Dear all,

I’ve tried to find examples online for my question, but couldn’t find any. I was wondering whether you could maybe point me in the right direction?

I am trying to fit a hierarchical model with several hierarchical levels. I am trying to figure out how to include correlation/covariance matrices in the hierarchy.

My hierarchy is as follows: Group (1) -> Subject (6) -> Session (5 per subject)-> Measurements per session (~150 per session). The measurements (1 or 0) at the session level are fed into a logistic regression with 4 regressors.

An easier example would be where I only have group level and sessions in the hierarchy.

In this case I would use correlation/covariance matrices of size number of regressors (i.e. 4x4) [ as in the stan manual in the section 6.12 on multivariate priors for hierarchical models].

Now, how to add an additional level in the hierarchy?

I’ve considered having a covar/corr matrix at the highest level of size 4 x4. And then to have additionally covar/corr matrices for each subject of size 4x4 (i.e. that describe correlations within each subject across sessions. However, I don’t know how the link up the matrices at these two levels.

I thought about drawing them from a normal distribution, but I don’t think this is right:

parameters{

corr_matrix[nregs] corrGroup; //correlation matrix at group level

matrix<lower=0>[nregs,nregs] corrSigma; // standard deviation for each correlation to go from group to individual subject

corr_matrix[nregs] corrSub[nsub]; // correlation matrix for each individual subject

}

transformed parameters {

-> go from correlation matrix to covariance

}

model {

corrGroup ~ lkj_corr(2);

for (isub in 1:nsub){

for (ireg in 1:nregs){

for (jreg in (ireg+1):nregs){

corrSub[isub,ireg,jreg] ~ normal(corrGroup[ireg],corrSigma[ireg,jreg]);}}}