@spinkney @andrjohns

Quick syntax question as I manipulate some of your copula code. I paste the full model below. I have not gotten the ordinal probit coded up yet, but in the meantime, I am just testing on continuous data to make sure I have the code up and running there first. Note, this is not āefficientā or anything. Just testing some code.

That said, I am just adjusting small parts for my own use. This includes my own mean function \mu (instead of the linear model) and I also want to customize the sd \sigma - basically I want sigma to vary as a function of x. Iāve gotten this to work in general models like here . My attempt at this is seen in the code below in the model block (I even write HELP to stand out :)). I know I need to manipulate this area AND manipulate the `normal_marginal`

function from above because as written it only takes a vector of 2 SDs (assumes constant noise) - essentially I am trying to model heteroscedasticity here.

Youāll see in some of my commented areas Iāve attempted a few things including declaring a new matrix. I always get an error related to incorrect syntax either in the `normal_marinal`

function or during my initial declaration in the model block.

I hope all of this makes sense!

```
functions{
matrix chol2inv2(matrix L) {
int K = rows(L);
matrix[K, K] K_identity = diag_matrix(rep_vector(1.0, K));
matrix[K, K] L_inv = mdivide_left_tri_low(L, K_identity);
matrix[K, K] rtn;
if (K == 0) {
return L;
}
if (K == 1) {
rtn[1, 1] = inv_square(L[1, 1]);
} else {
for (k in 1:K) {
rtn[k, k] = dot_self(tail(L_inv[ : , k], K + 1 - k));
for (j in (k + 1):K) {
int Kmj = K - j;
rtn[k, j] = dot_product(tail(L_inv[ : , k], Kmj + 1),
tail(L_inv[ : , j], Kmj + 1));
rtn[j, k] = rtn[k, j];
}
}
}
return rtn;
}
real multi_normal_cholesky_copula_lpdf(matrix U, matrix L) {
int N = rows(U);
int J = cols(U);
matrix[J, J] Gammainv = chol2inv2(L);
return -N * sum(log(diagonal(L))) - 0.5 * sum(add_diag(Gammainv, -1.0) .* crossprod(U));
}
real centered_gaussian_copula_cholesky_(matrix[,] marginals, matrix L, int[] order) {
// Extract dimensions of final outcome matrix
int N = rows(marginals[1][1]);
int J = rows(L);
matrix[N, J] U;
// Iterate through marginal arrays, concatenating the outcome matrices by column
// and aggregating the log-likelihoods (from continuous marginals) and jacobian
// adjustments (from discrete marginals)
real adj = 0;
int pos = 1;
for (m in 1 : size(marginals)) {
int curr_cols = cols(marginals[m][1]);
U[ : , pos : (pos + curr_cols - 1)] = marginals[m][1];
adj += sum(marginals[m][2]);
pos += curr_cols;
}
// Return the sum of the log-probability for copula outcomes and jacobian adjustments
return multi_normal_cholesky_copula_lpdf(U[ : , order] | L) + adj;
}
matrix[] normal_marginal(matrix y, matrix mu_glm, vector sigma) {
int N = rows(mu_glm);
int J = cols(mu_glm);
matrix[N, J] rtn[2];
//matrix[N, J] sigma2; HELP
// Initialise the jacobian adjustments to zero, as vectorised lpdf will be used
rtn[2] = rep_matrix(0, N, J);
for (j in 1 : J) {
rtn[1][ : , j] = (y[ : , j] - mu_glm[ : , j]) / sigma[1];
rtn[2][1, j] = normal_lpdf(y[ : , j] | mu_glm[ : , j], sigma[2]);
}
return rtn;
}
}
data{
int<lower=1> N; // total number of obs
vector[N] y1; // first continuous response
vector[N] y2; // second continuous response
vector[N] x;
int<lower=1> nresp; // number of responses
}
transformed data{
int Outcome_Order[2]; //response array
matrix[N,2] Y_gaussian; //response array
Outcome_Order[1]=1;
Y_gaussian[ : ,1] = y1;
Outcome_Order[2] = 2;
Y_gaussian[ : ,2] = y2;
}
parameters{
real <lower=0> a1;
real <lower=0> a2;
real <lower=0> r1;
real <lower=0> r2;
real b1;
real b2;
real <lower=0> kappa1;
real <lower=0> kappa2;
real <lower=0> sigma_y1;
real <lower=0> sigma_y2;
cholesky_factor_corr[nresp] Lrescor;
}
model{
// priors
a1 ~ normal(0,10); // half-normal
r1 ~ normal(0,1); //half-normal
b1 ~ normal(0,10);
a2 ~ normal(0,10); // half-normal
r2 ~ normal(0,1); //half-normal
b2 ~ normal(0,10);
kappa1 ~ normal(0,1); //half-normal
kappa2 ~ normal(0,1); //half-normal
sigma_y1 ~ exponential(2);
sigma_y2 ~ exponential(2);
Lrescor ~ lkj_corr_cholesky(1);
// likelihood
vector[N] mu1 = a1*x^r1+b1;
vector[N] mu2 = a2*x^r2+b2;
//vector[N] s1 = sigma_y1*(1+kappa1*x); HELP
//vector[N] s2 = sigma_y2*(1+kappa2*x); HELP
matrix[N,2] Mu_gaussian;
vector[2] sigma = transpose([sigma_y1, sigma_y2]);
Mu_gaussian[ : , 1] = mu1;
Mu_gaussian[ : , 2] = mu2;
//matrix[N,2] sigma; HELP
//sigma[ : , 1] = s1; HELP
//sigma[ : , 2] = s2; HELP
target += centered_gaussian_copula_cholesky_({normal_marginal(Y_gaussian, Mu_gaussian, sigma)}, Lrescor, Outcome_Order);
}
generated quantities{
corr_matrix[nresp] Rescor = multiply_lower_tri_self_transpose(Lrescor);
}
```