Negative Spatial Autocorrelation and its Impacts on Georeferenced Data Analyses : With Case Studies of Cancer Incidences

Spatial autocorrelation has been a popular research topic in spatial analysis for decades, mainly attributable to its frequent detection in georeferenced phenomenon. In addition, the presence of spatial autocorrelation complicates statistical analysis, because it violates the independence assumption in conventional statistics. However, most research, to date, focus on positive spatial autocorrelation while works about negative spatial autocorrelation relatively are scant. Negative spatial autocorrelation has long been neglected in literature, largely because of its rare observation in empirical data. This dissertation aims to contribute to the understanding of negative spatial autocorrelation with two major goals. One goal is to examine the impacts of spatial autocorrelation on statistical random variables with both positive and negative spatial autocorrelation being assessed and contrasted with each other. The literature is replete with acknowledgments that positive spatial autocorrelation inflates the variance of a random variable, and it also may alter other random variable distributional properties. Moreover, due to different quantifications of negative and positive spatial autocorrelation, their impacts on random variables are expected to differ. The other goal is to explore simultaneous materialization of negative spatial autocorrelation with positive spatial autocorrelation in empirical data, and a potential treatment of spatial autocorrelation mixture in spatial statistical analysis. Moran scatterplot and local Moran statistics can furnish efficient methods to uncover spatial autocorrelation mixture patterns. Other statistical

methodologies are also employed to identify and capture negative spatial autocorrelation, including a spatial autoregressive model with two-spatial autocorrelation-parameters, the mixed regressive spatial autoregressive moving average model, and Moran eigenvector spatial filtering method.