Multicollinearity and correlation among local regression coefficients in geographically weighted regression

By David Wheeler, Michael Tiefelsdorf. Journal of Geographical Systems, 2005

800 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4e944436b0458b9d53cde5edb9905e41d01a2ced

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Citations in the corpus

Maximum likelihood estimation of spatially varying coefficient models for large data with an application to real estate price prediction (2020, background): “As mentioned before, multicollinearity issues with local regressions are raised (Wheeler and Tiefelsdorf, 2005; Wheeler and Calder, 2007), cf.”
Living with Collinearity in Local Regression Models (2012, background): “These remedies build on the geographically weighted models proposed by Wheeler (2007; 2009), following the initial highlighting of this issue presented in Wheeler and Tiefelsdorf (2005).”
Spatial-Filtering-Based Contributions to a Critique of Geographically Weighted Regression (GWR) (2008, background): “This GWR shortcoming is emphasized by Wheeler and Tiefelsdorf (2005), and is counter to the global-to-local decomposition principle promoted by Anselin (1995), which implies that the sum of a variable's local coefficients for all locations is proportional to its global coefficient.”
Geographically Weighted Regression (2015, background): “2, it is clear that the forcing artefacts found by Wheeler and Tiefelsdorf (2005) in a different data set are replicated here.”
A Moran coefficient-based mixed effects approach to investigate spatially varying relationships (2016, methodology): “70 After Wheeler and Tiefelsdorf (2005) demonstrate that GWR coefficients 71 essentially are collinear, active discussion shifted to regularized GWR.”
Extreme Coefficients in Geographically Weighted Regression and Their Effects on Mapping (2009, background): “All rights reserved. regression coefficients (Wheeler and Tiefelsdorf, 2005), and (3) extreme coefficients including sign reversals (Farber and Páez, 2007).”
Geographically weighted regression bandwidth selection and spatial autocorrelation: an empirical example using Chinese agriculture data (2010, background): “…the presence of extreme coefficients to greater degrees is problematic because it may be a sign of over-fitting in the local models, the presence of local multicollinearity or some other local violation of weighted-least-squares regression (Wheeler and Tiefelsdorf, 2005; Farber and Páez, 2007).”
Estimation and inference in spatially varying coefficient models (2018, methodology): “Third, by introducing the roughness penalty into the BST, the BPST can alleviate the adverse effect of the collinearity problem in GWR (Wheeler & Tiefelsdorf, 2005) and provide more accurate estimators of the coefficient functions.”
Simultaneous Coefficient Penalization and Model Selection in Geographically Weighted Regression: The Geographically Weighted Lasso (2009, background): “…apparently be increased by the GWR spatial kernel weights, and moderate collinearity of locally weighted explanatory variables can lead to potentially strong dependence in the local estimated coefficients (Wheeler and Tiefelsdorf, 2005), which makes interpreting individual coefficients problematic.”
Non‐stationarity and local approaches to modelling the distributions of wildlife (2007, background): “P. E. Osborne et al. © 2007 The Authors 320 Diversity and Distributions, 13, 313–323, Journal compilation © 2007 Blackwell Publishing Ltd VCM does not suffer this restriction (see also Wheeler & Tiefelsdorf (2005) for other issues on the use of (GWR).”
A Simulation-Based Study of Geographically Weighted Regression as a Method for Investigating Spatially Varying Relationships (2011, methodology): “For comparability and extensibility, in the experiments we use the same geographical system employed by Wheeler and Tiefelsdorf (2005) (ie, 159 counties in Georgia), as well as a larger system of 1003 census tracts in the City of Toronto to assess the potential effect of small sampling, and thus…”
GWmodel: An R Package for Exploring Spatial Heterogeneity Using Geographically Weighted Models (2013, methodology): “…models Collinearity is a problem in any form of regression modelling and the importance of assessing and taking action has been raised by the many commentaries on local collinearity in GW regression (Wheeler and Tiefelsdorf 2005; Wheeler 2007, 2009, 2010, 2013a; Griffith 2008; Páez et al. 2011).”
Accuracy measurement of Random Forests and Linear Regression for mass appraisal models that estimate the prices of residential apartments in Nicosia, Cyprus (2018, neutral): “4, for the associations among the most frequent keywords, the Geographically Weighted Regression (Wheeler and Tiefelsdorf, 2005) is the most frequent as well as close to the property Valuations keyword (and thus more times referred simultaneously), while the Random Forests method does not even exist”