Hierarchical model with subject-specific (spatial) correlation

Dear all,

I would like to develop a stan-model which I previously implemented as a linear mixed effects model using the nlme package in R. I have longitudinal data with up to n_k datapoints from k subjects. Means should be random among subjects and relationships between the individual points should be described via a multivariate normal distribution with correlations depending on the distance (in time) between the datapoints.

So basically the model would be a mixed model with random intercepts and spatial correlation. It is slightly more complicated since the correlation should further depend on covariates, so ideally I would define a function which sets up the covariance matrix for each subject individually (varying number of points per subject, different times and covariates) depending on a small set of estimated variance/covariance parameters. For the nlme package, I wrote a function which generates the subject-wise covariance matrix, but I don’t really have an idea how to do this with stan. Before extensive trial and error, is this generally feasible with stan and are there any tutorials on this matter I didn’t come across yet?

Thanks a lot in advance

It should generally be feasible unless your dataset is quite large.

I believe something at least close to what you aim for should be possible with the brms package (checkout cor_car and cor_sar), but I didn’t find a good tutorial. This would let you avoid writing Stan code yourself and generally has a more relaxed learning curve. If brms won’t be enough, I would suggest you start with the CAR code at https://github.com/mbjoseph/CARstan and rewrite the code for the precisions/covariance matrix.