

non-linear models and the possibility to insert transformed parameters and other more sophisticated stuff. My question is whether could be possible to implement this model in `brms`

. Given that I have never used other than the standard `lme4-like`

syntax in `brms`

I am not sure if `brms`

can handle this.

This is the Github repo https://github.com/richarddmorey/mass-at-chance and this is the raw STAN code:

```
data {
int<lower=1> I;
int<lower=1> J;
int N[I,J];
int y[I,J];
real<lower=0,upper=1> chance_p;
}
parameters {
vector[I] alpha;
vector<lower=0>[I] theta;
vector[J] beta;
real<lower=0> sigma_alpha;
real<lower=0> sigma_theta;
}
transformed parameters{
real p[I,J];
real x[I,J];
real q[I,J];
for(i in 1:I)
for(j in 1:J){
x[i,j] = theta[i] * (alpha[i] - beta[j]);
q[i,j] = x[i,j] > 0 ? Phi( x[i,j] ) : 0.5 ;
p[i,j] = (q[i,j] - 0.5) * 2 * (1 - chance_p) + chance_p;
}
}
model {
alpha ~ normal(0, sigma_alpha);
theta ~ normal(0, sigma_theta);
beta ~ normal(0, 1);
// I chose the parameters to approximately match
// the medians of the gamma priors on precision
// in the JAGS model
sigma_alpha ~ cauchy(0, 0.775);
sigma_theta ~ cauchy(0, 0.775);
for(i in 1:I)
for(j in 1:J)
y[i,j] ~ binomial(N[i,j], p[i,j]);
}
```

Reading the paper I think that the most critical parts are:

- the
`truncated-probit link function`

- the
`latent parameter`

estimated from data