Geographically Weighted Regression Coefficients Research Articles

Spatially clustered patterns of suicide mortality rates in South Korea: a geographically weighted regression analysis

BackgroundSuicide mortality remains a global health concern, and community characteristics affect regional variations in suicide. This study investigated spatially clustered patterns of suicide mortality rates in South Korea and evaluated the impact of community factors on suicide.MethodsSuicide mortality rates were estimated by sex, age group, and district, using the 2021 Cause of Death Statistics in South Korea from the MicroData Integrated Service. Community-determinant data for 2021 or the nearest year were collected from the Korean Statistical Information Service. The spatial autocorrelation of suicide by sex and age was examined based on Global Moran’s I index. Geographically weighted regression (GWR) was used to discern the influence of community determinants on suicide.ResultsSuicide mortality rates were significantly higher among men (40.64 per 100,000) and adults over the age of 65 years (43.18 per 100,000). The male suicide mortality rates exhibited strong spatial dependence, as indicated by a high global Moran’s I with p < 0.001, highlighting the importance of conducting spatial analysis. In the GWR model calibration, a subset of the community’s age structure, single-person household composition, access to mental healthcare centers, and unmet medical needs were selected to explain male suicide mortality. These determinants disproportionately increased the risk of male suicide, varying by region. The GWR coefficients of each variable vary widely across 249 districts: aging index (Q1:0.06–Q3:0.46), single-person households (Q1:0.22–Q3:0.35), psychiatric clinics (Q1:-0.20–Q3:-0.01), and unmet medical needs (Q1:0.09–Q3:0.14).ConclusionsCommunity cultural and structural factors exacerbate regional disparities in suicide among men. The influencing factors exhibit differential effects and significance depending on the community, highlighting the need for efficient resource allocation for suicide. A regionally tailored approach is crucial for the effective control of the community’s mental health management system.

Intra-urban differences underlying leprosy spatial distribution in central Brazil: geospatial techniques as potential tools for surveillance.

This ecological study identified an aggregation of urban neighbourhoods spatial patterns in the cumulative new case detection rate (NCDR) of leprosy in the municipality of Rondonópolis, central Brazil, as well as intra-urban socioeconomic differences underlying this distribution. Scan statistics of all leprosy cases reported in the area from 2011 to 2017 were used to investigate spatial and spatiotemporal clusters of the disease at the neighbourhood level. The associations between the log of the smoothed NCDR and demographic, socioeconomic, and structural characteristics were explored by comparing multivariate models based on ordinary least squares (OLS) regression, spatial lag, spatial error, and geographically weighted regression (GWR). Leprosy cases were observed in 84.1% of the neighbourhoods of Rondonópolis, where 848 new cases of leprosy were reported corresponding to a cumulative NCDR of 57.9 cases/100,000 inhabitants. Spatial and spatiotemporal high-risk clusters were identified in western and northern neighbourhoods, whereas central and southern areas comprised low-risk areas. The GWR model was selected as the most appropriate modelling strategy (adjusted R²: 0.305; AIC: 242.85). By mapping the GWR coefficients, we identified that low literacy rate and low mean monthly nominal income per household were associated with a high NCDR of leprosy, especially in the neighbourhoods located within high-risk areas. In conclusion, leprosy presented a heterogeneous and peripheral spatial distribution at the neighbourhood level, which seems to have been shaped by intra-urban differences related to deprivation and poor living conditions. This information should be considered by decision-makers while implementing surveillance measures aimed at leprosy control.

Assessing the spatial structure of the association between attendance at preschool and children's developmental vulnerabilities in Queensland, Australia.

Demographic and educational factors are essential, influential factors of early childhood development. This study aimed to investigate spatial patterns in the association between attendance at preschool and children's developmental vulnerabilities in one or more domain(s) in their first year of full-time school at a small area level in Queensland, Australia. This was achieved by applying geographically weighted regression (GWR) followed by K-means clustering of the regression coefficients. Three distinct geographical clusters were found in Queensland using the GWR coefficients. The first cluster covered more than half of the state of Queensland, including the Greater Brisbane region, and displays a strong negative association between developmental vulnerabilities and attendance at preschool. That is, areas with high proportions of preschool attendance tended to have lower proportions of children with at least one developmental vulnerability in the first year of full-time school. Clusters two and three were characterized by stronger negative associations between developmental vulnerabilities, English as the mother language, and geographic remoteness, respectively. This research provides evidence of the need for collaboration between health and education sectors in specific regions of Queensland to update current service provision policies and to ensure holistic and appropriate care is available to support children with developmental vulnerabilities.

Catchment and climatic influences on spatio-temporal variations in suspended sediment transport dynamics in rivers

Abstract Suspended sediment concentration (SSC) is an important attribute for water resources management. However, the interactions between climate and catchment characteristics that control the temporal variability of SSC in rivers are not fully resolved. The study aim is to evaluate how these variables influence spatial and seasonal variations in SSC dynamics at a continental scale. Daily SSC (mg/l) and site attribute data from 120 sites (USA) with minimum 10 years of record (1971–2000) were analysed. New indicators of SSC dynamics (magnitude and frequency) were developed and applied annually and seasonally. Geographically weighted regression (GWR) models were created for each ordinary least squares (OLS) regression model, and GWR coefficients were analysed by ecoregion. Land cover, rainfall and erosivity, baseflow index and soil texture were the most common variables in the OLS models. GWR coefficients displayed significant variation across the continent. Agricultural cover was positively associated with low frequency SSC events, while urban and forest cover predicted higher frequency events, except in the desert areas. PPT30 was generally a negative predictor for SSC magnitude, except the marine west coasts forests. These findings on catchment and climate controls on SSC will support future predictive models of SS transport dynamics.

The thermal performance of urban form – An analysis on urban structure types in Berlin

Increasing urban heat issues induced by climatic changes and growing urban populations exacerbate the need for adaptation. The present study intends to foster the so far quite rarely realized transfer from research to real-world planning. Subject of investigation is the thermal performance and characterization of urban structure types (USTs) in Berlin, Germany. Applying Landsat 8 derived land surface temperatures (LSTs), we first determine differences in the temperature patterns of the regarded USTs. Second, after running correlation analyses with LST and potentially influencing factors (NDVI – normalized difference vegetation index, imperviousness, building ratio, and building height), we fit ordinary least square (OLS) and geographically weighted regression (GWR) models. Finally, we relate the GWR results to the USTs and determine the effect of each variable on the respective LST regime. We find significant differences in the thermal performance of USTs, strong correlations between explaining variables and LST, and a sophisticated picture concerning GWR coefficients at various locations. Quasi-global r2 for the GWR (0.83) improves the OLS model value (0.53) considerably. The spatially explicit GWR method in combination with results aggregated on the planning-relevant UST-level provides crucially important information for climate adaptation and planning while being adaptable and transferable to other urban areas.

Context sensitivity of surface urban heat island at the local and regional scales

In this study we analysed the multi-annual (2002–2011) average summer surface urban heat island (SUHI) intensity of the 5000 largest urban clusters in Europe. We investigated its relationship with a proposed Gravitational Urban Morphology (GUM) index that can capture the local context sensitivity of SUHI. The GUM index was found to be an effective predictor of SUHI intensity. Together with other urban factors we built different multivariate linear regression models and a climate space based geographically weighted regression (GWR) model that can better predict SUHI intensity. As the GWR model captures the variation of influence from different urban factors on SUHI, it considerably outperformed linear models in predicting SUHI intensity in terms of R2 and other statistical criteria. By investigating the variation of GWR coefficients against background climate factors, we further built a nonlinear regression model that takes into account the sensitivity of SUHI to regional climate context. The nonlinear model showed comparable performance to that of the GWR model and it prevailed against all the linear models. Our work underlines the potential of SUHI reduction through optimising urban morphology, as well as the importance of integrating future urbanisation and climate change into the implementation of urban heat mitigation strategies.

Spatio-temporal stability of housing submarkets. Tracking spatial location of clusters of geographically weighted regression estimates of price determinants

This paper fills the gap in rich housing literature by testing the spatio-temporal stability of real estate submarkets. We start with standard Geographically Weighted Regression (GWR) estimation of the hedonic model on point data, and we cluster model coefficients to detect housing submarkets. We check spatio-temporal stability - we add novelty by comparing if clusters move over space or stay in the same place. We rasterise surface and apply the Rand Index and Jaccard Similarity to check if clusters assigned to raster cells yield stable spatial structure. This approach allows for quantitative assessments of how much determinants of price are stable over time and space. The same mechanism applied to standard errors of GWR coefficients is a good test of the spatio-temporal stability of local heteroscedasticity. A Case study of apartments' transactions in Warsaw-Poland for the 2006–2015 period, evidences relatively high spatio-temporal stability.

Uncovering the spatial variability of recent deforestation drivers in the Brazilian Cerrado

In recent years, the Cerrado deforestation has increased considerably, reaching rates higher than in the Amazonian realm. Although the effects of deforestation are well known, the understanding of its drives at regional levels is incipient. Most studies consider that a driver influences deforestation likewise in all regions. However, deforestation has a strong spatial structure that can lead drivers to vary their influence on deforestation in different regions. Here, we evaluated the spatial variability in the relationship between the recent Cerrado deforestation and socioeconomic, environmental, and structural drivers at a regional scale. We used a geographically weighted regression (GWR) to assess the spatial variability of predictor variables. We identified regions that respond similarly to the drivers by grouping municipalities, considering their GWR coefficients through hierarchical clustering. The analyses that consider the spatial variability of predictors are more appropriated to assess the causes of recent deforestation. Remnant natural vegetation influenced the recent deforestation in all defined regions. Greater access to rural credit concession was the main driving force of deforestation in the northeast region defined here. Distance to roads increased deforestation in the northeast and north regions, while it inhibited deforestation in the central-east and southeast regions. Rainfall inhibited deforestation in the northeast, north, and southwest regions. Steep slope prevented deforestation mainly in the northeast, north, and southwest regions. Our results highlight that, to effectively reduce Cerrado deforestation, public policies should integrate strategies focusing not only at national and biome levels but also at the regional spatial level.

Spatial heterogeneity of the associations of economic and health care factors with infant mortality in China using geographically weighted regression and spatial clustering.

Economic factors and health care resources are important influential factors of infant mortality. We aimed to examine prefecture-level spatial heterogeneity and clustering of the associations of economic and health care factors with infant mortality rates (IMR) in China. IMR data in 348 prefectures were calculated and adjusted, and economic and health care data were collected in each prefecture in China, 2010. Stepwise regression was used to select important variables, and geographically weighted regression (GWR) was applied to examine the spatial variations of the relationships between economic and health care factors and IMR. The k-means clustering was developed to elucidate the spatial clustering patterns of the GWR coefficients. The results showed that three important variables were selected in the multivariable regression model, including per capita income of rural residents, Engel's coefficient of rural residents, and proportion of government health expenditure. The GWR with these three variables revealed spatial heterogeneity of the associations between IMR and economic and health care factors; western China generally had higher GWR R-squares and stronger associations between IMR and all the three variables than the middle-eastern part of China. Based on the GWR coefficients, three distinct spatial clusters were identified. This study contributes new findings on the spatial heterogeneity of the associations between economic and health care factors and infant mortality rate in China, which calls for region-specific policies to reduce infant mortality in China.

Investigation of the spatially varying relationships of PM2.5 with meteorology, topography, and emissions over China in 2015 by using modified geographically weighted regression

PM2.5 pollution is caused by multiple factors and determining how these factors affect PM2.5 pollution is important for haze control. In this study, we modified the geographically weighted regression (GWR) model and investigated the relationships between PM2.5 and its influencing factors. Experiments covering 368 cities and 9 urban agglomerations were conducted in China in 2015 and more than 20 factors were considered. The modified GWR coefficients (MGCs) were calculated for six variables, including two emission factors (SO2 and NO2 concentrations), two meteorological factors (relative humidity and lifted index), and two topographical factors (woodland percentage and elevation). Then the spatial distribution of MGCs was analyzed at city, cluster, and region scales. Results showed that the relationships between PM2.5 and the different factors varied with location. SO2 emission positively affected PM2.5, and the impact was the strongest in the Beijing–Tianjin–Hebei (BTH) region. The impact of NO2 was generally smaller than that of SO2 and could be important in coastal areas. The impact of meteorological factors on PM2.5 was complicated in terms of spatial variations, with relative humidity and lifted index exerting a strong positive impact on PM2.5 in Pearl River Delta and Central China, respectively. Woodland percentage mainly influenced PM2.5 in regions of or near deserts, and elevation was important in BTH and Sichuan. The findings of this study can improve our understanding of haze formation and provide useful information for policy-making.

Spatiotemporal patterns and drivers of ecosystem service supply and demand across the conterminous United States: A multiscale analysis

Land-use and land-cover changes associated with urbanization have significantly influenced biodiversity and ecosystem functions, as well as the supply and demand of ecosystem services (ESs). Assessing ESs and exploring their drivers are critical for regional land-use planning and ecological sustainability. In this study, the supply-demand matrix approach was used to quantify ES supply, demand, and their gap at multiple scales across the conterminous United States from 1940 to 2011. A new integrated measurement framework was proposed to offset ES deficits by identifying an optimal land-use conversion strategy. We focused on exploring the scale and spatial effects of the impacts of various drivers on ESs using ordination and regression analysis. The results showed that the expansion of developed land led to decreased ES supply and increased ES demand during the past seven decades, generating growing ES deficits at different scales, especially in highly urbanized metropolitan areas. To alleviate or offset ES deficits, promoting the intensive utilization of developed land and converting cropland, pasture, and barren land into forests would be the optimal land use strategies. Moreover, the drivers of ESs exhibited not only scale dependence but also spatial heterogeneity. The smaller the scale, the more diverse the drivers. The natural and socioeconomic drivers explained less variation at the metropolitan scale than at the state scale. Economic factors were key drivers for ESs at the state scale, while social factors were key drivers at the metropolitan scale. The regression coefficients for the drivers of ESs in the geographically weighted regression (GWR) model showed remarkable spatial heterogeneity. The GWR coefficients might have important implications for decision making in ES management. Localized and efficient land-use strategies and management policies are needed to reduce the ecological footprints of urban areas and thus achieve regional sustainability.

Urban and Peri-Urban Residential Rental Markets in Wallonia: Similar or Different?

Residential rents are analysed in the Walloon region in Belgium. In this region, affected by urban sprawl, households rent accommodation in urbanised areas as well as in their peripheries. While there is no statistical difference between the average observed rents per square meter in urban agglomerations and suburbs, does it mean that these areas compose a single market with identical rent determinants? Or that the same level of rents is determined by different drivers? The paper analyses the regional territorial structure and aims at determining the geographical rental submarkets based on urban / peri-urban delimitation. Traditional ordinary least squares (OLS) and geographically weighted regression (GWR) techniques are applied. With the latter method, the spatial autocorrelation in the residuals decreases, but remains significant. Particular attention is payed to the spatial distribution of the GWR coefficients. The Chow test and the weighted standard error provide an evidence of the existence of spatial-structural submarkets in the agglomerations and in the peri-urban areas in the biggest residential urban complexes of the region. The calculated market rent of a hypothetical standardized dwelling reveals a substantial dissimilarity between two areas: the rent of a typical dwelling is higher in peri-urban zones, up to 43.5% according to the OLS and up to 17.7% according to the GWR. With more recent dataset, we found that this tendency, which contradicts the classical urban theory, increases in time.

A spatial analysis of proximate greenspace and mental wellbeing in London

While local-area greenspace is associated with reduced symptoms of mental distress and greater life satisfaction, most previous research has measured the amount of local-area greenspace within administrative boundaries, and found mixed results for associations between greenspace and multidimensional mental wellbeing. The study was designed to examine whether the amount of greenspace within a radius of individuals’ homes was associated with mental wellbeing, testing the government guideline that greenspace should be available within 300 m of homes.Individual and Household-level data were drawn from the Annual Population Survey at postcode level (APS, Pooled Dataset 2012–2015), which includes 3 mental wellbeing measures, covering aspects of life satisfaction, sense of worth, and happiness, as well as a range of socio-demographic variables. Greenspace data were obtained Greenspace Information for Greater London Group (GiGL), and was used to calculated the amount of greenspace within a 300 m radius of individuals. Linear regression models revealed positive and statistically significant associations between the amount of greenspace and indicators of life satisfaction and worth. Moran's I, an indicator of spatial autocorrelation, revealed statistically significant clustering of the residuals of these models, so Geographically Weighted Regression (GWR) models were calculated, in order to adjust for underlying spatial processes within the data and investigate the geographic variation in the association between local greenspace and mental wellbeing. The global GWR model revealed that an increase in 1 ha of greenspace within 300 m of residents was associated with a statistically significant 0.803 increase in life satisfaction, 0.740 and 0.521 for worth and happiness, respectively. This therefore provides some support for the inclusion of greenspace within 300 m of homes. Local GWR coefficients revealed slight variation in the strength of these associations across the study space. Therefore, further analyses are required to investigate whether the walking (network distance), absolute size, or type of each greenspace are able to explain this spatial variation.

Parameter Estimation of Locally Compensated Ridge-Geographically Weighted Regression Model

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 least square method is , where the ridge parameter, λ, varies across space. The LCR-GWR is not necessarily calibrates the ridge regressions everywhere; only at locations where collinearity is likely to be an issue. And the parameter significance test using t-test, t = .

Examining Spatial Regimes of Child Maltreatment Allegations in a Social Vulnerability Framework.

The present research examines child maltreatment allegations (CMAs) in San Diego County, California, exploring spatial patterns of Child Protective Services involvement and multiple, multidimensional measures of neighborhood social vulnerability. Results showed significant patterns of spatial clustering (i.e., hot and cold spots) of CMAs across the county (Moran's I = .316, p < .001). A geographically weighted regression (GWR) was implemented to examine the relationship between CMAs and social vulnerability at the census-tract level, thereby overcoming the deficiencies of global models. Nonstationarity was detected across four indices of vulnerability (socioeconomic status, race/ethnicity, household composition, and health vulnerability) as well as proximity to on-premise alcohol outlets, percentage of residents in each census tract affected by food deserts, and population density, in some cases showing countervailing effects depending on spatial location. A hierarchical clustering was performed on the GWR coefficients to identify spatial regimes, or clusters, across the county. The results yielded six spatial regimes of social vulnerability differentially related to CMA rates. The present study demonstrates the novelty of GWR in combination with a hierarchical cluster analysis for exploring how local contextual processes influence child maltreatment reporting rates across the county.

Spatial Modelling of Current and Future Piped Domestic Water Demand in Athi River Town, Kenya

Water scarcity is currently still a global challenge despite the fact that water sustains life on earth. An understanding of domestic water demand is therefore vital for effective water management. In order to understand and predict future water demand, appropriate mathematical models are needed. The present work used Geographic Information Systems (GIS) based regression models; Geographically weighted regression (GWR) and Ordinary Least Square (OLS) to model domestic water demand in Athi river town. We identified a total of 7 water determinant factors in our study area. From these factors, 4 most significant ones (household size, household income, meter connections and household rooms) were identified using OLS. Further, GWR technique was used to investigate any intrinsic relationship between the factors and water demand occurrence. GWR coefficients values computed were mapped to exhibit the relationship and strength of each explanatory variable to water demand. By comparing OLS and GWR models with both AIC value and R2 value, the results demonstrated GWR model as capable of projecting water demand compared to OLS model. The GWR model was therefore adopted to predict water demand in the year 2022. It revealed domestic water demand in 2017 was estimated at 721,899 m3 compared to 880,769 m3 in 2022, explaining an increase of about 22%. Generally, the results of this study can be used by water resource planners and managers to effectively manage existing water resources and as baseline information for planning a cost-effective and reliable water supply sources to the residents of a town.

Dynamic land use change simulation using cellular automata with spatially nonstationary transition rules

The dynamic relationships between land use change and its driving forces vary spatially and can be identified by geographically weighted regression (GWR). We present a novel cellular automata (GWR-CA) model that incorporates GWR-derived spatially varying relationships to simulate land use change. Our GWR-CA model is characterized by spatially nonstationary transition rules that fully address local interactions in land use change. More importantly, each driving factor in our GWR model contains effects that both promote and resist land use change. We applied GWR-CA to simulate rapid land use change in Suzhou City on the Yangtze River Delta from 2000 to 2015. The GWR coefficients were visualized to highlight their spatial patterns and local variation, which are closely associated with their effects on land use change. The transition rules indicate low land conversion potential in the city’s center and outer suburbs, but higher land conversion potential in the inner near suburbs along the belt expressway. Residual statistics show that GWR fits the input data better than logistic regression (LR). Compared with an LR-based CA model, GWR-CA improves overall accuracy by 4.1% and captures 5.5% more urban growth, suggesting that GWR-CA may be superior in modeling land use change. Our results demonstrate that the GWR-CA model is effective in capturing spatially varying land transition rules to produce more realistic results, and is suitable for simulating land use change and urban expansion in rapidly urbanizing regions.

Spatial analysis of the regional variation of hypertensive disease mortality and its socio-economic correlates in South Korea.

This paper presents a cross-sectional study based on the cause of death statistics in 2011 extracted from all 229 local governments in South Korea. The standardised hypertensive disease mortality rate (SHDMR) was defined by age- and sex-adjusted mortality by hypertensive diseases distinguished by International Classification of Disease- 10 (ICD-10). Variables taken into account were the number of doctors per 100,000 persons, the proportion with higher education (including university students and high school graduates), the number of recipients of basic livelihood support per 100,000 persons, the annual national health insurance premium per capita and the proportion of persons classified as high-risk drinkers. Ordinary least square (OLS) regression and geographically weighted regression (GWR) were applied to identify the potential associations. The statistical analysis was conducted with SAS ver. 9.3, while ArcGIS ver. 10.0 was utilised for the spatial analysis. The OLS results showed that the number of basic livelihood recipients per 100,000 persons had a significant positive association with the SHDMR, and the proportion with higher education had a significant negative one. GWR coefficients varied depending on region investigated and some regional variables had various directions. GWR showed higher adjusted R2 than that of OLS. It was found that the SHDMR was affected by socio-economic status, but as the effects observed were not consistent in all regions of the country, the development of health policies will need to consider the potential for regional variation.

A Closer Examination of Spatial-Filter-Based Local Models

GIScience 2016 Short Paper Proceedings A Closer Examination of Spatial-Filter-Based Local Models Taylor Oshan, A. Stewart Fotheringham Arizona State University, Tempe, Arizona 85281 Email: {toshan; stewart.fotheringham}@asu.edu Abstract Local modeling is a spatial analysis technique that explores spatial non-stationarity in data- generating processes. Geographically weighted regression (GWR) is one method that has been widely applied across domains, which has helped uncover local spatial relationships and gener- ally increases model goodness-of-fit. Despite this, some have criticized GWR for being extra susceptible to issues such as multicollinearity and spatial autocorrelation. Spatial-filtering- based local regression (SFLR) has been suggested as a solution. While SFLR is claimed to be approximately equivalent to GWR, it is also touted as superior. Therefore, it is of interest to compare the output from these two techniques. We do this by examining how well both techniques replicate the known coefficient values derived by simulating data that is represen- tative of spatially varying processes. The results indicate that the original SFLR specification is prone to overfitting, while an alternative specification that minimizes the mean square error produces coefficients similar to GWR. Introduction and Background Non-stationarity in data-generating processes goes largely undetected in traditional global models. Hence, local models, which explicitly allow regression coefficients to vary over space, are necessary to capture such heterogenous processes. One local modeling technique that has become particularly popular is geographically weighted regression (GWR) (Fotheringham et al. 2002). Despite its usefulness, GWR has been critiqued as being highly susceptible to multicollinearity (Wheeler & Tiefelsdorf 2005), whereby multicollinearity amongst explana- tory variables causes intolerable levels of correlation amongst GWR coefficients. However, results show that when the sample size is large, GWR is robust to even remarkably high levels of multicollinearity (Paez et al. 2011; Fotheringham & Oshan Submitted). Still, the work of Wheeler and Tiefelsdorf (Wheeler & Tiefelsdorf 2005) sparked much subsequent critiques of GWR. Specifically, spatial-filter-based local regression (SFLR) has been suggested as a supe- rior alternative to GWR (Griffith 2008). While Griffith (2008) posits that SFLR and GWR are approximately equivalent, he also points out that local coefficients produced from GWR and SFLR are minimally correlated, suggesting that the two models are producing much different results, thereby implying a contradiction within the SFLR method. To the knowledge of the authors, the SFLR method has not been applied outside its original conception (Griffith 2008), while GWR has produced agreeable results in many studies. Therefore, the primarily goal of this paper is to employ simulated data in order to test which of the techniques can more reliably estimate the true coefficients of non-stationary processes. Some modifications of the SFLR routine are investigated and several issues of the SFLR framework are highlighted. A basic GWR model may be specified as p y i = b i0 + Â b ik x ik + e i , k=1 i = 1, ..., n,

GIS-based analysis of obesity and the built environment in the US

This paper examines the statewide relationship between built environment and obesity at the county scale by using the Geographically Weighted Regression (GWR) method. The independent variables include three built environment factors – street connectivity, walk score, fast-food/full-service restaurants ratio – and two sociodemographic variables, race heterogeneity and poverty rate. The urban influence is considered as a covariate in the analysis. Through the regression model we found that walk score and street connectivity are negatively related to obesity, poverty rate and metro are positively related, and the fast-food/full-service restaurants ratio is not significant. A regionalization method is used to group US counties to regions based on their GWR coefficients. Qualitative inferences of policies are made available to facilitate better understanding of the obesity problem associated with the built environment in these regions.