Multicollinearity and correlation among local regression coefficients in geographically weighted regression

2005 ◽  
Vol 7 (2) ◽  
pp. 161-187 ◽  
Author(s):  
David Wheeler ◽  
Michael Tiefelsdorf
Keyword(s):  
Geographically Weighted Regression ◽  
Regression Coefficients ◽  
Weighted Regression ◽  
Local Regression

scholarly journals Exploring spatial nonstationary environmental effects on Yellow Perch distribution in Lake Erie

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7350
Author(s):  
Changdong Liu ◽  
Junchao Liu ◽  
Yan Jiao ◽  
Yanli Tang ◽  
Kevin B. Reid
Keyword(s):  
Environmental Effects ◽  
Geographically Weighted Regression ◽  
Regression Models ◽  
Yellow Perch ◽  
Lake Erie ◽  
Regression Coefficients ◽  
Weighted Regression ◽  
Local Regression ◽  
Spatially Varying ◽  
Spatial Locations

Background Global regression models under an implicit assumption of spatial stationarity were commonly applied to estimate the environmental effects on aquatic species distribution. However, the relationships between species distribution and environmental variables may change among spatial locations, especially at large spatial scales with complicated habitat. Local regression models are appropriate supplementary tools to explore species-environment relationships at finer scales. Method We applied geographically weighted regression (GWR) models on Yellow Perch in Lake Erie to estimate spatially-varying environmental effects on the presence probabilities of this species. Outputs from GWR were compared with those from generalized additive models (GAMs) in exploring the Yellow Perch distribution. Local regression coefficients from the GWR were mapped to visualize spatially-varying species-environment relationships. K-means cluster analyses based on the t-values of GWR local regression coefficients were used to characterize the distinct zones of ecological relationships. Results Geographically weighted regression resulted in a significant improvement over the GAM in goodness-of-fit and accuracy of model prediction. Results from the GWR revealed the magnitude and direction of environmental effects on Yellow Perch distribution changed among spatial locations. Consistent species-environment relationships were found in the west and east basins for adults. The different kinds of species-environment relationships found in the central management unit (MU) implied the variation of relationships at a scale finer than the MU. Conclusions This study draws attention to the importance of accounting for spatial nonstationarity in exploring species-environment relationships. The GWR results can provide support for identification of unique stocks and potential refinement of the current jurisdictional MU structure toward more ecologically relevant MUs for the sustainable management of Yellow Perch in Lake Erie.

A General Framework for Estimation and Inference of Geographically Weighted Regression Models: 1. Location-Specific Kernel Bandwidths and a Test for Locational Heterogeneity

2002 ◽  
Vol 34 (4) ◽  
pp. 733-754 ◽  
Author(s):  
Antonio Páez ◽  
Takashi Uchida ◽  
Kazuaki Miyamoto
Keyword(s):  
Geographically Weighted Regression ◽  
Degrees Of Freedom ◽  
Likelihood Function ◽  
Error Variance ◽  
Model Specification ◽  
Weighted Regression ◽  
Regularity Conditions ◽  
Local Regression ◽  
Specification Tests ◽  
Geographically Weighted Regression Model

Geographically weighted regression (GWR) has been proposed as a technique to explore spatial parametric nonstationarity. The method has been developed mainly along the lines of local regression and smoothing techniques, a strategy that has led to a number of difficult questions about the regularity conditions of the likelihood function, the effective number of degrees of freedom, and in general the relevance of extending the method to derive inference and model specification tests. In this paper we argue that placing GWR within a different statistical context, as a spatial model of error variance heterogeneity, or what might be termed locational heterogeneity, solves these difficulties. A maximum-likelihood-based framework for estimation and inference of a general geographically weighted regression model is presented that leads to a method to estimate location-specific kernel bandwidths. Moreover, a test for locational heterogeneity is derived and its use exemplified with a case study.

Spatial-Filtering-Based Contributions to a Critique of Geographically Weighted Regression (GWR)

2008 ◽  
Vol 40 (11) ◽  
pp. 2751-2769 ◽  
Author(s):  
Daniel A Griffith
Keyword(s):  
Geographically Weighted Regression ◽  
Spatial Filtering ◽  
Spatial Filter ◽  
Regression Coefficients ◽  
Weighted Regression ◽  
Interaction Terms

Interaction terms are constructed with georeferenced attribute variables and spatial filter eigenvectors, and then used to compute geographically varying regression coefficients. These coefficients, which are analogous to geographically weighted regression (GWR) coefficients, display preferable properties, and this specification is used to critique selected features of GWR. Comparisons are illustrated with the Georgia data appearing in the standard GWR tutorial.

Diagnostic Tools and a Remedial Method for Collinearity in Geographically Weighted Regression

2007 ◽  
Vol 39 (10) ◽  
pp. 2464-2481 ◽  
Author(s):  
David C Wheeler
Keyword(s):  
Ridge Regression ◽  
Geographically Weighted Regression ◽  
Model Building ◽  
Weighted Regression ◽  
Diagnostic Tools ◽  
Local Regression ◽  
Explanatory Variables ◽  
Building Process ◽  
Global Regression ◽  
Spatially Varying

Geographically weighted regression (GWR) is drawing attention as a statistical method to estimate regression models with spatially varying relationships between explanatory variables and a response variable. Local collinearity in weighted explanatory variables leads to GWR coefficient estimates that are correlated locally and across space, have inflated variances, and are at times counterintuitive and contradictory in sign to the global regression estimates. The presence of local collinearity in the absence of global collinearity necessitates the use of diagnostic tools in the local regression model building process to highlight areas in which the results are not reliable for statistical inference. The method of ridge regression can also be integrated into the GWR framework to constrain and stabilize regression coefficients and lower prediction error. This paper presents numerous diagnostic tools and ridge regression in GWR and demonstrates the utility of these techniques with an example using the Columbus crime dataset.

scholarly journals Distance metric choice can both reduce and induce collinearity in geographically weighted regression

2018 ◽  
Vol 47 (3) ◽  
pp. 489-507 ◽  
Author(s):  
Alexis Comber ◽  
Khanh Chi ◽  
Man Q Huy ◽  
Quan Nguyen ◽  
Binbin Lu ◽  
...  
Keyword(s):  
Geographically Weighted Regression ◽  
House Price ◽  
Elastic Net ◽  
Weighted Regression ◽  
Manhattan Distance ◽  
Distance Metrics ◽  
Distance Metric ◽  
Local Regression ◽  
Spatially Varying ◽  
The Impact

This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power =  0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power  = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work.

scholarly journals Nonmeteorological Influences on Severe Thunderstorm Warning Issuance: A Geographically Weighted Regression-Based Analysis of County Warning Area Boundaries, Land Cover, and Demographic Variables

2017 ◽  
Vol 9 (3) ◽  
pp. 421-439 ◽  
Author(s):  
Megan L. White ◽  
J. Anthony Stallins
Keyword(s):  
Land Cover ◽  
Geographically Weighted Regression ◽  
Weather Forecast ◽  
Demographic Variables ◽  
Weighted Regression ◽  
Median Income ◽  
Local Regression ◽  
Severe Thunderstorm ◽  
Global Trend ◽  
Explained Variance

Abstract Studies have shown that the spatial distribution of severe thunderstorm warnings demonstrates variation beyond what can be attributed to weather and climate alone. Investigating spatial patterns of these variations can provide insight into nonmeteorological factors that might lead forecasters to issue warnings. Geographically weighted regression was performed on a set of demographic and land cover descriptors to ascertain their relationships with National Weather Service (NWS) severe thunderstorm warning polygons issued by 36 NWS forecast offices in the central and southeastern United States from 2008 to 2015. County warning area (CWA) boundaries and cities were predominant sources of variability in warning counts. Global explained variance in verified and unverified severe thunderstorm warnings ranged from 67% to 81% for population, median income, and percent imperviousness across the study area, which supports the spatial influence of these variables on warning issuance. Local regression coefficients indicated that verified and unverified warning counts increased disproportionately in larger cities relative to the global trend, particularly for NWS weather forecast office locations. However, local explained variance tended to be lower in cities, possibly due to greater complexity of social and economic factors shaping warning issuance. Impacts of thunderstorm type and anthropogenic modification of existing storms should also be considered when interpreting the results of this study.

scholarly journals Modeling spatial determinates of teenage pregnancy in Ethiopia; geographically weighted regression

2021 ◽  
Vol 21 (1) ◽  
Author(s):  
Seblewongel Tigabu ◽  
Alemneh Mekuriaw Liyew ◽  
Bisrat Misganaw Geremew
Keyword(s):  
Spatial Distribution ◽  
Geographically Weighted Regression ◽  
Teenage Pregnancy ◽  
Wealth Quintile ◽  
Ordinary Least Squares ◽  
Weighted Regression ◽  
Contraceptive Methods ◽  
Hotspot Analysis ◽  
Increased Risk ◽  
Risk Areas

Abstract Background In developing countries, 20,000 under 18 children give birth every day. In Ethiopia, teenage pregnancy is high with Afar and Somalia regions having the largest share. Even though teenage pregnancy has bad maternal and child health consequences, to date there is limited evidence on its spatial distribution and driving factors. Therefore, this study is aimed to assess the spatial distribution and spatial determinates of teenage pregnancy in Ethiopia. Methods A secondary data analysis was conducted using 2016 EDHS data. A total weighted sample of 3381 teenagers was included. The spatial clustering of teenage pregnancy was priorly explored by using hotspot analysis and spatial scanning statistics to indicate geographical risk areas of teenage pregnancy. Besides spatial modeling was conducted by applying Ordinary least squares regression and geographically weighted regression to determine factors explaining the geographic variation of teenage pregnancy. Result Based on the findings of exploratory analysis the high-risk areas of teenage pregnancy were observed in the Somali, Afar, Oromia, and Hareri regions. Women with primary education, being in the household with a poorer wealth quintile using none of the contraceptive methods and using traditional contraceptive methods were significant spatial determinates of the spatial variation of teenage pregnancy in Ethiopia. Conclusion geographic areas where a high proportion of women didn’t use any type of contraceptive methods, use traditional contraceptive methods, and from households with poor wealth quintile had increased risk of teenage pregnancy. Whereas, those areas with a higher proportion of women with secondary education had a decreased risk of teenage pregnancy. The detailed maps of hotspots of teenage pregnancy and its predictors had supreme importance to policymakers for the design and implementation of adolescent targeted programs.

scholarly journals Spatiotemporal Distribution Characteristics and Driving Forces of PM2.5 in Three Urban Agglomerations of the Yangtze River Economic Belt

2021 ◽  
Vol 18 (5) ◽  
pp. 2222
Author(s):  
Jin-Wei Yan ◽  
Fei Tao ◽  
Shuai-Qian Zhang ◽  
Shuang Lin ◽  
Tong Zhou
Keyword(s):  
Geographically Weighted Regression ◽  
Yangtze River ◽  
National Level ◽  
National Development ◽  
Urban Agglomeration ◽  
Spatiotemporal Distribution ◽  
Weighted Regression ◽  
Series Data ◽  
The Yangtze River ◽  
Urban Agglomerations

As part of one of the five major national development strategies, the Yangtze River Economic Belt (YREB), including the three national-level urban agglomerations (the Cheng-Yu urban agglomeration (CY-UA), the Yangtze River Middle-Reach urban agglomeration (YRMR-UA), and the Yangtze River Delta urban agglomeration (YRD-UA)), plays an important role in China’s urban development and economic construction. However, the rapid economic growth of the past decades has caused frequent regional air pollution incidents, as indicated by high levels of fine particulate matter (PM2.5). Therefore, a driving force factor analysis based on the PM2.5 of the whole area would provide more information. This paper focuses on the three urban agglomerations in the YREB and uses exploratory data analysis and geostatistics methods to describe the spatiotemporal distribution patterns of air quality based on long-term PM2.5 series data from 2015 to 2018. First, the main driving factor of the spatial stratified heterogeneity of PM2.5 was determined through the Geodetector model, and then the influence mechanism of the factors with strong explanatory power was extrapolated using the Multiscale Geographically Weighted Regression (MGWR) models. The results showed that the number of enterprises, social public vehicles, total precipitation, wind speed, and green coverage in the built-up area had the most significant impacts on the distribution of PM2.5. The regression by MGWR was found to be more efficient than that by traditional Geographically Weighted Regression (GWR), further showing that the main factors varied significantly among the three urban agglomerations in affecting the special and temporal features.

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