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Many data sources report related variables of interest that are alsoreferenced over geographic regions and time; however, there are relatively fewgeneral statistical methods that one can readily use that incorporate thesemultivariate spatio-temporal dependencies. Additionally, many multivariatespatio-temporal areal data sets are extremely high dimensional, which leads topractical issues when formulating statistical models. For example, we analyzeQuarterly Workforce Indicators (QWI) published by the US Census Bureau'sLongitudinal Employer-Household Dynamics (LEHD) program. QWIs are available bydifferent variables, regions, and time points, resulting in millions oftabulations. Despite their already expansive coverage, by adopting a fullyBayesian framework, the scope of the QWIs can be extended to provide estimatesof missing values along with associated measures of uncertainty. Motivated bythe LEHD, and other applications in federal statistics, we introduce themultivariate spatio-temporal mixed effects model (MSTM), which can be used toefficiently model high-dimensional multivariate spatio-temporal areal datasets. The proposed MSTM extends the notion of Moran's I basis functions to themultivariate spatio-temporal setting. This extension leads to severalmethodological contributions, including extremely effective dimensionreduction, a dynamic linear model for multivariate spatio-temporal arealprocesses, and the reduction of a high-dimensional parameter space using anovel parameter model.

Multivariate spatio-temporal models for high-dimensional areal data with application to Longitudinal Employer-Household Dynamics