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Abstract:
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Spatial cluster detections often divided into general and focused tests. The general test is to detect a global or overall clustering trend, while the focus test is to identify the location of a local cluster. Although some tests are developed for the general, and some are developed for the focused, and some for both, the relationship between global and local has not been fully defined. In this paper, I first provide the taxonomy of global clustering and local clusters. I pointed out that global clustering and local clusters sometime are attributable the existence of local clusters, or the combination of both global and local trends. In some situations, even just a global trend could result the significant test results for both general and focused tests. Second, I define some global trends that may render different influence on the detection of a local cluster. Some global trends can be captured by spatial autoregressive models, some can be captured by explanatory variables, and some can be dealt with non-parametrically. Third, I relate global trends to common spatial events and point out that global trends are almost as a rule in spatial events rather than an exception. Both simulations and case studied are provided. In the case studied, infant mortality data from Guangxi province, China are used. It shows that without accounting for the global clustering trend, the detection of local clusters can be a moving target with significant local clusters almost covering the entire province. When the global trend is accounted for by elevation, which is a proxy of many factors, a number of significant local clusters can be detected.
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