MULTIVARIATE SPATIO-TEMPORAL MODELS FOR HIGH-DIMENSIONAL AREAL DATA WITH APPLICATION TO LONGITUDINAL EMPLOYER-HOUSEHOLD DYNAMICS
MULTIVARIATE SPATIO-TEMPORAL MODELS FOR HIGH-DIMENSIONAL AREAL DATA WITH APPLICATION TO LONGITUDINAL EMPLOYER-HOUSEHOLD DYNAMICS
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DOI：
10.1214/15-aoas862
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发表时间：
2015-12-01
影响因子：
1.8
通讯作者：
Wikle, Christopher K.
中科院分区：
文献类型：
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作者：
Bradley, Jonathan R.;Holan, Scott H.;Wikle, Christopher K.
许多数据源报告了也在地理区域和时间上引用的相关感兴趣的变量；然而，人们可以容易地使用的结合这些多变量时空相关性的通用统计方法相对较少。此外，许多多变量时空面状数据集具有极高的维度，这导致在建立统计模型时存在实际问题。例如，我们分析了美国人口普查局的纵向雇主-家庭动态(LEHD)计划发布的季度劳动力指标(QWI)。量化指标按不同的变量、地区和时间点提供，产生了数以百万计的表格。尽管它们的覆盖面已经很广，但通过采用完全贝叶斯框架，QWI的范围可以扩大，以提供对遗漏价值的估计以及相关的不确定性衡量标准。受LEHD等联邦统计学应用的启发，我们引入了多变量时空混合效应模型(MSTM)，该模型可以有效地对高维多变量时空面状数据集进行建模。所提出的MSTM将Moran的I基函数的概念扩展到多变量时空环境中。这一扩展导致了几个方法论上的贡献，包括极其有效的降维，用于多变量时空区域过程的动态线性模型，以及使用新的参数模型来降低高维参数空间。
Many data sources report related variables of interest that are also referenced over geographic regions and time; however, there are relatively few general statistical methods that one can readily use that incorporate these multivariate spatio-temporal dependencies. Additionally, many multivariate spatio-temporal areal data sets are extremely high dimensional, which leads to practical issues when formulating statistical models. For example, we analyze Quarterly Workforce Indicators (QWI) published by the US Census Bureau's Longitudinal Employer-Household Dynamics (LEHD) program. QWIs are available by different variables, regions, and time points, resulting in millions of tabulations. Despite their already expansive coverage, by adopting a fully Bayesian framework, the scope of the QWIs can be extended to provide estimates of missing values along with associated measures of uncertainty. Motivated by the LEHD, and other applications in federal statistics, we introduce the multivariate spatio-temporal mixed effects model (MSTM), which can be used to efficiently model high-dimensional multivariate spatio-temporal areal data sets. The proposed MSTM extends the notion of Moran's I basis functions to the multivariate spatio-temporal setting. This extension leads to several methodological contributions, including extremely effective dimension reduction, a dynamic linear model for multivariate spatio-temporal areal processes, and the reduction of a high-dimensional parameter space using a novel parameter model.