// generated with brms 2.14.0
functions {
  /* turn a vector into a matrix of defined dimension 
   * stores elements in row major order
   * Args: 
   *   X: a vector 
   *   N: first dimension of the desired matrix
   *   K: second dimension of the desired matrix 
   * Returns: 
   *   a matrix of dimension N x K 
   */ 
  matrix as_matrix(vector X, int N, int K) { 
    matrix[N, K] Y; 
    for (i in 1:N) {
      Y[i] = to_row_vector(X[((i - 1) * K + 1):(i * K)]); 
    }
    return Y; 
  } 
 /* compute correlated group-level effects
  * Args: 
  *   z: matrix of unscaled group-level effects
  *   SD: vector of standard deviation parameters
  *   L: cholesky factor correlation matrix
  * Returns: 
  *   matrix of scaled group-level effects
  */ 
  matrix scale_r_cor(matrix z, vector SD, matrix L) {
    // r is stored in another dimension order than z
    return transpose(diag_pre_multiply(SD, L) * z);
  }
}
data {
  int<lower=1> N;  // total number of observations
  int<lower=1> N_CardiacOutcome;  // number of observations
  int<lower=2> ncat_CardiacOutcome;  // number of categories
  int Y_CardiacOutcome[N_CardiacOutcome];  // response variable
  int<lower=1> K_muAcute_CardiacOutcome;  // number of population-level effects
  matrix[N_CardiacOutcome, K_muAcute_CardiacOutcome] X_muAcute_CardiacOutcome;  // population-level design matrix
  int<lower=1> Ksp_muAcute_CardiacOutcome;  // number of special effects terms
  int<lower=1> K_muChronic_CardiacOutcome;  // number of population-level effects
  matrix[N_CardiacOutcome, K_muChronic_CardiacOutcome] X_muChronic_CardiacOutcome;  // population-level design matrix
  int<lower=1> Ksp_muChronic_CardiacOutcome;  // number of special effects terms
  int<lower=1> K_muT1MI_CardiacOutcome;  // number of population-level effects
  matrix[N_CardiacOutcome, K_muT1MI_CardiacOutcome] X_muT1MI_CardiacOutcome;  // population-level design matrix
  int<lower=1> Ksp_muT1MI_CardiacOutcome;  // number of special effects terms
  int<lower=1> K_muT2MI_CardiacOutcome;  // number of population-level effects
  matrix[N_CardiacOutcome, K_muT2MI_CardiacOutcome] X_muT2MI_CardiacOutcome;  // population-level design matrix
  int<lower=1> Ksp_muT2MI_CardiacOutcome;  // number of special effects terms
  int<lower=1> N_TroponinSecondMeasure;  // number of observations
  vector[N_TroponinSecondMeasure] Y_TroponinSecondMeasure;  // response variable
  int<lower=0> Nmi_TroponinSecondMeasure;  // number of missings
  int<lower=1> Jmi_TroponinSecondMeasure[Nmi_TroponinSecondMeasure];  // positions of missings
  int<lower=1> K_TroponinSecondMeasure;  // number of population-level effects
  matrix[N_TroponinSecondMeasure, K_TroponinSecondMeasure] X_TroponinSecondMeasure;  // population-level design matrix
  // data for group-level effects of ID 1
  int<lower=1> N_1;  // number of grouping levels
  int<lower=1> M_1;  // number of coefficients per level
  int<lower=1> J_1_CardiacOutcome[N_CardiacOutcome];  // grouping indicator per observation
  // group-level predictor values
  vector[N_CardiacOutcome] Z_1_muAcute_CardiacOutcome_1;
  vector[N_CardiacOutcome] Z_1_muAcute_CardiacOutcome_2;
  int<lower=1> NC_1;  // number of group-level correlations
  // data for group-level effects of ID 2
  int<lower=1> N_2;  // number of grouping levels
  int<lower=1> M_2;  // number of coefficients per level
  int<lower=1> J_2_CardiacOutcome[N_CardiacOutcome];  // grouping indicator per observation
  // group-level predictor values
  vector[N_CardiacOutcome] Z_2_muChronic_CardiacOutcome_1;
  vector[N_CardiacOutcome] Z_2_muChronic_CardiacOutcome_2;
  int<lower=1> NC_2;  // number of group-level correlations
  // data for group-level effects of ID 3
  int<lower=1> N_3;  // number of grouping levels
  int<lower=1> M_3;  // number of coefficients per level
  int<lower=1> J_3_CardiacOutcome[N_CardiacOutcome];  // grouping indicator per observation
  // group-level predictor values
  vector[N_CardiacOutcome] Z_3_muT1MI_CardiacOutcome_1;
  vector[N_CardiacOutcome] Z_3_muT1MI_CardiacOutcome_2;
  int<lower=1> NC_3;  // number of group-level correlations
  // data for group-level effects of ID 4
  int<lower=1> N_4;  // number of grouping levels
  int<lower=1> M_4;  // number of coefficients per level
  int<lower=1> J_4_CardiacOutcome[N_CardiacOutcome];  // grouping indicator per observation
  // group-level predictor values
  vector[N_CardiacOutcome] Z_4_muT2MI_CardiacOutcome_1;
  vector[N_CardiacOutcome] Z_4_muT2MI_CardiacOutcome_2;
  int<lower=1> NC_4;  // number of group-level correlations
  int prior_only;  // should the likelihood be ignored?
}
transformed data {
  int Kc_muAcute_CardiacOutcome = K_muAcute_CardiacOutcome - 1;
  matrix[N_CardiacOutcome, Kc_muAcute_CardiacOutcome] Xc_muAcute_CardiacOutcome;  // centered version of X_muAcute_CardiacOutcome without an intercept
  vector[Kc_muAcute_CardiacOutcome] means_X_muAcute_CardiacOutcome;  // column means of X_muAcute_CardiacOutcome before centering
  int Kc_muChronic_CardiacOutcome = K_muChronic_CardiacOutcome - 1;
  matrix[N_CardiacOutcome, Kc_muChronic_CardiacOutcome] Xc_muChronic_CardiacOutcome;  // centered version of X_muChronic_CardiacOutcome without an intercept
  vector[Kc_muChronic_CardiacOutcome] means_X_muChronic_CardiacOutcome;  // column means of X_muChronic_CardiacOutcome before centering
  int Kc_muT1MI_CardiacOutcome = K_muT1MI_CardiacOutcome - 1;
  matrix[N_CardiacOutcome, Kc_muT1MI_CardiacOutcome] Xc_muT1MI_CardiacOutcome;  // centered version of X_muT1MI_CardiacOutcome without an intercept
  vector[Kc_muT1MI_CardiacOutcome] means_X_muT1MI_CardiacOutcome;  // column means of X_muT1MI_CardiacOutcome before centering
  int Kc_muT2MI_CardiacOutcome = K_muT2MI_CardiacOutcome - 1;
  matrix[N_CardiacOutcome, Kc_muT2MI_CardiacOutcome] Xc_muT2MI_CardiacOutcome;  // centered version of X_muT2MI_CardiacOutcome without an intercept
  vector[Kc_muT2MI_CardiacOutcome] means_X_muT2MI_CardiacOutcome;  // column means of X_muT2MI_CardiacOutcome before centering
  int Kc_TroponinSecondMeasure = K_TroponinSecondMeasure - 1;
  matrix[N_TroponinSecondMeasure, Kc_TroponinSecondMeasure] Xc_TroponinSecondMeasure;  // centered version of X_TroponinSecondMeasure without an intercept
  vector[Kc_TroponinSecondMeasure] means_X_TroponinSecondMeasure;  // column means of X_TroponinSecondMeasure before centering
  for (i in 2:K_muAcute_CardiacOutcome) {
    means_X_muAcute_CardiacOutcome[i - 1] = mean(X_muAcute_CardiacOutcome[, i]);
    Xc_muAcute_CardiacOutcome[, i - 1] = X_muAcute_CardiacOutcome[, i] - means_X_muAcute_CardiacOutcome[i - 1];
  }
  for (i in 2:K_muChronic_CardiacOutcome) {
    means_X_muChronic_CardiacOutcome[i - 1] = mean(X_muChronic_CardiacOutcome[, i]);
    Xc_muChronic_CardiacOutcome[, i - 1] = X_muChronic_CardiacOutcome[, i] - means_X_muChronic_CardiacOutcome[i - 1];
  }
  for (i in 2:K_muT1MI_CardiacOutcome) {
    means_X_muT1MI_CardiacOutcome[i - 1] = mean(X_muT1MI_CardiacOutcome[, i]);
    Xc_muT1MI_CardiacOutcome[, i - 1] = X_muT1MI_CardiacOutcome[, i] - means_X_muT1MI_CardiacOutcome[i - 1];
  }
  for (i in 2:K_muT2MI_CardiacOutcome) {
    means_X_muT2MI_CardiacOutcome[i - 1] = mean(X_muT2MI_CardiacOutcome[, i]);
    Xc_muT2MI_CardiacOutcome[, i - 1] = X_muT2MI_CardiacOutcome[, i] - means_X_muT2MI_CardiacOutcome[i - 1];
  }
  for (i in 2:K_TroponinSecondMeasure) {
    means_X_TroponinSecondMeasure[i - 1] = mean(X_TroponinSecondMeasure[, i]);
    Xc_TroponinSecondMeasure[, i - 1] = X_TroponinSecondMeasure[, i] - means_X_TroponinSecondMeasure[i - 1];
  }
}
parameters {
  vector[Kc_muAcute_CardiacOutcome] b_muAcute_CardiacOutcome;  // population-level effects
  real Intercept_muAcute_CardiacOutcome;  // temporary intercept for centered predictors
  vector[Ksp_muAcute_CardiacOutcome] bsp_muAcute_CardiacOutcome;  // special effects coefficients
  vector[Kc_muChronic_CardiacOutcome] b_muChronic_CardiacOutcome;  // population-level effects
  real Intercept_muChronic_CardiacOutcome;  // temporary intercept for centered predictors
  vector[Ksp_muChronic_CardiacOutcome] bsp_muChronic_CardiacOutcome;  // special effects coefficients
  vector[Kc_muT1MI_CardiacOutcome] b_muT1MI_CardiacOutcome;  // population-level effects
  real Intercept_muT1MI_CardiacOutcome;  // temporary intercept for centered predictors
  vector[Ksp_muT1MI_CardiacOutcome] bsp_muT1MI_CardiacOutcome;  // special effects coefficients
  vector[Kc_muT2MI_CardiacOutcome] b_muT2MI_CardiacOutcome;  // population-level effects
  real Intercept_muT2MI_CardiacOutcome;  // temporary intercept for centered predictors
  vector[Ksp_muT2MI_CardiacOutcome] bsp_muT2MI_CardiacOutcome;  // special effects coefficients
  vector[Nmi_TroponinSecondMeasure] Ymi_TroponinSecondMeasure;  // estimated missings
  vector[Kc_TroponinSecondMeasure] b_TroponinSecondMeasure;  // population-level effects
  real Intercept_TroponinSecondMeasure;  // temporary intercept for centered predictors
  real<lower=0> sigma_TroponinSecondMeasure;  // residual SD
  vector<lower=0>[M_1] sd_1;  // group-level standard deviations
  matrix[M_1, N_1] z_1;  // standardized group-level effects
  cholesky_factor_corr[M_1] L_1;  // cholesky factor of correlation matrix
  vector<lower=0>[M_2] sd_2;  // group-level standard deviations
  matrix[M_2, N_2] z_2;  // standardized group-level effects
  cholesky_factor_corr[M_2] L_2;  // cholesky factor of correlation matrix
  vector<lower=0>[M_3] sd_3;  // group-level standard deviations
  matrix[M_3, N_3] z_3;  // standardized group-level effects
  cholesky_factor_corr[M_3] L_3;  // cholesky factor of correlation matrix
  vector<lower=0>[M_4] sd_4;  // group-level standard deviations
  matrix[M_4, N_4] z_4;  // standardized group-level effects
  cholesky_factor_corr[M_4] L_4;  // cholesky factor of correlation matrix
}
transformed parameters {
  matrix[N_1, M_1] r_1;  // actual group-level effects
  // using vectors speeds up indexing in loops
  vector[N_1] r_1_muAcute_CardiacOutcome_1;
  vector[N_1] r_1_muAcute_CardiacOutcome_2;
  matrix[N_2, M_2] r_2;  // actual group-level effects
  // using vectors speeds up indexing in loops
  vector[N_2] r_2_muChronic_CardiacOutcome_1;
  vector[N_2] r_2_muChronic_CardiacOutcome_2;
  matrix[N_3, M_3] r_3;  // actual group-level effects
  // using vectors speeds up indexing in loops
  vector[N_3] r_3_muT1MI_CardiacOutcome_1;
  vector[N_3] r_3_muT1MI_CardiacOutcome_2;
  matrix[N_4, M_4] r_4;  // actual group-level effects
  // using vectors speeds up indexing in loops
  vector[N_4] r_4_muT2MI_CardiacOutcome_1;
  vector[N_4] r_4_muT2MI_CardiacOutcome_2;
  // compute actual group-level effects
  r_1 = scale_r_cor(z_1, sd_1, L_1);
  r_1_muAcute_CardiacOutcome_1 = r_1[, 1];
  r_1_muAcute_CardiacOutcome_2 = r_1[, 2];
  // compute actual group-level effects
  r_2 = scale_r_cor(z_2, sd_2, L_2);
  r_2_muChronic_CardiacOutcome_1 = r_2[, 1];
  r_2_muChronic_CardiacOutcome_2 = r_2[, 2];
  // compute actual group-level effects
  r_3 = scale_r_cor(z_3, sd_3, L_3);
  r_3_muT1MI_CardiacOutcome_1 = r_3[, 1];
  r_3_muT1MI_CardiacOutcome_2 = r_3[, 2];
  // compute actual group-level effects
  r_4 = scale_r_cor(z_4, sd_4, L_4);
  r_4_muT2MI_CardiacOutcome_1 = r_4[, 1];
  r_4_muT2MI_CardiacOutcome_2 = r_4[, 2];
}
model {
  // likelihood including all constants
  if (!prior_only) {
    // vector combining observed and missing responses
    vector[N_TroponinSecondMeasure] Yl_TroponinSecondMeasure = Y_TroponinSecondMeasure;
    // initialize linear predictor term
    vector[N_CardiacOutcome] muAcute_CardiacOutcome = Intercept_muAcute_CardiacOutcome + Xc_muAcute_CardiacOutcome * b_muAcute_CardiacOutcome;
    // initialize linear predictor term
    vector[N_CardiacOutcome] muChronic_CardiacOutcome = Intercept_muChronic_CardiacOutcome + Xc_muChronic_CardiacOutcome * b_muChronic_CardiacOutcome;
    // initialize linear predictor term
    vector[N_CardiacOutcome] muT1MI_CardiacOutcome = Intercept_muT1MI_CardiacOutcome + Xc_muT1MI_CardiacOutcome * b_muT1MI_CardiacOutcome;
    // initialize linear predictor term
    vector[N_CardiacOutcome] muT2MI_CardiacOutcome = Intercept_muT2MI_CardiacOutcome + Xc_muT2MI_CardiacOutcome * b_muT2MI_CardiacOutcome;
    // linear predictor matrix
    vector[ncat_CardiacOutcome] mu_CardiacOutcome[N_CardiacOutcome];
    // initialize linear predictor term
    vector[N_TroponinSecondMeasure] mu_TroponinSecondMeasure = Intercept_TroponinSecondMeasure + Xc_TroponinSecondMeasure * b_TroponinSecondMeasure;
    Yl_TroponinSecondMeasure[Jmi_TroponinSecondMeasure] = Ymi_TroponinSecondMeasure;
    for (n in 1:N_CardiacOutcome) {
      // add more terms to the linear predictor
      muAcute_CardiacOutcome[n] += (bsp_muAcute_CardiacOutcome[1]) * Yl_TroponinSecondMeasure[n] + r_1_muAcute_CardiacOutcome_1[J_1_CardiacOutcome[n]] * Z_1_muAcute_CardiacOutcome_1[n] + r_1_muAcute_CardiacOutcome_2[J_1_CardiacOutcome[n]] * Z_1_muAcute_CardiacOutcome_2[n];
    }
    for (n in 1:N_CardiacOutcome) {
      // add more terms to the linear predictor
      muChronic_CardiacOutcome[n] += (bsp_muChronic_CardiacOutcome[1]) * Yl_TroponinSecondMeasure[n] + r_2_muChronic_CardiacOutcome_1[J_2_CardiacOutcome[n]] * Z_2_muChronic_CardiacOutcome_1[n] + r_2_muChronic_CardiacOutcome_2[J_2_CardiacOutcome[n]] * Z_2_muChronic_CardiacOutcome_2[n];
    }
    for (n in 1:N_CardiacOutcome) {
      // add more terms to the linear predictor
      muT1MI_CardiacOutcome[n] += (bsp_muT1MI_CardiacOutcome[1]) * Yl_TroponinSecondMeasure[n] + r_3_muT1MI_CardiacOutcome_1[J_3_CardiacOutcome[n]] * Z_3_muT1MI_CardiacOutcome_1[n] + r_3_muT1MI_CardiacOutcome_2[J_3_CardiacOutcome[n]] * Z_3_muT1MI_CardiacOutcome_2[n];
    }
    for (n in 1:N_CardiacOutcome) {
      // add more terms to the linear predictor
      muT2MI_CardiacOutcome[n] += (bsp_muT2MI_CardiacOutcome[1]) * Yl_TroponinSecondMeasure[n] + r_4_muT2MI_CardiacOutcome_1[J_4_CardiacOutcome[n]] * Z_4_muT2MI_CardiacOutcome_1[n] + r_4_muT2MI_CardiacOutcome_2[J_4_CardiacOutcome[n]] * Z_4_muT2MI_CardiacOutcome_2[n];
    }
    for (n in 1:N_CardiacOutcome) {
      mu_CardiacOutcome[n] = transpose([muAcute_CardiacOutcome[n], muChronic_CardiacOutcome[n], 0, muT1MI_CardiacOutcome[n], muT2MI_CardiacOutcome[n]]);
    }
    for (n in 1:N_CardiacOutcome) {
      target += categorical_logit_lpmf(Y_CardiacOutcome[n] | mu_CardiacOutcome[n]);
    }
    target += normal_lpdf(Yl_TroponinSecondMeasure | mu_TroponinSecondMeasure, sigma_TroponinSecondMeasure);
  }
  // priors including all constants
  target += student_t_lpdf(b_muAcute_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(bsp_muAcute_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(b_muChronic_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(bsp_muChronic_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(b_muT1MI_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(bsp_muT1MI_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(b_muT2MI_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(bsp_muT2MI_CardiacOutcome | 3,0,5);
  target += student_t_lpdf(b_TroponinSecondMeasure | 3,0,5);
  target += student_t_lpdf(sigma_TroponinSecondMeasure | 3, 0, 5.9)
    - 1 * student_t_lccdf(0 | 3, 0, 5.9);
  target += student_t_lpdf(sd_1 | 3, 0, 2.5)
    - 2 * student_t_lccdf(0 | 3, 0, 2.5);
  target += std_normal_lpdf(to_vector(z_1));
  target += lkj_corr_cholesky_lpdf(L_1 | 2);
  target += student_t_lpdf(sd_2 | 3, 0, 2.5)
    - 2 * student_t_lccdf(0 | 3, 0, 2.5);
  target += std_normal_lpdf(to_vector(z_2));
  target += lkj_corr_cholesky_lpdf(L_2 | 2);
  target += student_t_lpdf(sd_3 | 3, 0, 2.5)
    - 2 * student_t_lccdf(0 | 3, 0, 2.5);
  target += std_normal_lpdf(to_vector(z_3));
  target += lkj_corr_cholesky_lpdf(L_3 | 2);
  target += student_t_lpdf(sd_4 | 3, 0, 2.5)
    - 2 * student_t_lccdf(0 | 3, 0, 2.5);
  target += std_normal_lpdf(to_vector(z_4));
  target += lkj_corr_cholesky_lpdf(L_4 | 2);
}
generated quantities {
  // actual population-level intercept
  real b_muAcute_CardiacOutcome_Intercept = Intercept_muAcute_CardiacOutcome - dot_product(means_X_muAcute_CardiacOutcome, b_muAcute_CardiacOutcome);
  // actual population-level intercept
  real b_muChronic_CardiacOutcome_Intercept = Intercept_muChronic_CardiacOutcome - dot_product(means_X_muChronic_CardiacOutcome, b_muChronic_CardiacOutcome);
  // actual population-level intercept
  real b_muT1MI_CardiacOutcome_Intercept = Intercept_muT1MI_CardiacOutcome - dot_product(means_X_muT1MI_CardiacOutcome, b_muT1MI_CardiacOutcome);
  // actual population-level intercept
  real b_muT2MI_CardiacOutcome_Intercept = Intercept_muT2MI_CardiacOutcome - dot_product(means_X_muT2MI_CardiacOutcome, b_muT2MI_CardiacOutcome);
  // actual population-level intercept
  real b_TroponinSecondMeasure_Intercept = Intercept_TroponinSecondMeasure - dot_product(means_X_TroponinSecondMeasure, b_TroponinSecondMeasure);
  // compute group-level correlations
  corr_matrix[M_1] Cor_1 = multiply_lower_tri_self_transpose(L_1);
  vector<lower=-1,upper=1>[NC_1] cor_1;
  // compute group-level correlations
  corr_matrix[M_2] Cor_2 = multiply_lower_tri_self_transpose(L_2);
  vector<lower=-1,upper=1>[NC_2] cor_2;
  // compute group-level correlations
  corr_matrix[M_3] Cor_3 = multiply_lower_tri_self_transpose(L_3);
  vector<lower=-1,upper=1>[NC_3] cor_3;
  // compute group-level correlations
  corr_matrix[M_4] Cor_4 = multiply_lower_tri_self_transpose(L_4);
  vector<lower=-1,upper=1>[NC_4] cor_4;
  // extract upper diagonal of correlation matrix
  for (k in 1:M_1) {
    for (j in 1:(k - 1)) {
      cor_1[choose(k - 1, 2) + j] = Cor_1[j, k];
    }
  }
  // extract upper diagonal of correlation matrix
  for (k in 1:M_2) {
    for (j in 1:(k - 1)) {
      cor_2[choose(k - 1, 2) + j] = Cor_2[j, k];
    }
  }
  // extract upper diagonal of correlation matrix
  for (k in 1:M_3) {
    for (j in 1:(k - 1)) {
      cor_3[choose(k - 1, 2) + j] = Cor_3[j, k];
    }
  }
  // extract upper diagonal of correlation matrix
  for (k in 1:M_4) {
    for (j in 1:(k - 1)) {
      cor_4[choose(k - 1, 2) + j] = Cor_4[j, k];
    }
  }
}