Introduction to Methods for Areal (Lattice) Data

We present a review of both exploratory tools and modeling approaches which are customarily applied to data collected for areal units. We have in mind general, possibly irregular geographic units (as for example are common in spatial disease mapping) but of course include the special case of regular grids of cells (pixels). After a brief summary of common exploratory tools (such as Moran's I and Geary's C), we proceed on to a development of various results in Markov random field theory that underlie spatial lattice modeling, such as Brook's Lemma. Conditionally autoregressive (CAR), intrinsically autoregressive (IAR), and simultaneously autoregressive (SAR) models are also described and compared. We then outline use of these models in spatial disease mapping, highlighting computational issues, especially those related to model identifiability and use of the WinBUGS software. If time permits, we will also highlight multivariate generalizations of these models (e.g., the so-called MCAR model) and further related application areas (e.g., the use of CAR and and MCAR models in spatial and spatio-temporal frailty modeling).