A multivariate CAR model for mismatched lattices

In this paper, we develop a multivariate Gaussian conditional autoregressive model for use on mismatched lattices. Most current multivariate CAR models are designed for each multivariate outcome to utilize the same lattice structure. In many applications, a change of basis will allow different lattices to be utilized, but this is not always the case, because a change of basis is not always desirable or even possible. Our multivariate CAR model allows each outcome to have a different neighborhood structure which can utilize different lattices for each structure. The model is applied in two real data analysis. The first is a Bayesian learning example in mapping the 2006 Iowa Mumps epidemic, which demonstrates the importance of utilizing multiple channels of infection flow in mapping infectious diseases. The second is a multivariate analysis of poverty levels and educational attainment in the American Community Survey.