# Multilevel bayesian with AR1 correlation structure

How do I fit a bayesian multilevel model with with AR(1) correlation structure?

I am trying to teach myself bayesian modelling and I am wondering how you could specify a multilevel model with an AR(1) correlation structure.

e.g how do i get the equivalent from nlme using either JAGS or stan?

lme(y ~ time + x, random=~time|subject, corr=corAR1())


I never tried it my self, so at best you should trust, but verify.

I don't know the syntax of nlme (I use lmer4 in R), so I'll guess some stuff here.

Assuming your (non hierarchical) model is something like:

$y_{i,t} \sim N(a+b*y_{i,t-1} + c*t_{i} + d*x_{i}, \sigma^{2})$

And the hierarchical version (grouping by subject) would be:

$y_{i,t} \sim N(a[i] +b*y_{i,t-1} + c*t_{i} + d*x_{i}, \sigma^{2})$

$a[i] \sim N( \mu, \sigma_{a}^{2})$

Now just write your priors and hyperpriors and program it in Jags or Stan.

I suggest you to use tsbugs package. It will help you to create code to winbugs.