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Generalized Hierarchical Multivariate CAR Models for Areal Data
Author(s) -
Jin Xiaoping,
Carlin Bradley P.,
Banerjee Sudipto
Publication year - 2005
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/j.1541-0420.2005.00359.x
Subject(s) - multivariate statistics , deviance information criterion , autoregressive model , markov chain , markov chain monte carlo , markov random field , statistics , computer science , multivariate normal distribution , spatial analysis , marginal model , mathematics , data mining , monte carlo method , artificial intelligence , regression analysis , segmentation , image segmentation
Summary In the fields of medicine and public health, a common application of areal data models is the study of geographical patterns of disease. When we have several measurements recorded at each spatial location (for example, information on p ≥ 2 diseases from the same population groups or regions), we need to consider multivariate areal data models in order to handle the dependence among the multivariate components as well as the spatial dependence between sites. In this article, we propose a flexible new class of generalized multivariate conditionally autoregressive (GMCAR) models for areal data, and show how it enriches the MCAR class. Our approach differs from earlier ones in that it directly specifies the joint distribution for a multivariate Markov random field (MRF) through the specification of simpler conditional and marginal models. This in turn leads to a significant reduction in the computational burden in hierarchical spatial random effect modeling, where posterior summaries are computed using Markov chain Monte Carlo (MCMC). We compare our approach with existing MCAR models in the literature via simulation, using average mean square error (AMSE) and a convenient hierarchical model selection criterion, the deviance information criterion (DIC; Spiegelhalter et al., 2002, Journal of the Royal Statistical Society, Series B 64, 583–639). Finally, we offer a real‐data application of our proposed GMCAR approach that models lung and esophagus cancer death rates during 1991–1998 in Minnesota counties.