Int J Health Geogr - A modified version of Moran's I.


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CKGROUND: Investigation of global clustering patterns across regions is very important in spatial data analysis. Moran's I is a widely used spatial statistic for detecting global spatial patterns such as an east-west trend or an unusually large cluster. Here, we intend to improve Moran's I for evaluating global clustering patterns by including the weight function in the variance, introducing a population density (PD) weight function in the statistics, and conducting Monte Carlo simulation for testing. We compare our modified Moran's I with Oden's I*pop for simulated data with homogeneous populations. The proposed method is applied to a census tract data set.METHODS: We present a modified version of Moran's I which includes information about the strength of the neighboring association when estimating the variance for the statistic. We provide a power analysis on Moran's I, a modified version of Moran's I, and I*pop in a simulation study. Data were simulated under two common spatial correlation scenarios of local and global clustering.RESULTS: For simulated data with a large cluster pattern, the modified Moran's I has the highest power (43.4%) compared to Moran's I (39.9%) and I*pop (12.4%) when the adjacent weight function is used with 5%, 10%, 15%, 20%, or 30% of the total population as the geographic range for the cluster.For two global clustering patterns, the modified Moran's I (power > 25.3%) performed better than both Moran's I (> 24.6%) and I*pop (> 7.9%) with the adjacent weight function. With the population density weight function, all methods performed equally well.In the real data example, all statistics indicate the existence of a global clustering pattern in a leukemia data set. The modified Moran's I has the lowest p-value (.0014) followed by Moran's I (.0156) and I*pop (.011).CONCLUSIONS: Our power analysis and simulation study show that the modified Moran's I achieved higher power than Moran's I and I*pop for evaluating global and local clustering patterns on geographic data with homogeneous populations. The inclusion of the PD weight function which in turn redefines the neighbors seems to have a large impact on the power of detecting global clustering patterns. Our methods to improve the original version of Moran's I for homogeneous populations can also be extended to some alternative versions of Moran's I methods developed for heterogeneous populations.

Resumo Limpo

ckground investig global cluster pattern across region import spatial data analysi moran wide use spatial statist detect global spatial pattern eastwest trend unusu larg cluster intend improv moran evalu global cluster pattern includ weight function varianc introduc popul densiti pd weight function statist conduct mont carlo simul test compar modifi moran oden ipop simul data homogen popul propos method appli census tract data setmethod present modifi version moran includ inform strength neighbor associ estim varianc statist provid power analysi moran modifi version moran ipop simul studi data simul two common spatial correl scenario local global clusteringresult simul data larg cluster pattern modifi moran highest power compar moran ipop adjac weight function use total popul geograph rang clusterfor two global cluster pattern modifi moran power perform better moran ipop adjac weight function popul densiti weight function method perform equal wellin real data exampl statist indic exist global cluster pattern leukemia data set modifi moran lowest pvalu follow moran ipop conclus power analysi simul studi show modifi moran achiev higher power moran ipop evalu global local cluster pattern geograph data homogen popul inclus pd weight function turn redefin neighbor seem larg impact power detect global cluster pattern method improv origin version moran homogen popul can also extend altern version moran method develop heterogen popul

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