nu_objects_central_distance_saliency_horizontal.stan

// hierarchical wald-mixture model
functions{
#include stan/helpers/load_functions.stan
}
data{
  int N_obs; // total number of observations
  int order[N_obs]; // number that indexed observation within ppt and img
  real x[N_obs]; // x position of fixation
  real y[N_obs]; // y position of fixation
  real<lower=0> duration[N_obs]; // fixation duration
  int N_obj; // total number of objects across all scenes
  vector[N_obj] obj_center_x; // x position of the center of objects
  vector[N_obj] obj_center_y; // y position of the center of objects
  vector[N_obj] obj_width; // width of objects
  vector[N_obj] obj_height; // height of objects
  int N_ppt; // number of participants
  int<lower=1,upper=N_ppt> id_ppt[N_obs]; // number that indexes the participant
  int N_img; // number of images (stimuli)
  int<lower=1,upper=N_img> id_img[N_obs]; // number that indexed the image (stimulus)
  int obj_index_from[N_img]; // the number that starts the indexes of objects that belong to an image
  int obj_index_to[N_img]; // the number that ends the indexes of objects that belong to an image
  int N_obj_in_img[N_img]; // the number of objects in each stimulus
  real log_lik_saliency[N_obs]; // the log likelihood of (x,y) given the saliency
  int max_neighbors;
  int<lower=1,upper=max_neighbors> N_neighbors[N_obs]; // the number of closest pixels that we take into account when calculating the drift rate
  vector[max_neighbors] mean_sq_distances[N_obs];      // distances of the neighbors to the fixation locations
  vector[max_neighbors] saliency_log[N_obs];           // log of saliences of the neighbors
  
  int N_pix;
  real half_width_pixel;
  vector[N_pix] saliency_center_x;
  vector[N_pix] saliency_center_y;
  simplex[N_pix] saliency[N_img];
}
parameters{
  real<lower=0> sigma_center; // width of the central bias
  real<lower=0> sigma_distance; // width of the distance bias
  real<lower=0> scale_obj; // scaling factor of the object size
  real<lower=0> kappa; // concentration of the von Mises mixture (horizontal bias)
  simplex[5] weights; // objects, saliency, central bias, distance
  vector[N_obj] z_weights_obj; // logits of weights of individual objects
  //real mu_log_alpha; // population mean of the log of the decision boundary
  //real sigma_log_alpha; // population sigma of the log of the decision boundary 
  //vector[N_ppt] z_log_alpha; // individual offsets of boundary (on the log scale) for non-centered parametrization
  //real mu_log_sigma_attention; // population mean of the log of the width of attention window
  //real sigma_log_sigma_attention; // population sigma of the log ot the width of attention window 
  //vector[N_ppt] z_log_sigma_attention; // individual offsets of width (on the log scale) for non-centered parametrization
  vector[5] log_weights;
  vector[N_ppt] alpha;
  vector[N_ppt] sigma_attention;
}
transformed parameters{
  
}
model{
}
generated quantities{
  real<lower=0> nu[N_obs];
  real<lower=0> duration_mean[N_obs];
  
  for(i in 1:N_obs){
    int current_order = order[i];
    int current_ppt   = id_ppt[i];
    int current_img   = id_img[i];
    int current_nei   = N_neighbors[i];
    int from          = obj_index_from[current_img];
    int to            = obj_index_to[current_img];
    vector[N_obj_in_img[current_img]] weights_obj = softmax(z_weights_obj[from:to]);
    vector[2] log_lik_xy = log_weights[1:2]; // this vector stores the logs of (x, y) under each factor
    vector[2] att_filter = log_weights[1:2]; // only objects and saliency included in the calculation of drift
    
    // object oriented behavior
    log_lik_xy[1] += mixture_normals(x[i], y[i], weights_obj, 
                                     obj_center_x[from:to], scale_obj * obj_width [from:to],
                                     obj_center_y[from:to], scale_obj * obj_height[from:to]);  
                                     
    att_filter[1] += log_integral_attention_mixture_2d(x[i], y[i], weights_obj, 
                                                       obj_center_x[from:to], scale_obj * obj_width [from:to],
                                                       obj_center_y[from:to], scale_obj * obj_height[from:to],
                                                       sigma_attention[current_ppt], sigma_attention[current_ppt]);
                                                       
    // saliency
    log_lik_xy[2] += log_lik_saliency[i];
    
    att_filter[2] += log_sum_exp(saliency_log[i][1:current_nei] - mean_sq_distances[i][1:current_nei] / square(sigma_attention[current_ppt]));

    nu[i] = log_sum_exp(log_weights[1:2]) - log_sum_exp(att_filter);
    duration_mean[i] = alpha[current_ppt] / nu[i];
  }
}