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Copy pathdirect_access_h.stan
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direct_access_h.stan
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functions {
real psi_max(vector u_psi, int[] subj, vector RT) {
real psi_max;
psi_max = positive_infinity();
for (i in 1:num_elements(RT))
psi_max = fmin(psi_max, log(RT[i]) - u_psi[subj[i]]);
return (psi_max);
}
real da(int winner, real RT, vector beta, real P_b, real mu_da,
real mu_b, real sigma, real psi){
// theta = softmax(beta)
// log(P(w = 1 | theta, P_b)):
real log_P_w1;
// Prob of direct access given winner = 1
real log_P_da_gw1;
// Prob of backtracking given winner = 1
real log_P_b_gw1;
// Equation (10) in log:
log_P_w1 = log_sum_exp(categorical_logit_lpmf(1 | beta),
log(P_b)+ log1m_exp(categorical_logit_lpmf(1|beta)));
// Equation (14) in log:
log_P_da_gw1 = categorical_logit_lpmf(1 | beta) - log_P_w1;
// Equation (15) in log:
log_P_b_gw1 = log(P_b) + log1m_exp(categorical_logit_lpmf(1 | beta)) -
log_P_w1;
if(winner==1) {
return (log_P_w1 + // Increment on likelihood due to winner=1
// Increment on likelihood due to RT:
log_sum_exp(log_P_da_gw1 + lognormal_lpdf(RT - psi| mu_da, sigma),
log_P_b_gw1 + lognormal_lpdf(RT - psi | mu_da + mu_b, sigma) ));
} else {
return (log1m(P_b) + categorical_logit_lpmf(winner | beta) +
// Increment on likelihood due to RT:
lognormal_lpdf(RT - psi | mu_da, sigma));
}
}
vector da_rng(vector theta, real P_b, real mu_da, real mu_b, real sigma,
real psi) {
int orig_choice;
int backtracking;
vector[2] gen;
orig_choice = categorical_rng(theta);
backtracking = 0;
if (orig_choice!=1) backtracking = bernoulli_rng(P_b);
# Change the answer to 1 if there was backtracking:
gen[1] = backtracking ? 1 : orig_choice;
{ real mu; # it adds the mu_b if there is backtracking:
mu = mu_da + (backtracking ? mu_b : 0);
gen[2] = psi + lognormal_rng(mu, sigma);
}
return(gen);
}
}
data {
int<lower=0> N_obs;
int<lower=1> N_choices;
vector<lower=0>[N_obs] RT;
int<lower=1,upper=N_choices> winner[N_obs];
int<lower = 1> subj[N_obs];
int<lower = 1> N_subj;
int<lower = 1> item[N_obs];
int<lower = 1> N_item;
}
transformed data {
real<lower=0> min_RT;
real logmean_RT;
min_RT = min(RT);
logmean_RT = log(mean(RT));
}
parameters{
real<lower=0> sigma;
real<lower=0> mu_da_0raw;
real<lower=0> mu_b_0;
vector[N_choices-2] beta_incorrect;
real<lower=0> beta_added;
vector<lower = 0> [N_choices - 1] tau_u;
cholesky_factor_corr[N_choices - 1] L_u;
matrix[N_choices - 1, N_subj] z_u;
vector<lower = 0> [2] tau_u_RT;
cholesky_factor_corr[2] L_u_RT;
matrix[2, N_subj] z_u_RT;
vector<lower = 0> [N_choices - 1] tau_w;
cholesky_factor_corr[N_choices - 1] L_w;
matrix[N_choices - 1, N_item] z_w;
vector<lower = 0> [2] tau_w_RT;
cholesky_factor_corr[2] L_w_RT;
matrix[2, N_item] z_w_RT;
real<lower=0,upper=1> P_b;
vector[N_subj] u_psi;
real<lower = 0> tau_psi;
real<upper = psi_max(u_psi, subj, RT) / logmean_RT> psi_0raw;
}
transformed parameters{
real<lower=0> mu_da_0;
vector[N_choices] beta_0;
matrix[2, N_subj] u_RT;
matrix[N_choices, N_subj] u;
matrix[2, N_item] w_RT;
matrix[N_choices, N_item] w;
real psi_0;
u_RT = diag_pre_multiply(tau_u_RT, L_u_RT) * z_u_RT;
u[1:N_choices-1] = diag_pre_multiply(tau_u, L_u) * z_u;
u[N_choices] = rep_row_vector(0,N_subj);
w_RT = diag_pre_multiply(tau_w_RT, L_w_RT) * z_w_RT;
w[1:N_choices-1] = diag_pre_multiply(tau_w, L_w) * z_w;
w[N_choices] = rep_row_vector(0,N_item);
beta_0[1] = beta_added + fmax(max(beta_incorrect),0);
beta_0[2:N_choices-1] = beta_incorrect;
beta_0[N_choices] = 0;
mu_da_0 = mu_da_0raw * logmean_RT;
psi_0 = psi_0raw * logmean_RT;
}
model {
vector[N_obs] log_lik;
sigma ~ normal(0,2);
beta_added ~ normal(0,2);
beta_incorrect ~ normal(0,2);
psi_0raw ~ normal(0, 1);
tau_psi ~ normal(0, 1);
u_psi ~ normal(0, tau_psi);
to_vector(z_u_RT) ~ normal(0, 1);
to_vector(z_u) ~ normal(0, 1);
tau_u_RT ~ normal(0, 1);
tau_u ~ normal(0, 1);
L_u_RT ~ lkj_corr_cholesky(2.0);
L_u ~ lkj_corr_cholesky(2.0);
to_vector(z_w_RT) ~ normal(0, 1);
to_vector(z_w) ~ normal(0, 1);
tau_w_RT ~ normal(0, 1);
tau_w ~ normal(0, 1);
L_w_RT ~ lkj_corr_cholesky(2.0);
L_w ~ lkj_corr_cholesky(2.0);
P_b ~ beta(1,1);
mu_da_0raw ~ normal(0,1);
mu_b_0 ~ normal(0,2);
for (n in 1:N_obs) {
real mu_da;
real mu_b;
vector[N_choices] beta;
real psi;
mu_da = mu_da_0 + u_RT[1,subj[n]] + w_RT[1,item[n]];
mu_b = mu_b_0 + u_RT[2,subj[n]] + w_RT[2,item[n]];
beta = beta_0 + u[,subj[n]] + w[,item[n]];
psi = exp(psi_0 + u_psi[subj[n]]);
log_lik[n] = da(winner[n], RT[n], beta, P_b, mu_da, mu_b, sigma, psi);
}
target += log_lik;
}
generated quantities {
vector[N_choices] theta_0;
matrix[N_choices-1, N_choices-1] Cor_u;
matrix[N_choices-1, N_choices-1] Cor_w;
matrix[2, 2] Cor_u_RT;
matrix[2, 2] Cor_w_RT;
vector[N_obs] gen_RT;
vector[N_obs] gen_winner;
vector[N_obs] log_lik;
theta_0 = softmax(beta_0);
Cor_u = tcrossprod(L_u);
Cor_w = tcrossprod(L_w);
Cor_u_RT = tcrossprod(L_u_RT);
Cor_w_RT = tcrossprod(L_w_RT);
for (n in 1:N_obs) {
real mu_da;
real mu_b;
vector[N_choices] beta;
real psi;
vector[2] gen;
mu_da = mu_da_0 + u_RT[1,subj[n]] + w_RT[1,item[n]];
mu_b = mu_b_0 + u_RT[2,subj[n]] + w_RT[2,item[n]];
beta = beta_0 + u[,subj[n]] + w[,item[n]];
psi = exp(psi_0 + u_psi[subj[n]]);
gen = da_rng(softmax(beta), P_b, mu_da, mu_b, sigma, psi);
gen_winner[n] = gen[1];
gen_RT[n] = gen[2];
log_lik[n] = da(winner[n], RT[n], beta, P_b, mu_da, mu_b, sigma, psi);
}
}