Hey all,

I’m trying to fitting a model with three free parameters from a MVN (full model code at the end, parts to emphasize the problem). The Problem is, that one Parameter is on the logit scale, whereas others are on are normal. Thus, I have to assign different constraints for the hyper and the subject parameters for the parameters, if I want to them to sample from a MVN, with reasonable results).

I managed the hyper par contraints with the following code:

```
data
{
vector[J] L; // vector of three lower boundaries
}
parameters
{
vector<lower=0>[J] hyper_pars_raw;
}
model
{
hyper_pars = L + hyper_pars_raw;
}
```

This seems to work fine, but I have problems to apply the same Solution with the subject parameters. I did it this way:

```
data {
vector[J] L; // vector of three lower boundaries
}
parameters {
vector<lower=0>[J] subj_pars_raw[N];
}
// Apply Bounds for Subject Pars
transformed parameters
{
for (k in 1:N) // is the Number of Subjects.
{
subj_pars[k,1] = L[1] + subj_pars_raw[k,1];
subj_pars[k,2] = L[2] + subj_pars_raw[k,2];
subj_pars[k,3] = L[3] + subj_pars_raw[k,3];
}
}
model
{
target += sum(hyper_pars);
// priors for hyper parameters
Omega ~ lkj_corr(1);
sigma ~ gamma(1,0.01);
hyper_pars[1] ~ normal(20,5);
hyper_pars[2] ~ normal(20,5);
hyper_pars[3] ~ normal(0,10);
// Sample Parameters
subj_pars[,1:3] ~ multi_normal(hyper_pars, Sigma);
for(i in 1:N)
{
// draw data from probabilities determined by parms
count[i,] ~ multinomial(probs[i,]);*
}
}
```

I got now the following error, which I can’t relate:

```
Chain 1: Rejecting initial value:
Chain 1: Error evaluating the log probability at the initial value.
Chain 1: Exception: multinomial_lpmf: Probabilities parameter is not a valid simplex.
sum(Probabilities parameter) = nan, but should be 1
(in 'model567430963fc4_ComplexSpan_LKJ' at line 114)
```

I also tried to define two varibales as constrained vector and one as unconstrained vector, to bound them together with append_col. But as the MVN needs a vector and can’t handle Matrices, this also didn’t worked.

I transformed it with to_vector, but got a dimension error then.

Here is the full model code:

```
data {
int <lower=0> N; // number of subjects
int <lower=0> K; // categories
int <lower=0> J; // Dims of Cov Matrix
vector[J] L;
int R[K]; // number of responses per category
int count[N,K]; // observed data
real scale_b; // set scaling for background noise
}
parameters {
// subject parameters
corr_matrix[J] Omega;
vector<lower=0>[J] sigma;
vector<lower=0>[J] hyper_pars_raw;
vector<lower=0>[J] subj_pars_raw[N];
}
transformed parameters{
vector[J] subj_pars[N];
vector[J] hyper_pars;
cov_matrix[J] Sigma;
// Transform f Parameter
real f[N] = inv_logit(subj_pars[,3]);
real mu_f = inv_logit(hyper_pars[3]);
// activations
vector[K] acts[N];
real SummedActs[N];
// probabilities
vector[K] probs[N];
// Transformations
hyper_pars = L + hyper_pars_raw;
for (k in 1:N)
{
subj_pars[k,1] = L[1] + subj_pars_raw[k,1];
subj_pars[k,2] = L[2] + subj_pars_raw[k,2];
subj_pars[k,3] = L[3] + subj_pars_raw[k,3];
}
// Transform Sigma
Sigma = quad_form_diag(Omega, sigma);
// loop over subjects to compute activations and probabilites
for (i in 1:N){
acts[i,1] = scale_b + subj_pars[i,1] + subj_pars[i,2]; // Item in Position
acts[i,2] = scale_b + subj_pars[i,1]; // Item in Other Position
acts[i,3] = scale_b + f[i]* (subj_pars[i,1]+subj_pars[i,2]);// Distractor in Position
acts[i,4] = scale_b + f[i]*subj_pars[i,1]; // Distractor in other Position
acts[i,5] = scale_b; // non presented Lure
SummedActs[i] = R[1] * acts[i,1] + R[2] * acts[i,2] + R[3] * acts[i,3]+ R[4] * acts[i,4]+ R[5] * acts[i,5];
probs[i,1] = (R[1] * acts[i,1]) ./ (SummedActs[i]);
probs[i,2] = (R[2] * acts[i,2]) ./ (SummedActs[i]);
probs[i,3] = (R[3] * acts[i,3]) ./ (SummedActs[i]);
probs[i,4] = (R[4] * acts[i,4]) ./ (SummedActs[i]);
probs[i,5] = (R[5] * acts[i,5]) ./ (SummedActs[i]);
}
}
model{
target += sum(hyper_pars);
// priors for hyper parameters
Omega ~ lkj_corr(1);
sigma ~ gamma(1,0.01);
hyper_pars[1] ~ normal(20,5);
hyper_pars[2] ~ normal(20,5);
hyper_pars[3] ~ normal(0,10);
// Sample Parameters
subj_pars[,1:3] ~ multi_normal(hyper_pars, Sigma);
// Loop over subjects
for(i in 1:N){
// draw data from probabilities determined by MMM parms
count[i,] ~ multinomial(probs[i,]);
}
}
```

Thanks for your time! Hopefully someone has similiar issues!