Hi there,
I am trying to fit a reference point model inspired by the prospect theory on some agents doing the risky choice task (e.g.choosing lottery 100 with p = 0.5 or guaranteed 10). The stan model appears to be syntactically correct, but it kept showing Error in object@stan_args[[1]] : subscript out of bounds. I couldn’t quite figure out why. Below is my model. Any help is appreciated, many thanks!
// simple model fitting the individual as prospect-theory agent with a reference point
functions {
real subj_utility(real kappa, real alpha, real ref, real x){
real u; // subjective utility
if (ref == 0) {
u = x ^ alpha;
} else if (x > ref) {
u = (x - ref) ^ alpha;
} else if (x < ref) {
u = -kappa * (ref - x) ^ alpha;
}
return u;
}
real choiceprob(real kappa, real alpha, real beta, real ref, real lott_value, real lott_prob, real sb_value, real rew_multi) {
real y;
real v_sb; // subjective value of sb
real v_lott; // subjective value of lottery
v_sb = subj_utility(kappa, alpha, ref, sb_value*rew_multi);
v_lott = subj_utility(kappa, alpha, ref, lott_value*rew_multi) * lott_prob + subj_utility(kappa, alpha, ref, 0) * (1 - lott_prob);
y = beta * (v_lott - v_sb);
return y;
}
}
data {
int<lower=0> N; // Number of trials we have
vector[N] lott_value; // Lottery value for that choice
vector[N] lott_prob; // Lottery probabilities for that choice
vector[N] sb_value; // Surebet values for that choice
vector[N] rew_multi; // rew_multi values
vector[N] prev_reward; // previous reward values
int<lower=0,upper=1> y[N]; // Choices we observe (1 if they pick lottery)
}
parameters {
real<lower=0> kappa; // loss aversion
real<lower=0> alpha; // exponent of utility function
real<lower=0> beta; // perceptual sensitivity, the same beta as in beta-rho
real<lower=0> ref_0; // reference point value if reward(t-1) == 0
real<lower=0> ref_1; // reference point value if reward(t-1) != 0
}
model {
vector[N] thetas;
// kappa ~ normal(1,2);
// alpha ~ normal(0.5,1);
// beta ~ normal(0.8,1);
// ref_0 ~ normal(15,10);
// ref_1 ~ normal(15,10);
for(n in 1:N){
if (prev_reward[n] == 0) {
thetas[n] = choiceprob(kappa, alpha, beta, ref_0, lott_value[n], lott_prob[n], sb_value[n], rew_multi[n]);
} else if (prev_reward[n] > 0) {
thetas[n] = choiceprob(kappa, alpha, beta, ref_1, lott_value[n], lott_prob[n], sb_value[n], rew_multi[n]);
}
}
y ~ bernoulli_logit(thetas);
}
generated quantities {
vector[N] log_lik;
for(n in 1:N) {
if (prev_reward[n] == 0) {
log_lik[n] = bernoulli_logit_lpmf(y[n] | choiceprob(kappa, alpha, beta, ref_0, lott_value[n], lott_prob[n], sb_value[n], rew_multi[n]));
} else if (prev_reward[n] > 0) {
log_lik[n] = bernoulli_logit_lpmf( y[n] | choiceprob(kappa, alpha, beta, ref_1, lott_value[n], lott_prob[n], sb_value[n], rew_multi[n]));
}
}
}