Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Wheeler, David C.; Tiefelsdorf, Michael

doi:10.1007/s10109-005-0155-6

Cited by 647 publications

(455 citation statements)

References 24 publications

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“…Local estimation is therefore particularly useful for identifying the heterogeneity and providing practical implications by visualizing the local regression coefficients (Wheeler & Tiefelsdorf, 2005). Different approaches have been proposed to estimate the parameters of local models such as GWR (Páez et al, 2002;Yang & Fik, 2014) and SALE (Pace & LeSage, 2004).…”

Section: Local Estimationmentioning

confidence: 99%

Tourism and regional income inequality: Evidence from China

Chen

et al. 2016

Annals of Tourism Research

182

120

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Section: Local Estimationmentioning

confidence: 99%

Tourism and regional income inequality: Evidence from China

Chen

et al. 2016

Annals of Tourism Research

182

120

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“…Previous studies have shown that a GWR model outperformed an OLS model in terms of predicting the relationship between UHI and its associated driving forces, including LUC. Mathematically, a general form of GWR model takes the following form [43]:…”

Section: The Application Of Gwr To Model the Uhi Effectmentioning

confidence: 99%

Correlation or Causality between Land Cover Patterns and the Urban Heat Island Effect? Evidence from Brisbane, Australia

2016

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Numerous studies have identified associations between the surface urban heat island (SUHI) effect (i.e., SUHI, hereinafter is referred to as UHI) and urban growth, particularly changes in land cover patterns. This research questions their causal links to answer a key policy question: If cities restrict urban expansion and encourage people to live within existing urban areas, will that help in controlling UHI? The question has been answered by estimating four models using data from Brisbane, Australia: Model 1-cross-sectional ordinary least square (OLS) regression-to examine the association between the UHI effect and land cover patterns in 2013; Model 2-cross-sectional geographically weighted regression (GWR)-to examine whether the outputs generated from Model 1 possess significant spatial variations; Model 3-longitudinal OLS-to examine whether changes in land cover patterns led to changes in UHI effects between 2004 and 2013; and Model 4-longitudinal GWR-to examine whether the outputs generated from Model 3 vary significantly over space. All estimations were controlled for potential confounding effects (e.g., population, employment and dwelling densities). Results from the cross-sectional OLS and GWR models were consistent with previous findings and showed that porosity is negatively associated with the UHI effect in 2013. In contrast, population density has a positive association. Results from the longitudinal OLS and GWR models confirm their causal linkages and showed that an increase in porosity level reduced the UHI effect, whereas an increase in population density increased the UHI effect. The findings suggest that even a containment of population growth within existing urban areas will lead to the UHI effect. However, this can be significantly minimized through proper land use planning, by creating a balance between urban and non-urban uses of existing urban areas.

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“…As early as 2005, Wheeler investigated multicollinearity problems in GWR models and pioneered the ridge regression method to introduce multiple variables and eliminate the collinearity problem in GWR models (Wheeler and Tiefelsdorf, 2005;Wheeler, 2007). Additionally, Wheeler (2009) developed the use of LASSO (least absolute shrinkage and selection operator) algorithms in GWR models to limit the effects of explanatory variable correlation.…”

Section: Introductionmentioning

confidence: 99%

Impacts of land use and population density on seasonal surface water quality using a modified geographically weighted regression

Chen

Mei

Dahlgren

et al. 2016

Science of The Total Environment

169

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• The modified GWR models had higher R 2 and reflected the actual spatial features.• A manual variable excluding-selecting method is explored to avoid multicollinearity.• Influences of the dominant indicator on water quality varied with space and seasons.• Protection policies need consider sitespecific conditions and seasonal variations. G R A P H I C A L A B S T R A C Ta b s t r a c t a r t i c l e i n f o As an important regulator of pollutants in overland flow and interflow, land use has become an essential research component for determining the relationships between surface water quality and pollution sources. This study investigated the use of ordinary least squares (OLS) and geographically weighted regression (GWR) models to identify the impact of land use and population density on surface water quality in the Wen-Rui Tang River watershed of eastern China. A manual variable excluding-selecting method was explored to resolve multicollinearity issues. Standard regression coefficient analysis coupled with cluster analysis was introduced to determine which variable had the greatest influence on water quality. Results showed that: (1) Impact of land use on water quality varied with spatial and seasonal scales. Both positive and negative effects for certain land-use indicators were found in different subcatchments. (2) Urban land was the dominant factor influencing N, P and chemical oxygen demand (COD) in highly urbanized regions, but the relationship was weak as the pollutants were mainly from point sources. Agricultural land was the primary factor influencing N and P in suburban and rural areas; the relationship was strong as the pollutants were mainly from agricultural surface runoff. Subcatchments located in suburban areas were identified with urban land as the primary influencing factor during the wet season while agricultural land was identified as a more prevalent influencing factor during the dry season. (3) Adjusted R 2 values in OLS models using the manual variable excluding-selecting method averaged 14.3% higher than using stepwise multiple linear regressions. However, the corresponding GWR models had adjusted R 2~5 9.2% higher than the optimal OLS models, confirming that GWR models demonstrated better prediction accuracy. Based on our findings, water resource protection policies should consider site-specific land-use Contents lists available at ScienceDirectScience of the Total Environment j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / s c i t o t e n v conditions within each watershed to optimize mitigation strategies for contrasting land-use characteristics and seasonal variations.

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Multicollinearity and correlation among local regression coefficients in geographically weighted regression

Abstract: Geographically weighted regression, Multicollinearity, Local regression diagnostics, Spatial eigenvectors, Experimental spatial design,

Cited by 647 publications

References 24 publications

Tourism and regional income inequality: Evidence from China

Tourism and regional income inequality: Evidence from China

Correlation or Causality between Land Cover Patterns and the Urban Heat Island Effect? Evidence from Brisbane, Australia

Impacts of land use and population density on seasonal surface water quality using a modified geographically weighted regression

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