Continuous field statistical methods for spatial analysis in the social sciences.

摘要

Many standard references on spatial analysis separate techniques into continuous field techniques and discrete field, or "lattice-based" techniques. The continuous field techniques, which receive their most complete development within the field of geostatistics, are founded on the premise of covariance stationarity and the existence of a known model of spatial covariance. These assumptions have been regarded as implausible by many spatial analysts in the social sciences, particularly for the analysis of areal data. Thus, the continuous field methods have been largely dismissed as irrelevant for social science research.; This dissertation presents three new continuous field techniques to help alleviate these concerns. First, a nonparametric estimator is presented that generates valid spatial covariance functions, thus relaxing the requirement of a known spatial covariance function. This estimator is simpler than existing nonparametric estimators and relies on derivative constraints that are well-known in the geostatistics literature.; Second, a method for specifying the covariance structure for areal data from a stationary, parametric covariance model is specified. It is shown that within some limitations it is possible to estimate the parameters of the covariance function when only areal data are present. Monte Carlo simulation results suggest that this covariance estimator provides correctly sized confidence intervals when used in a feasible generalized least squares procedure for the spatial linear regression model.; Third, a generalized method of moments (GMM) estimator is proposed for situations when both geographically aggregated areal data and aspatial microdata are available, as is the case for many census data. Monte Carlo evidence suggest that the GMM estimator effectively combines information from both data, providing correctly sized confidence intervals and improved precision over the areal data estimators.