I have a model that predicts a binary decision given current costs and biases built up over previous trials. However, some of my outcome data is missing. Currently I pass these data points as they are useful for updating my biases, but ignore them in the model block. I’m wondering what the correct way to handle these data points are in the model block, and also when generating my log liklihood. See my model below, thanks.

```
data {
int<lower=0> N_trial;
int<lower=0> trial_num[N_trial];
int<lower=0, upper=2> resp[N_trial];
int<lower=0, upper=1> error[N_trial];
vector[2] costs[N_trial];
}
parameters {
real<lower=0.0001> temp;
real<lower=0> max_bias;
real<lower=0, upper=1> bias_rate;
}
transformed parameters {
simplex[2] p[N_trial];
vector[2] bias;
vector[2] offset_inv_costs;
for (i in 1:N_trial) {
int t = trial_num[i];
if (t == 1) {
bias[1] = 0;
bias[2] = 0;
} else {
if(error[i-1] == 1) {
bias[1] = bias[1] * (1 - bias_rate);
bias[2] = bias[2] * (1 - bias_rate);
} else if (resp[i-1] == 1) {
bias[1] = bias[1] * (1 - bias_rate);
bias[2] = bias[2] + (max_bias - bias[2]) * bias_rate;
} else {
bias[1] = bias[1] + (max_bias - bias[1]) * bias_rate;
bias[2] = bias[2] * (1 - bias_rate);
}
}
offset_inv_costs[1] = 1 / (costs[i, 1] * (1 - bias[1]));
offset_inv_costs[2] = 1 / (costs[i, 2] * (1 - bias[2]));
p[i] = softmax(offset_inv_costs / temp);
}
}
model {
temp ~ normal(0.03, 0.01);
max_bias ~ normal(0.05, 0.015);
bias_rate ~ normal(0.5, 0.1);
for (i in 1:N_trial) {
if (resp[i] != 2) {
resp[i] ~ bernoulli(p[i, 2]);
}
}
}
generated quantities {
vector[N_trial] log_lik;
// log likelihood
for (i in 1:N_trial){
if (resp[i] != 2) {
log_lik[i] = bernoulli_lpmf(resp[i] | p[i, 2]);
}
}
}
```