Statistical Tests for Spatial Nonstationarity Based on the Geographically Weighted Regression Model

By Yee Leung, Changlin Mei, Wenxiu Zhang. 2000

490 citations recorded by the source corpus.

Subfields: Economics and Econometrics, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/5f3de3d424b84058c149c7de799d38b648d2be97

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Citations in the corpus

Modeling spatial variation in tree diameter–height relationships (2004, background): “However, the hat matrix S0 in OLS is symmetric and idempotent, but S1 in GWR is generally not because of the weighting matrix Wi (it is different at each location i) (Leung et al., 2000).”
Estimation and inference in spatially varying coefficient models (2018, methodology): “Moreover, Leung et al. (2000) introduced another RSS-based statistics to test for the global stationarity of the regression relationship.”
Extreme Coefficients in Geographically Weighted Regression and Their Effects on Mapping (2009, background): “…are globally stationary (Brunsdon et al., 1996, 1999, 2001; McMillen, 1996; Fotheringham et al., 1998, 2002; Fotheringham and Brunsdon, 1999; Leung et al., 2000a, 2000b; Huang and Leung, 2002; Yu and Wu, 2004; Laffan et al., 2005; Cho et al., 2006, 2009a; Lambert et al., 2006; Yu, 2006,…”
Spatial Heterogeneity in Hedonic House Price Models: The Case of Austria (2014, methodology): “…transformed sales price of observation 𝑖, 𝑖 ∈ 1, … ,𝑛, 𝛽𝑗 are the global coefficients of covariates 𝑥𝑖𝑗 , 𝑗 ∈ 1, … ,𝑘 , and are the 𝛽𝑙(𝑢𝑖,𝑣𝑖) , 𝑙 ∈ 𝑘 + 1, … ,𝑚 , the local coefficients of covariates 𝑥𝑖𝑙 at the coordinates (𝑢𝑖 , 𝑣𝑖) of observation 𝑖. Leung et al.…”
Local Linear Estimation of Spatially Varying Coefficient Models: An Improvement on the Geographically Weighted Regression Technique (2008, background): “…problems that have been addressed in the context of the basic GWR (for example, see Brunsdon et al, 1999a; Fotheringham et al, 2002; Leung et al, 2000a; 2000b), some other hypotheses on the functional forms of the coefficients bj (u, v) ( j 1, 2, . . . , p) may be further tested,…”
Geographically weighted regression bandwidth selection and spatial autocorrelation: an empirical example using Chinese agriculture data (2010, background): “, 2000a , b ; Huang and Leung, 2002 ; Paez et al.”
Testing for Spatial Autocorrelation among the Residuals of the Geographically Weighted Regression (2000, methodology): “…see Hocking, 1996; Neter et al, 1996), the locally weighted regression technique (for example, see Cleveland, 1979; Cleveland and Devlin, 1988; Cleveland et al, 1988), and the GWR technique (see Brunsdon et al, 1999; Leung et al, 2000) for the varyingparameter regression model in equation (1).”
Modelling hedonic residential rents for land use and transport simulation while considering spatial effects (2010, methodology): “Several advanced methods have been proposed to incorporate spatial structural instability, spatial dri and spatial lag into models (Leung et al. 2000, 10). ese models commonly propose tomake use of the spatial characteristics of variables to improve the results (Gao et al. 2006, 1040).”
Local spatial modeling of white-tailed deer distribution (2006, methodology): “The objective of the test for local nonstationarity was to determine if parameter estimates in the GWR model were significantly different across the study area (Brunsdon et al., 1996; Leung et al., 2000).”
Local regression models for spatial interpolation of urban heat island—an example from Wrocław, SW Poland (2012, methodology): “The detailed equations are provided by Leung et al. (2000).”
Spatially varying development mechanisms in the Greater Beijing Area: a geographically weighted regression investigation (2006, methodology): “To answer this question, another F test (the F3 test in Leung et al. 2000a), based on the sample variance of the estimated model coefficients (Brunsdon et al. 1996; Leung et al. 2000a ), was implemented in the R environment as well (for detailed technique discussions, see Leung et al. 2000a ,p2 1–2”
Links, comparisons and extensions of the geographically weighted regression model when used as a spatial predictor (2011, background): “effective number of parameters of the GWR fit (Leung et al. 2000).”
Testing the Importance of the Explanatory Variables in a Mixed Geographically Weighted Regression Model (2006, methodology): “The cross-validation (CV) procedure that has been used in the GWR technique (for example, see Brunsdon et al, 1996; 1998; Fotheringham et al, 1997a; 1997b; Leung et al, 2000a; 2000b) can be directly extended to the case of the MGWR models.”
Modeling Spatial Dimensions of Housing Prices in Milwaukee, WI (2007, background): “In addition, the coefficient nonstationarity test (Leung et al, 2000a) indicates that all the coefficients of the GWR model significantly vary over space (at more than a 99% confidence level).”