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1.
Present methodological research on geographically weighted regression (GWR) focuses primarily on extensions of the basic GWR model, while ignoring well-established diagnostics tests commonly used in standard global regression analysis. This paper investigates multicollinearity issues surrounding the local GWR coefficients at a single location and the overall correlation between GWR coefficients associated with two different exogenous variables. Results indicate that the local regression coefficients are potentially collinear even if the underlying exogenous variables in the data generating process are uncorrelated. Based on these findings, applied GWR research should practice caution in substantively interpreting the spatial patterns of local GWR coefficients. An empirical disease-mapping example is used to motivate the GWR multicollinearity problem. Controlled experiments are performed to systematically explore coefficient dependency issues in GWR. These experiments specify global models that use eigenvectors from a spatial link matrix as exogenous variables.This study was supported by grant number 1 R1 CA95982-01, Geographic-Based Research in Cancer Control and Epidermiology, from the National Cancer Institute. The author thank the anonymous reviewers and the editor for their helpful comments.  相似文献   

2.
This study evaluates the influences of air pollution in China using a recently proposed model—multi‐scale geographically weighted regression (MGWR). First, we review previous research on the determinants of air quality. Then, we explain the MGWR model, together with two global models: ordinary least squares (OLS) and OLS containing a spatial lag variable (OLSL) and a commonly used local model: geographically weighted regression (GWR). To detect and account for any variation of the spatial autocorrelation of air pollution over space, we construct two extra local models which we call GWR with lagged dependent variable (GWRL) and MGWR with lagged dependent variable (MGWRL) by including the lagged form of the dependent variable in the GWR model and the MGWR model, respectively. The performances of these six models are comprehensively examined and the MGWR and MGWRL models outperform the two global models as well as the GWR and GWRL models. MGWRL is the most accurate model in terms of replicating the observed air quality index (AQI) values and removing residual dependency. The superiority of the MGWR framework over the GWR framework is demonstrated—GWR can only produce a single optimized bandwidth, while MGWR provides covariate‐specific optimized bandwidths which indicate the different spatial scales that different processes operate.  相似文献   

3.
Based on remote sensing and GIS, this study models the spatial variations of urban growth patterns with a logistic geographically weighted regression (GWR) technique. Through a case study of Springfield, Missouri, the research employs both global and local logistic regression to model the probability of urban land expansion against a set of spatial and socioeconomic variables. The logistic GWR model significantly improves the global logistic regression model in three ways: (1) the local model has higher PCP (percentage correctly predicted) than the global model; (2) the local model has a smaller residual than the global model; and (3) residuals of the local model have less spatial dependence. More importantly, the local estimates of parameters enable us to investigate spatial variations in the influences of driving factors on urban growth. Based on parameter estimates of logistic GWR and using the inverse distance weighted (IDW) interpolation method, we generate a set of parameter surfaces to reveal the spatial variations of urban land expansion. The geographically weighted local analysis correctly reveals that urban growth in Springfield, Missouri is more a result of infrastructure construction, and an urban sprawl trend is observed from 1992 to 2005.  相似文献   

4.
Geographically Weighted Regression (GWR) is a method of spatial statistical analysis used to explore geographical differences in the effect of one or more predictor variables upon a response variable. However, as a form of local analysis, it does not scale well to (especially) large data sets because of the repeated processes of fitting and then comparing multiple regression surfaces. A solution is to make use of developing grid infrastructures, such as that provided by the National Grid Service (NGS) in the UK, treating GWR as an "embarrassing parallel" problem and building on existing software platforms to provide a bridge between an open source implementation of GWR (in R) and the grid system. To demonstrate the approach, we apply it to a case study of participation in Higher Education, using GWR to detect spatial variation in social, cultural and demographic indicators of participation.  相似文献   

5.
 Industry is the most important sector in the Chinese economy. To identify the spatial interaction between the level of regional industrialisation and various factors, this paper takes Jiangsu province of China as a case study. To unravel the existence of spatial nonstationarity, geographically weighted regression (GWR) is employed in this article. Conventional regression analysis can only produce `average' and `global' parameter estimates rather than `local' parameter estimates which vary over space in some spatial systems. Geographically weighted regression (GWR), on the other hand, is a relatively simple, but useful new technique for the analysis of spatial nonstationarity. Using the GWR technique to study regional industrialisation in Jiangsu province, it is found that there is a significant difference between the ordinary linear regression (OLR) and GWR models. The relationships between the level of regional industrialisation and various factors show considerable spatial variability. Received: 4 April 2001 / Accepted: 17 November 2001  相似文献   

6.
Geographically weighted regression (GWR) is an important local method to explore spatial non‐stationarity in data relationships. It has been repeatedly used to examine spatially varying relationships between epidemic diseases and predictors. Malaria, a serious parasitic disease around the world, shows spatial clustering in areas at risk. In this article, we used GWR to explore the local determinants of malaria incidences over a 7‐year period in northern China, a typical mid‐latitude, high‐risk malaria area. Normalized difference vegetation index (NDVI), land surface temperature (LST), temperature difference, elevation, water density index (WDI) and gross domestic product (GDP) were selected as predictors. Results showed that both positively and negatively local effects on malaria incidences appeared for all predictors except for WDI and GDP. The GWR model calibrations successfully depicted spatial variations in the effect sizes and levels of parameters, and also showed substantially improvements in terms of goodness of fits in contrast to the corresponding non‐spatial ordinary least squares (OLS) model fits. For example, the diagnostic information of the OLS fit for the 7‐year average case is R2 = 0.243 and AICc = 837.99, while significant improvement has been made by the GWR calibration with R2 = 0.800 and AICc = 618.54.  相似文献   

7.
This study analyses the relationship between fire incidence and some environmental factors, exploring the spatial non-stationarity of the phenomenon in sub-Saharan Africa. Geographically weighted regression (GWR) was used to study the above relationship. Environment covariates comprise land cover, anthropogenic and climatic variables. GWR was compared to ordinary least squares, and the hypothesis that GWR represents no improvement over the global model was tested. Local regression coefficients were mapped, interpreted and related with fire incidence. GWR revealed local patterns in parameter estimates and also reduced the spatial autocorrelation of model residuals. All the covariates were non-stationary and in terms of goodness of fit, the model replicates the data very well (R 2 = 87%). Vegetation has the most significant relationship with fire incidence, with climate variables being more important than anthropogenic variables in explaining variability of the response. Some coefficient estimates exhibit locally different signs, which would have gone undetected by a global approach. This study provides an improved understanding of spatial fire–environment relationships and shows that GWR is a valuable complement to global spatial analysis methods. When studying fire regimes, effects of spatial non-stationarity need to be incorporated in vegetation-fire modules to have better estimates of burned areas and to improve continental estimates of biomass burning and atmospheric emissions derived from vegetation fires.  相似文献   

8.
The principal rationale for applying geographically weighted regression (GWR) techniques is to investigate the potential spatial non-stationarity of the relationship between the dependent and independent variables—i.e., that the same stimulus would provoke different responses in different locations. The calibration of GWR employs a geographically weighted local least squares regression approach. To obtain meaningful inference, it assumes that the regression residual follows a normal or asymptotically normal distribution. In many classical econometric analyses, the assumption of normality is often readily relaxed, although it has been observed that such relaxation might lead to unreliable inference of the estimated coefficients' statistical significance. No studies, however, have examined the behavior of residual non-normality and its consequences for the modeled relationships in GWR. This study attempts to address this issue for the first time by examining a set of tobacco-outlet-density and demographic variables (i.e., percent African American residents, percent Hispanic residents, and median household income) at the census tract level in New Jersey in a GWR analysis. The regression residual using the raw data is apparently non-normal. When GWR is estimated using the raw data, we find that there is no significant spatial variation of the coefficients between tobacco outlet density and percentage of African American and Hispanics. After transforming the dependent variable and making the residual asymptotically normal, all coefficients exhibit significant variation across space. This finding suggests that relaxation of the normality assumption could potentially conceal the spatial non-stationarity of the modeled relationships in GWR. The empirical evidence of the current study implies that researchers should verify the normality assumption prior to applying GWR techniques in analyses of spatial non-stationarity.  相似文献   

9.
遥感技术具备实时快速、时空连续、广覆盖尺度等独特优势,在全球气候恶化大背景下,利用遥感干旱监测方法相比于传统地面监测手段,能够提供实时、准确、稳定的旱情信息,辅助科学决策。目前常用遥感旱情监测方法大多依赖全域性数学模型建模,假定了旱情模式的空间平稳特性,因而难以准确反映旱情模式的局部差异特征。本文提出利用地理加权回归模型GWR (Geographically Weighted Regression),考虑旱情模式的空间非平稳特性,综合多种遥感地面旱情监测指数,以实现传统全域旱情监测模型的局部优化。以美国大陆为研究区,监测2002年—2011年共10年的旱情状态。研究表明,GWR模型能够提供空间变化的局部最佳估计模型参数,监测结果更加吻合标准美国旱情监测USDM (U.S Drought Monitor)验证数据,且与地面实测值的最高相关系数R达到0.8552,均方根误差RMSE达到0.972,显著优于其他遥感旱情监测模型。GWR模型具备空间非平稳探测优势,实现了旱情模式的局部精细探测,能够显著提升遥感旱情监测精度,具备较好的应用前景。  相似文献   

10.
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.  相似文献   

11.
互联网记录了人们的日常生活,对带有位置信息的搜索引擎数据进行分析和挖掘可以获得隐藏于其中的地理信息。本文通过分析中国各省流感月度发病数与相关关键词百度搜索指数之间的相关性,选取相关性较高关键词的百度指数作为解释变量,发病数作为因变量,在采用主成分分析法消除变量共线性后,分别使用普通最小二乘回归（OLS）、地理加权回归（GWR）及时空地理加权回归（GTWR）构建流感发病数的空间分布模型。模型的拟合度能够从OLS的0.737、GWR的0.915提高到GTWR的0.959,赤池信息准则（AIC）也表明,GTWR模型明显优于OLS与GWR模型。验证结果显示,GTWR模型能准确识别流感高发地区,将该方法与搜索引擎数据结合能较好地模拟流感空间分布,为空间流行病学的研究提供预测模型和统计解释。  相似文献   

12.
Abstract

Geographically weighted regression (GWR) is a local spatial statistical technique for exploring spatial nonstationarity. Previous approaches to mapping the results of GWR have primarily employed an equal step classification and sequential no-hue colour scheme for choropleth mapping of parameter estimates. This cartographic approach may hinder the exploration of spatial nonstationarity by inadequately illustrating the spatial distribution of the sign, magnitude, and significance of the influence of each explanatory variable on the dependent variable. Approaches for improving mapping of the results of GWR are illustrated using a case study analysis of population density–median home value relationships in Philadelphia, Pennsylvania, USA. These approaches employ data classification schemes informed by the (nonspatial) data distribution, diverging colour schemes, and bivariate choropleth mapping.  相似文献   

13.
邓悦  刘洋  刘纪平  徐胜华  罗安 《测绘通报》2018,(3):32-37,42
近年来,我国大部分地区屡遭洪涝与干旱两种自然灾害侵袭,对重洪涝干旱区域进行空间插值具有重要的意义。针对传统地理加权回归（GWR）模型建模过程中模型识别和参数估计易受观测值异常点影响的问题,本文提出了一种基于吉布斯采样的贝叶斯地理加权回归（GBGWR）方法。运用基于吉布斯采样的马尔可夫链蒙特卡罗贝叶斯方法,估计地理加权回归模型参数,通过平滑函数降低观测值中异常点位数据,最后对湖南省1985-2015年35个观测站点的降水观测数据进行了空间分布模拟。试验结果表明,本文提出的方法相较于GWR模型性能提高了19.8%,相较于BGWR模型性能提高了8.2%,该方法可以有效降低异常值和"弱数据"对回归结果的影响,能够更加真实地模拟湖南省降水量的空间分布。  相似文献   

14.
高精度降水场是水文、气象以及环境分析的重要数据支撑,直接影响相关服务的准确性。传统降水分布模拟大多依赖站点空间维的驱动因素,而忽略了降水时序变化特征对其空间分布的影响。使用2015—2017年中国湖北省83个国家气象观测站点和28个省级观测站点近3 a月平均累积降水资料,通过相关性分析,引入站点降水时序理论变差函数模型的拱高值(C)和块金值(C0)作为影响因素,使用地理加权回归(geographically weighted regression, GWR)建立湖北省月平均降水分布模型。结果表明:（1）各站点降水的时序变差函数曲线与降水的季节性基本吻合。站点时序理论变差函数模型中,有25.3%能够在4个月内达到平稳,36.14%在6个月内达到平稳。（2）站点降水时序理论变差函数模型的C和C0与逐年12月平均累积降水在0.01水平（双侧）上显著相关,平均相关系数分别为0.745和0.526,大于地理位置和高程对降水的影响。（3）引入C和C0 有助于提升GWR模型的整体拟合优度和插值精度。对比仅使用经纬度的GWR模型和引入时序理论变差函数特征的GWR模型,3 a平均整体拟合优度从0.852提升至0.912。验证集站点插值精度评价显示,3 a绝对误差、均方根误差和平均绝对百分误差下降幅度均大于60%。因此,引入时序理论变差函数特征的时空GWR模型能够获得较高精度的降水模拟结果,更适合具有丰富历史降水资料地区的降水空间分布估算。  相似文献   

15.
The realization in the statistical and geographical sciences that a relationship between an explanatory variable and a response variable in a linear regression model is not always constant across a study area has led to the development of regression models that allow for spatially varying coefficients. Two competing models of this type are geographically weighted regression (GWR) and Bayesian regression models with spatially varying coefficient processes (SVCP). In the application of these spatially varying coefficient models, marginal inference on the regression coefficient spatial processes is typically of primary interest. In light of this fact, there is a need to assess the validity of such marginal inferences, since these inferences may be misleading in the presence of explanatory variable collinearity. In this paper, we present the results of a simulation study designed to evaluate the sensitivity of the spatially varying coefficients in the competing models to various levels of collinearity. The simulation study results show that the Bayesian regression model produces more accurate inferences on the regression coefficients than does GWR. In addition, the Bayesian regression model is overall fairly robust in terms of marginal coefficient inference to moderate levels of collinearity, and degrades less substantially than GWR with strong collinearity.  相似文献   

16.
This paper describes the results of a geo-statistical analysis carried out at the provincial level in Southern Europe to model wildfire occurrence from socio-economic and demographic indicators together with land cover and agricultural statistics. We applied a classical ordinary least squares (OLS) linear regression together with a geographically weighted regression (GWR) to explain long-term wild-fire occurrence patterns (mean annual density of >1 ha fires). The explanatory power of the OLS model increased from 52% to 78% as a result of the non-constant relationships between fire occurrence and the underlying explanatory variables throughout the Mediterranean Basin. The global model we developed (i.e., OLS regression) was not sufficient to fully describe the underlying causal factors in wildfire occurrence modeling. Indeed, local approaches (i.e., GWR) can complement the global model in overcoming the problem of non-stationarity or missing variables. Our results confirm the importance of agrarian activities, land abandonment, and development processes as underlying factors of fire occurrence. The identification of regions with spatially varying relationships can contribute to the better understanding of the fire problem, especially over large geographic areas, while at the same time recognizing its local character. This can be very important for fire management and policy.  相似文献   

17.
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.  相似文献   

18.
In this paper, we compare and contrast a Bayesian spatially varying coefficient process (SVCP) model with a geographically weighted regression (GWR) model for the estimation of the potentially spatially varying regression effects of alcohol outlets and illegal drug activity on violent crime in Houston, Texas. In addition, we focus on the inherent coefficient shrinkage properties of the Bayesian SVCP model as a way to address increased coefficient variance that follows from collinearity in GWR models. We outline the advantages of the Bayesian model in terms of reducing inflated coefficient variance, enhanced model flexibility, and more formal measuring of model uncertainty for prediction. We find spatially varying effects for alcohol outlets and drug violations, but the amount of variation depends on the type of model used. For the Bayesian model, this variation is controllable through the amount of prior influence placed on the variance of the coefficients. For example, the spatial pattern of coefficients is similar for the GWR and Bayesian models when a relatively large prior variance is used in the Bayesian model.   相似文献   

19.
地理加权回归是常用的空间分析方法,已广泛应用于各个领域,但利用此方法进行回归分析前,往往忽略了对设计矩阵进行局部多重共线性的诊断,从而导致对模型的估计不准确。因此,本文在引入了全局模型的多重共线性诊断方法的基础上,对这些方法进行了改进,改进后构建了加权方差膨胀因子法和加权条件指标方法——分解比法,用于诊断地理加权回归模型设计矩阵的多重共线性问题。实验结果表明,多重共线性不存在于全局模型,而可能存在于局部模型中,构建的两种方法能够有效地诊断地理加权回归模型的多重共线性问题,且加权条件指标方法——分解比法比加权方差膨胀因子法在诊断多重共线性问题上更有优势。  相似文献   

20.
地理加权回归分析是对普通线性回归模型的扩展,将空间数据的地理位置嵌入线性回归参数之中,以此来研究空间关系的空间异质性或空间非平稳性,属于局部空间分析模型.通过地理加权回归分析可以确定两种或两种以上变量间相互依赖的定量关系,局部区域的参数估计可以得到地理空间存在的不同空间关系,核函数的选取规则和带宽参数的验证方法也是本文研究的内容.  相似文献   

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