Optimal Weights for Focused Tests of Clustering Using the Local Moran Statistic

Abstract

Local spatial statistics measure and test for spatial association for a variable or variables of interest in a geographic neighborhood surrounding a predefined location. Most applications adopt a single scale of analysis but give little attention to the scale of the process generating the data. Alternatively, when the researcher is uncertain about the process scale, local statistics may examine a number of scales. In these cases, it is important to include a correction for multiple testing when evaluating the statistical significance of each local statistic, something that is rarely done. Consequently, local statistics are more likely to identify significant relationships, even when no meaningful spatial association exists. In this article, we develop a methodology for the local Moran statistic that provides both an empirical estimate of the spatial scale of association and an assessment of the significance of the statistic for that scale. The key idea is to test a number of possible choices for the statistic's weight matrix and then account for the multiple testing associated with the number of weight matrices examined. Unlike previous research, our statistic avoids the use of simulation to determine statistical significance in the presence of multiple testing. To test the validity of our approach, we constructed a numerical example to assess the statistic's performance and conducted an empirical study using leukemia data from central New York state. The developed statistic addresses the need for the empirical determination of weights and spatial scale. The test therefore addresses the common weakness of many applications, where weights are defined exogenously, with little or no thought given to either the definition or its implications. Los indicadores locales (local spatial statistics) evalúan la asociación espacial de una o varias variables de interés dada un área predefinida y sus áreas vecinas. La mayoría de dichas medidas utilizan una escala única de análisis y prestan poca atención a la escala del proceso de generación de los datos. En los casos en los que el investigador no está seguro de la escala del proceso, las los indicadores locales pueden ser evaluados a varias escalas. En dichos casos, cuando se hace la evaluación de la significancia estadística de cada indicador local, es importante incorporar una corrección para pruebas múltiples (multiple tests), un ajuste que raramente se realiza en la gran mayoría de estudios. Debido al problema de pruebas múltiples, los indicadores locales son más propensos a identificar relaciones significativas, incluso cuando no existe asociación espacial significativa alguna. En este artículo los autores desarrollan una metodología que produce un índice local de Moran que proporciona tanto una estimación empírica de la escala espacial de la asociación así como una evaluación de la importancia del indicador para dicha escala. La idea clave es poner a prueba una serie de opciones posibles para la definición de la matriz de pesos espaciales (spatial weight matrix) del índi...

Analyzing Hotspots of Crime Using aBayesian Spatiotemporal Modeling Approach: A Case Study of Violent Crime in theGreaterTorontoArea

“…Under the ICAR specification, the mean of s i and also δ i is given by the mean of neighboring values of s i and δ i , respectively, where neighboring areas are defined as those that share one or more common vertices (also referred to as first‐order queen contiguity). In the absence of known information regarding the spatial structure of the phenomenon (as explained in the context of malaria in de Castro and Singer ()), this specification is common in geographical studies (Kim and Oleson ; Rogerson and Kedron ). The ICAR specification also captures spatial structure in risks due to time effect and unmeasured factors that have spatial structure, but has limitations that are beyond the scope of this research, particularly when areas have different sizes and shapes and are arranged irregularly (Goovaerts ).…”

Identifying the geographic extent of environmental inequalities: A comparison of pattern detection methods

“…Following the procedure of Rogerson and Kedron (2012), the proportion of minority residents and median household incomes of block group residents were standardized for analysis. A total of 294,722 residents lived in 585 census block groups within the study area at the time of sampling.…”

“…Following Rogerson and Kedron (2012), this approach used the distributional approximation of Yao and Davis (1986) to adjust for the multiple testing inherent in the SLMI procedure. In this analysis, the n census blocks within 3 km of each TRI site were examined.…”

“…Termed local scan statistics by Rogerson (2012), these tests iteratively increase spatial weights around a site of interest following defined expansion rules. Similarly, Rogerson (2011Rogerson ( , 2012 and Rogerson andKedron (2012, 2015) use adjusted versions of the Getis-Ord, chi-square, Stone, and Moran's I statistics to identify spatial changepoints around a site of interest. Similarly, Rogerson (2011Rogerson ( , 2012 and Rogerson andKedron (2012, 2015) use adjusted versions of the Getis-Ord, chi-square, Stone, and Moran's I statistics to identify spatial changepoints around a site of interest.…”

“…As a potential correction, Rogerson and Kedron (2012) suggest the possible use of a Bonferroni adjustment based on the total number of sites tested. Significant overlap in geographic areas tested introduces dependence between sites that would require additional adjustment.…”