An Ordinary Least Squares (OLS) Solution to Handling Spatial Autocorrelation Latent in Georeferenced Data

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The overall objective of this project is to exploit mathematical quantities related to the geography of georeferenced data-that is, data that are tagged to locations on the earth's surface. Its importance lies in its ability to allow scientists to work with more sophisticated and realistic models of various kinds of processes distributed across regions of the earth. The essence of the research is motivated by a recognition that the Moran Coefficient (a spatial autocorrelation index) can be decomposed into orthogonal map pattern components. This decomposition relates the Moran Coefficient directly to a standard linear regression, in which corresponding eigenvectors can be used as predictors. The algebraic structure is very similar to that of restricted maximum likelihood (REML) estimation. The analytical work will be complemented by numerical approaches that will focus on Markov Chain Monte Carlo (MCMC) analysis, empirical Bayes analysis, and simulation experiments. The basic knowledge advancement will be a description of auto-Poisson distributions containing positive spatial autocorrelation, and thus, a better understanding of how to interpret spatial data that are georeferenced (e.g. most satellite data). This research is significant to the advancement of scientific knowledge because it will establish the statistical theory necessary to convert georeferenced data into value-added information. The project addresses relevant societal concerns in at least three different ways: (1) it will contribute to an integration of satellite and social science data, a current goal of NASA; (2) it will help demystify spatial statistics, allowing maps to be viewed where today equations must be viewed; and, (3) it will make a sizeable part of statistics for spatial data more accessible to a larger audience by recasting this topic in conventional regression terms that are readily understood. Thus, the research will enable society's better understanding of such concerns as superfund remediation strategies pursued by the EPA, small-area estimation programs being implemented by various federal data collection agencies, and geographic disease cluster evaluations by national health organizations such as the NCI.