Spatial and Geographically Weighted Regression
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detecting local variations in spatial behavior and understanding local details, which may be masked by global regression models. Unlike SR, where regression coefficients for each independent variable and the intercept are obtained for the whole study region, in GWR, regression coefficients are computed for every spatial zone. Therefore, the regression coefficients can be mapped and the appropriateness of stationarity assumption in the conventional regression analyses can be checked.
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Spatial and Geographically Weighted Regression H. S EBNEM D ÜZGÜN , S ERKAN K EMEÇ Geodetic and Geographic Information Technologies, Middle East Technical University, Ankara, Turkey Synonyms Spatial prediction; Regression; Global and local spatial modeling; Simultaneous autoregression; Moving average regression; Conditional spatial regression Definition Spatial regression (SR) is a global spatial modeling technique in which spatial autocorrelation among the regression parameters are taken into account. SR is usually performed for spatial data obtained from spatial zones or areas. The basic aim in SR modeling is to establish the relationship between a dependent variable measured over a spatial zone and other attributes of the spatial zone, for a given study area, where the spatial zones are the subset of the study area. While SR is known to be a modeling method in spatial data analysis literature [1,2,3,4,5,6], in spatial data-mining literature it is considered to be a classification technique [7]. Geographically weighted regression (GWR) is a powerful exploratory method in spatial data analysis. It serves for
Historical Background Regression analysis is one of the basic methods for modeling variation in a dependent (response, endogenous) variable (Y) based on other (covariates or independent or explanatory or predictor or exogenous) variables (X 1 , X 2 , . . . , X n ). Owing to the nature of this technique it is mostly used in analysis of spatial data represented by spatial zones and areas, where several attributes are specified for each spatial zone or area. These spatial zones can be in regular lattice form (e. g., pixels of remotely sensed images) or irregular areas (e. g., administrative districts). As the spatial data contain autocorrelation, the lack of ability to include this property in non-SR led analysts to develop SR models for better treatment of spatial data. In this way, the elimination of the main shortcomings of non-SR, which are assumptions of identically and independently distributed (i.i.d.) explanatory variables (X i ’s) and uncorrelated error terms, is attempted by relaxing the regression method with the allowance of spatial autocorrelation. While initially, SR methods were widely used in econometrics [6,9], their utilization became popular in broa
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