ࡱ > O Q N R M bjbjT~T~ 80 6 6 ! + 8 5 , a l u L $ x! $ R ? ? ? ? ? ? 2jB } 0 , l$ c l$ l$ ? ? l$ : Text S5: Spatial statistics
In this study, we use three spatial statistics (Morans I, Getis Gi* (d) and semivariogram) to measure population distribution pattern. The Morans Index, I, was proposed by Moran in 1950 to evaluate whether a spatial pattern is clustered, dispersed, or random ADDIN EN.CITE Moran195098039803980317Moran, P.A.P.Notes on continuous stochastic phenomena.BiometrikaBiometrikaBiometrikaBiometrika17-23371950data analysis-PPN-Moran's ISecuringreadSecuring5Elsevier[1]. A Moran's Index value near +1.0 indicates clustering, an index value near -1.0 indicates dispersion, and an index of 0 indicates complete randomness. The specific formula for calculating the Morans I is as follows,
where N equals the number of observations; wij is the weight between locations i and j; xi and xj are the values at locations i and j; is the average over all locations of the variable. In this study, the weight wij is proportion to the inverse distance between houses.
The Getis Gi*(d) statistic is used in this study to identify hot spots for food inputs at individual houses. The formula for Gi*(d) is as follows ADDIN EN.CITE Getis199218518518517Getis, A.Ord, J. K.The analysis of spatial association by use of distance statisticsGeographical analysisGeographical AnalysisGeogr AnalGeogr. Anal.189-2062431992174file:///E:/Literature/Academic%20Journals/Aedes/Getis1992-%23185.pdfOrd199518818818817Ord, J. K.Getis, A.Local spatial autocorrelation statistics - distributional issues and an applicationGeographical analysisGeographical AnalysisGeogr AnalGeogr. Anal.286-3062741995175file:///E:/Literature/Academic%20Journals/Aedes/Ord1995-%23188.pdf[2,3],
where wij(d) is the weight between locations i and j with a specified threshold distance d, which is used to specify the neighborhood size around of the house of interest to examine if this house is a local high/low density spot; and S is the standard deviation of all observations. In this study, we select wij(d) based on the inverse distance throughout the study area (i.e., d is sufficiently big to incorporate all houses), which is same as that in the calculation of Moran's I. Gi*(d) has an asymptotic normal distribution. A z-score can be calculated to see if the population within a specific house is significantly higher/lower than its neighborhood.
The semivariogram is a function of distance describing the degree of spatial dependence of a spatial random process ADDIN EN.CITE Goovaerts19979451945194516Goovaerts, PGeostatistics for natural resources evaluation Ecology4831997New YorkOxford University Pressdata analysis-geostatistics-reviewxu's literature-GoovaertsreadPDF[4]. The formula is as follows,
where is the set of data point pairs (, ) that are distance h apart and represents the number of data point pairs. A higher value of indicates lower spatial autocorrelation. Generally, the spatial auto-correlation will decrease with distance h and finally stabilize. The range (i.e., the distance after which starts to stabilize) can be used to indicate the strength of spatial auto-correlation.
References:
ADDIN EN.REFLIST 1. Moran PAP (1950) Notes on continuous stochastic phenomena. Biometrika 37: 17-23.
2. Getis A, Ord JK (1992) The analysis of spatial association by use of distance statistics. Geogr Anal 24: 189-206.
3. Ord JK, Getis A (1995) Local spatial autocorrelation statistics - distributional issues and an application. Geogr Anal 27: 286-306.
4. Goovaerts P (1997) Geostatistics for natural resources evaluation. New York: Oxford University Press. 483 p.
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