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 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.

scholarly journals Spatial Analysis Of Foreign Migration In Poland In 2012 Using Geographically Weighted Regression

2014 ◽  
Vol 17 (4) ◽  
pp. 137-154 ◽  
Author(s):  
Karolina Lewandowska-Gwarda
Keyword(s):  
Geographically Weighted Regression ◽  
Graphical Representation ◽  
Emigration And Immigration ◽  
Weighted Regression ◽  
Model Parameters ◽  
Population Changes ◽  
Principal Influence ◽  
Gis Tools ◽  
Spatially Varying ◽  
The Impact

Migration has a principal influence on countries’ population changes. Thus, the issues connected with the causes, effects and directions of people’s movements are a common topic of political and academic discussions. The aim of this paper is to analyse the spatial distribution of officially registered foreign migration in Poland in 2012. GIS tools are implemented for data visualization and statistical analysis. Geographically weighted regression (GWR) is used to estimate the impact of unemployment, wages and other socioeconomic variables on the foreign emigration and immigration measure. GWR provides spatially varying estimates of model parameters that can be presented on a map, giving a useful graphical representation of spatially varying relationships.  

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.

Government failures and non-performing loans in European countries: a spatial approach

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ferdinando Ofria ◽  
Massimo Mucciardi
Keyword(s):  
Public Debt ◽  
Geographically Weighted Regression ◽  
European Countries ◽  
Weighted Regression ◽  
Second Step ◽  
Ols Regression ◽  
Content Type ◽  
The Impact ◽  
The Relationship ◽  
The Eu

PurposeThe purpose is to analyze the spatially varying impacts of corruption and public debt as % of GDP (proxies of government failures) on non-performing loans (NPLs) in European countries; comparing two periods: one prior to the crisis of 2007 and another one after that. The authors first modeled the NPLs with an ordinary lest square (OLS) regression and found clear evidence of spatial instability in the distribution of the residuals. As a second step, the authors utilized the geographically weighted regression (GWR) to explore regional variations in the relationship between NPLs and the proxies of “Government failures”.Design/methodology/approachThe authors first modeled the NPL with an OLS regression and found clear evidence of spatial instability in the distribution of the residuals. As a second step, the author utilized the Geographically Weighted Regression (GWR) (Fotheringham et al., 2002) to explore regional variations in the relationship between NPLs and proxies of “Government failures” (corruption and public debt as % of GDP).FindingsThe results confirm that corruption and public debt as % of GDP, after the crisis of 2007, have affected significantly on NPLs of the EU countries and the following countries neighboring the EU: Switzerland, Iceland, Norway, Montenegro, and Turkey.Originality/valueIn a spatial prospective, unprecedented in the literature, this research focused on the impact of corruption and public debt as % of GDP on NPLs in European countries. The positive correlation, as expected, between public debt and NPLs highlights that fiscal problems in Eurozone countries have led to an important rise of problem loans. The impact of institutional corruption on NPLs reports that the higher the corruption, the higher is the level of NPLs.

scholarly journals Valuing Environmental Amenities across Space: A Geographically Weighted Regression of Housing Preferences in Greenville County, SC

Land ◽  
2019 ◽  
Vol 8 (10) ◽  
pp. 147
Author(s):  
Hiebert ◽  
Allen
Keyword(s):  
Geographically Weighted Regression ◽  
City Planning ◽  
Spatial Dynamics ◽  
Ordinary Least Squares ◽  
Hedonic Model ◽  
Weighted Regression ◽  
Hedonic Price ◽  
Environmental Amenities ◽  
Forested Areas ◽  
The Impact

As global consumption and development rates continue to grow, there will be persistent stress placed on public goods, namely environmental amenities. Urban sprawl and development places pressure on forested areas, as they are often displaced or degraded in the name of economic development. This is problematic because environmental amenities are valued by the public, but traditional market analysis typically obscures the value of these goods and services that are not explicitly traded in a market setting. This research examines the non-market value of environmental amenities in Greenville County, SC, by utilizing a hedonic price model of home sale data in 2011. We overlaid home sale data with 2011 National Land Cover Data to estimate the value of a forest view, proximity to a forest, and proximity to agriculture on the value of homes. We then ran two regression models, an ordinary least squares (OLS) and a geographically weighted regression to compare the impact of space on the hedonic model variables. Results show that citizens in Greenville County are willing to pay for environmental amenities, particularly views of a forest and proximity to forested and agricultural areas. However, the impact and directionality of these variables differ greatly across space. These findings suggest the need for an integration of spatial dynamics into environmental valuation estimates to inform conservation policy and intentional city planning.

Sign in / Sign up

Export Citation Format

Share Document