Abstract
Moran’s index is a statistic that measures spatial autocorrelation, quantifying the degree of dispersion (or spread and properties) of components in some location/area. Recognizing that a single Moran’s statistic may not give a sufficient summary of the spatial autocorrelation measure, local spatial statistics have been gaining popularity. Accordingly, we propose to partition the area and compute the Moran’s statistic of each subarea. Patterns between the local neighbors are unveiled that would not otherwise be apparent. We consider the measures of Moran’s statistics while incorporating a time factor under a simulated multilevel Poisson phenomena where the dependence among the subareas is captured by the rate of increase of the phenomena over time, starting with a common factor in the scale. Our Moran’s statistics are calculated from an explicit algorithm in a Markov chain Monte Carlo simulation setting and further analyzed. The main consequence of our results is that trends and density of point patterns are captured from data and can serve as indices of local patterns. Results are compared to Geary’s statistics.
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The research for this paper was made possible by financial support from the U.S. Naval Academy. Material contained herein is solely the responsibility of the authors and is made available for the purpose of peer review and discussion. Its contents do not necessarily reflect the views of the Department of the Navy or the Department of Defense.
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Matthews, J.L., Diawara, N., Waller, L.A. (2019). Quantifying Spatio-Temporal Characteristics via Moran’s Statistics. In: Diawara, N. (eds) Modern Statistical Methods for Spatial and Multivariate Data. STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham. https://doi.org/10.1007/978-3-030-11431-2_9
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