Generalized hierarchical multivariate CAR models for areal data
Generalized hierarchical multivariate CAR models for areal data
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DOI：
10.1111/j.1541-0420.2005.00359.x
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发表时间：
2005-12-01
期刊：
影响因子：
1.9
通讯作者：
Banerjee, S
中科院分区：
文献类型：
--
作者：
Jin, XP;Carlin, BP;Banerjee, S
在医学和公共卫生领域，区域数据模型的一个常见应用是研究疾病的地理模式。当我们在每个空间位置记录多个测量值时（例如，来自相同人群或地区的p >= 2疾病的信息），我们需要考虑多变量区域数据模型，以处理多变量成分之间的依赖性以及站点之间的空间依赖性。在这篇文章中，我们提出了一个灵活的新类广义多元条件自回归（GMCAR）模型的面积数据，并显示它如何丰富的MCAR类。我们的方法不同于早期的，它直接指定的联合分布的多变量马尔可夫随机场（MRF）通过规范更简单的条件和边际模型。这反过来又导致显着减少分层空间随机效应建模的计算负担，其中后验汇总使用马尔可夫链蒙特卡罗（MCMC）计算。我们通过模拟将我们的方法与文献中现有的MCAR模型进行比较，使用平均均方误差（AMSE）和方便的分层模型选择标准，偏差信息标准（DIC; Spiegelhalter等人，2002，Journal of the皇家统计学会杂志，系列B 64，583-639）。最后，我们提供了一个真实的数据应用我们提出的GMCAR方法，模型肺癌和食道癌死亡率在1991年至1998年在明尼苏达州的县。
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.