Hierarchical Probit; bernoulli with transformed parameter

Modeling
1

Hi everyone!

I just started to use STAN and have a question about how to set up my parameters in a simple hierarchical probit regression.

I only have one predictor and two parameters (which jointly constitute an alpha parameter) to explain my binary outcome, and I want to let my parameters differ between each of the J individuals (who each made multiple choices) but sample from a common prior distribution.

I compute alpha in a for loop (there is probably a more efficient way) and apply the Bernoulli on the CDF of the individual alphas.

However, I get the following error: “Ill-typed arguments to ‘~’ statement. No distribution ‘bernoulli’ was found with the correct signature.” It seems like I supply (real,real) to bernoulli (I got that from the excellent tool here) whereas bernoulli expects something else.

To me, the error sounds a bit like I’m supplying a tuple of reals, but that shouldn’t be the case here. What do I miss?

Thank you (and apologies for making newbie mistakes)!
N

My model

data {
  int<lower=1> J; // number of individuals
  int<lower=1> N; // number of observations
  vector[N] x;    // predictor
  vector[N] y;    // outcome
  int<lower=1, upper=J> ind[N]; // individual indicator
}
parameters {
  vector<lower=0>[J] p1;
  vector<lower=0>[J] p2;
  
  real p1_mean;
  real p2_mean;
  
  real<lower=0> p1_var;
  real<lower=0> p2_var;

}

transformed parameters {
  vector[N] alpha;

  for (i in 1:N)
    alpha[i] = pow(p1[ind[i]], 2)/ (pow(p1[ind[i]], 2) + pow(p2[ind[i]], 2));
}

model {
  p1_mean ~ normal(0, 1);
  p2_mean ~ normal(0, 1);

  p1_var ~ normal(0, 1);
  p2_var ~ normal(0, 1);

  p1 ~ normal(p1_mean, p1_var);
  p2 ~ normal(p2_mean, p2_var);

for (n in 1:N)
    y[n] ~ bernoulli(Phi_approx(alpha[ind[n]]));
}
2

Welcome aboard!

I think the issue may be that the Bernoulli distribution is expecting the outcomes to be integers.

In the data block, you could try replacing
vector[N] y;
with
array[N] int y;

Let me know if that doesn’t work.

1 Like
3

Hi! Indeed, that solved the issue! Thanks so much!