Measuring local spatial autocorrelation with data reliability information

Authors: David Wong*, George Mason University, Hyeongmo Koo, Nanjing Normal University, Yongwan Chun, The University of Texas at Dallas
Topics: Spatial Analysis & Modeling
Keywords: Local Spatial Bhattacharyya coefficient, Local Moran, Local Geary, Generalized randomization approach, Spatial cluster detection
Session Type: Paper
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In measuring spatial autocorrelation (SA), popular measures such as Moran’s I, Geary Ratio and G-statistics adopt an implicit assumption that the observed values, which may be statistical estimates, have uniform error. However, this assumption is the exception rather than the norm. Current formulations of SA statistics and the associated assumption leads to two consequences: when estimate error is ignored, the estimated SA using traditional SA statistics are inflated; when these SA statistics are computed, users ignore estimate error information (often in standard error or margin of error) because it is not required to compute SA statistics. To accommodate estimate error in the evaluation of SA, the spatial Bhattacharyya coefficient (SBC) has been proposed as a global SA measure. When comparing two observations, the SBC considers not just their estimates but also their error. In fact, SBC compares two distributions and provides a distance to indicate their similarity level. This paper extends SBC by proposing a local version of SBC to analyze local SA patterns. Similar to other local SA statistics, the local SBC is computed for each unit, indicating how its distribution is similar to distributions in neighboring units. Significance tests for the local SBC are conducted under conditional and total randomization assumptions by using a generalized randomization approach. Through simulation experiments and an application to an American Community Survey dataset, we conclude that the local SBC successfully identifies spatial clusters to address the issue of utilizing data reliability information of estimates in assessing local SA.

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