# spatial - About Spatial Statistics From Fotheringham et al...

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About Spatial Statistics From Fotheringham et al., Geographically Weighted Regression; Bailey & Gatrell, Interactive Spatial Data Analysis; & Mitchell, The ESRI Guide to GIS Analysis, vol. 2. § Aspatial data contain only attribute (i.e. feature) information, while spatial data contain both attribute and locational information. o ‘Local attribute space’ vs. ‘local geographic space’ (see Fotheringham et al., 3-6). o Stationarity : a relationship is locationally uniform across space (i.e. is ‘global’); differences in values may depend on the relative location of the measurements (i.e. their distance and direction between two points) but not on the absolute location of the measurements. § Global statistics are valid for stationary relationships because the values of the observations are independent of each other. o Non-stationarity: a relationship varies by absolute location across space (i.e. has ‘local’ features). § Local statistics are valid for non-stationary relationships because the values of the observations are spatially dependent on each other (i.e. Tobler’s First Law of Geography: nearby objects are more alike than are objects that are farther away— spatial autocorrelation ). § Global trend is also called first order . Local trend is also called second order , § Non-stationarity can be anticipated for several reasons. o Spatially non-random human and/or software sources of error (i.e. non-sampling error that is spatial). o Spatially non-random sampling error. o Model misspecification that has spatial effects. o Intrinsic spatial variation in a relationship. § There are basic problems in trying to significant detect local patterns within global trends: o The global (i.e. first order) trend itself may be an artifact of the scale of geographic aggregation (‘modifiable areal unit problem’). o Testing for significance in local patterns is vulnerable to Type I error in multiple hypothesis testing. § Directional patterns of relationships: o Isotropic: the relationship varies only with distance between points. o Anisotropic: the relationship varies by distance and direction between points. § Three fundamental questions: o What are the spatial patterns? These must be visualized. o What are their dimensions? The patterns must be quanitified. o How can we explain them? The patterns must be modeled. § “A model is a simplication of, and approximation to, some aspect of the world” (King et al., Designing Social Inquiry , 49).

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o Models can be assessed as more or less plausible in the ways they abstract features of ‘reality’ as we conceptualize it. § Practical problems in analyzing spatial data o Geographic scale of analysis: patterned variation at one scale may be mere random variation at another scale. o
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spatial - About Spatial Statistics From Fotheringham et al...

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