I am just moving some of my ex-post analyses from the generated quantities block in Stan to R.

In Stan, I use the following code:

```
data{
int<lower = 1> N;
int<lower = 0, upper = 1> y[N];
int<lower = 0> K;
matrix[N, K] X;
...
parameters {
vector[K] alpha
...
}
generated quantities {
vector[N] y_pred;
for (t in 1:N) {
y_pred[t] = bernoulli_logit_lpmf(y[t] | X[t]*alpha)
}
}
```

In R, I translated this into the following formula:

```
ext_mod = rstan::extract(out)
N_draws = nrow(ext_mod$alpha)
y_pred = matrix(nrow = N_draws, ncol = N)
for(d in 1:N_draws){
for (t in 1:N) {
dbinom(y[t], size = 1,
prob = exp(X[t, ]%*%ext_mod$alpha[d, ]) /
(1+exp(X[t, ]%*%ext_mod$alpha[d, ])))
}
}
```

I was wondering if what I have specified in R using dbinom() corresponds to the log Bernoulli probability mass of y (bernoulli_logit_lpmf) I have specified in Stan. It is my best guess based on this page.

Background of the question is that I notice a discrepancy between the analyses performed in Stan in generated quantities and the analyses in R (…even though I exported the posterior output and then went through all the draws in R as well).

Thanks in advance.