Distance metric choice can both reduce and induce collinearity in geographically weighted regression (original) (raw)
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Procedia Environmental Sciences, 2011
Geographically Weighted Regression (GWR) is a local modelling technique to estimate regression models with spatially varying relationships. Generally, the Euclidean distance is the default metric for calibrating a GWR model in previous research and applications; however, it may not always be the most reasonable choice due to a partition by some natural or man-made features. Thus, we attempt to use a non-Euclidean distance metric in GWR. In this study, a GWR model is established to explore spatially varying relationships between house price and floor area with sampled house prices in London. To calibrate this GWR model, network distance is adopted. Compared with the other results from calibrations with Euclidean distance or adaptive kernels, the output using network distance with a fixed kernel makes a significant improvement, and the river Thames has a clear cut-off effect on the parameter estimations.
Geographically Weighted Regression using a non-euclidean distance metric with simulation data
Agro-Geoinformatics (Agro- …, 2012
Geographically Weighted Regression (GWR) is a local modelling technique to estimate regression models with spatially varying relationships. Generally, the Euclidean distance is the default metric for calibrating a GWR model in previous research and applications; however, it may not always be the most reasonable choice due to a partition by some natural or man-made features. Thus, we attempt to use a non-Euclidean distance metric in GWR. In this study, a GWR model is established to explore spatially varying relationships between house price and floor area with sampled house prices in London. To calibrate this GWR model, network distance is adopted. Compared with the other results from calibrations with Euclidean distance or adaptive kernels, the output using network distance with a fixed kernel makes a significant improvement, and the river Thames has a clear cut-off effect on the parameter estimations.
GEOGRAPHY, ENVIRONMENT, SUSTAINABILITY
Bandwidth plays a crucial role in the Geographically Weighted Regression modelas it affects the model’s ability to describe spatial dependencies. If the bandwidth is too large, the model will be similar to a normal regression model. Conversely, if it is too small, the model will be too rough. Bandwidth can be selected in several ways, e.g. manually determined by experts or using Akaike Information Criteria, Cross-Validation, and Lagrange Multiplier methods. This study offers an alternative approach to choosing bandwidth based on the covariance function representing a linear combination between the Bessel and Gaussian-Type functions. We applied this function to analyze the land price in Manado with four infrastructure accessibility variables, such as accessibility to government offices, education facilities, shopping centers, and healthcare facilities. Therefore, the proposed method is different from the index methods (AIC and CV) which have been used by other researchers. The result...
Parameter Estimation of Locally Compensated Ridge-Geographically Weighted Regression Model
IOP Conference Series: Materials Science and Engineering, 2019
Geographically weighted regression (GWR) is a spatial data analysis method where spatially varying relationships are explored between explanatory variables and a response variable. One unresolved problem with spatially varying coefficient regression models is local collinearity in weighted explanatory variables. The consequence of local collinearity is: estimation of GWR coefficients is possible but their standard errors tend to be large. As a result, the population values of the coefficients cannot be estimated with great precision or accuracy. In this paper, we propose a recently developed method to remediate the collinearity effects in GWR models using the Locally Compensated Ridge Geographically Weighted Regression (LCR-GWR). Our focus in this study was on reviewing the estimation parameters of LCR-GWR model. And also discussed an appropriate statistic for testing significance of parameters in the model. The result showed that Parameter estimation of LCR-GWR model using weighted...
Environment and Planning A, 1998
Geographically weighted regression and the expansion method are two statistical techniques which can be used to examine the spatial variability of regression results across a region and so inform on the presence of spatial nonstationarity. Rather than accept one set of 'global' regression results, both techniques allow the possibility of producing 'local' regression results from any point within the region so that the output from the analysis is a set of mappable statistics which denote local relationships. Within the paper, the application of each technique to a set of health data from northeast England is compared. Geographically weighted regression is shown to produce more informative results regarding parameter variation over space.
Living with Collinearity in Local Regression Models
Abstract In this study, we investigate the issue of local collinearity in the predictor data when using geographically weighted regression (GWR) to explore spatial relationships between response and predictor variables. Here we show how the ideas of condition numbers and variance inflation factors may belocalised'to detect and respond to problems caused by this phenomenon.
A Family of Geographically Weighted Regression Models
Advances in Spatial Science, 2004
A Bayesian treatment of locally linear regression methods introduced in and labeled geographically weighted regressions (GWR) in Brunsdon, is set forth in this paper. GWR uses distance-decay-weighted sub-samples of the data to produce locally linear estimates for every point in space. While the use of locally linear regression represents a true contribution in the area of spatial econometrics, it also presents problems. It is argued that a Bayesian treatment can resolve these problems and has a great many advantages over ordinary least-squares estimation used by the GWR method.