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In GWR, regression coefficients (parameters) are estimated locally for each geographic location or point, allowing for the modeling of spatial heterogeneity. [6] Geographically Weighted Regression is a cornerstone of GIS and spatial analysis, and is built into ArcGIS, as a package for the R (programming language), and as a plugin for QGIS.
The incorporation of Geographically Weighted Regression (GWR) into LURs involves applying a spatial weighting function to the spatial coordinates that divide a study area into various local neighborhoods. This can reduce the effects of spatial non-stationarity, a defect that occurs when variables form inconsistent relationships over large areas ...
Geographically weighted regression (GWR) is a local version of spatial regression that generates parameters disaggregated by the spatial units of analysis. [54] This allows assessment of the spatial heterogeneity in the estimated relationships between the independent and dependent variables.
In applied statistics and geostatistics, regression-kriging (RK) is a spatial prediction technique that combines a regression of the dependent variable on auxiliary variables (such as parameters derived from digital elevation modelling, remote sensing/imagery, and thematic maps) with interpolation of the regression residuals.
Alexander Stewart Fotheringham (1954) – contributed to the development of geographically weighted regression. Arthur Getis (1934–2022) – influential in spatial statistics; Brian Berry (1934) – contributed to the refinement of central place theory. Dana Tomlin – developer of map algebra
Local regression or local polynomial regression, [1] also known as moving regression, [2] is a generalization of the moving average and polynomial regression. [3] Its most common methods, initially developed for scatterplot smoothing, are LOESS (locally estimated scatterplot smoothing) and LOWESS (locally weighted scatterplot smoothing), both pronounced / ˈ l oʊ ɛ s / LOH-ess.
Digital elevation models, triangulated irregular networks, edge-finding algorithms, Thiessen polygons, Fourier analysis, (weighted) moving averages, inverse distance weighting, kriging, spline, and trend surface analysis are all mathematical methods to produce interpolative data.
Weighted least squares (WLS), also known as weighted linear regression, [1] [2] is a generalization of ordinary least squares and linear regression in which knowledge of the unequal variance of observations (heteroscedasticity) is incorporated into the regression.