assign14 - Assignment 14 Spatial Autocorrelation See...

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1 Assignment 14. Spatial Autocorrelation See Mitchell, The ESRI Guide to GIS Analysis , vol. 2, Spatial Measurements & Statistics ; Fotheringham et al., Geographically Weighted Regression ; GeoDa, instructions; CrimeStat , instructions. Conceptual Issues & Basic Measures § Always check for possible data errors (e.g., sum “Race,” gender, and housing tenure categories to make sure that they amount to the appropriate totals). § “Spatial statistics let you compare the spatial distribution of a set of features to a hypothetical random spatial distribution…” (Mitchell, 19). Alternatively, they compare local empirical distributions to average empirical distributions across the study area. o Null hypothesis: the features are evenly distributed across the study area. o “To the extent that your distribution differs from a random distribution, there is a trend or pattern in the data” (Mitchell, 19). Alternative hypothesis: there is a trend or pattern in the distribution of the features across the study area. § A pattern may vary according to the geographic scale of the study area and its borders : o Dispersed within a small study area but clustered within a larger area, or vice versa; or it may vary in other ways. o Study area borders can bias results; perhaps use border buffer to exclude border points from analysis or give higher weight to border points (which tend to have fewer neighbors). § How the data are represented influences the results of spatial statistics (Mitchell, pages 184-89): o Distance measures are straightforward for point data but not for line data (e.g., is distance measured at the midpoint, endpoint, or a randomly selected point on a line? is the line continuous or a series of short lines?). o For areas, centroid-to-centroid distance or distance between nearest locations on the boundaries are used, but centroids should be used only if areas are roughly the same size and shape and merged areas will alter distance calculations. o For raster data, smaller cell size creates many features (cells) with the same or very similar sizes and hence exaggerates spatial dependence. o Buffering a boundary area and excluding observations within it may compensate for the tendency of boundary observations to have fewer neighbors. Giving boundary observations higher weighting may also do the same. I § Measuring the pattern formed by the locations of features: quadrant analysis & nearest neighbor § Quadrant analysis : assess a feature’s spatial distribution by overlaying a grid and measuring the density of features (i.e. the number of features per unit
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2 area). E.g., for small tight clusters of events such as burglaries, emergency 911 calls, earthquakes, but not for features that have direct interaction with each other. o Quadrant analysis does not consider the proximity or relationship among features.
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