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1.
Geographically weighted regression (GWR) extends the familiar regression framework by estimating a set of parameters for any number of locations within a study area, rather than producing a single parameter estimate for each relationship specified in the model. Recent literature has suggested that GWR is highly susceptible to the effects of multicollinearity between explanatory variables and has proposed a series of local measures of multicollinearity as an indicator of potential problems. In this paper, we employ a controlled simulation to demonstrate that GWR is in fact very robust to the effects of multicollinearity. Consequently, the contention that GWR is highly susceptible to multicollinearity issues needs rethinking.  相似文献   

2.
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   

3.
Local regression methods such as geographically weighted regression (GWR) can provide specific information about individual locations (or places) in spatial analysis that is useful for mapping nonstationary covariate relationships. However, the distance-based weighting schemes used in GWR are only adaptable for spatial objects that are point or area features. In particular, spatial object-pairs pose a challenge for local analysis because they have a linear dimensionality rather than a point dimensionality. This paper proposes using an alternative local regression model – quantile regression (QR) – for investigating the stationarity of regression parameters with respect to these linear features as well as facilitating the visualization of the results. An empirical example of a gravity model analysis of trade patterns within Europe is used to illustrate the utility of the proposed method.  相似文献   

4.
混合地理加权回归模型算法研究   总被引：1，自引：0，他引：1  
以迭代算法为基础，推导出混合地理加权回归模型的常系数（全局参数）和变系数（局域参数）的计算方法，并以上海市住宅小区楼盘销售平均价格为例进行验证。结果表明，混合地理加权回归模型的计算量略大于地理加权回归模型，但对样本数据的拟合更好，局域参数估计更稳健。  相似文献   

5.
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   

6.
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   

7.
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   

8.
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   

9.
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   

10.
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   

11.
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   

12.
 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   

13.
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   

14.
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   

15.
The goal of this study was to evaluate whether harmonic regression coefficients derived using all available cloud-free observations in a given Landsat pixel for a three-year period can be used to estimate tree canopy cover (TCC), and whether models developed using harmonic regression coefficients as predictor variables are better than models developed using median composite predictor variables, the previous operational standard for the National Land Cover Database (NLCD). The two study areas in the conterminous USA were as follows: West (Oregon), bounded by Landsat Worldwide Reference System 2 (WRS-2) paths/rows 43/30, 44/30, and 45/30; and South (Georgia/South Carolina), bounded by WRS-2 paths/rows 16/37, 17/37, and 18/37. Plot-specific tree canopy cover (the response variable) was collected by experienced interpreters using a dot grid overlaid on 1 m spatial resolution National Agricultural Imagery Program (NAIP) images at two different times per region, circa 2010 and circa 2014. Random forest model comparisons (using 500 independent model runs for each comparison) revealed the following (1) harmonic regression coefficients (one harmonic) are better predictors for every time/region of TCC than median composite focal means and standard deviations (across times/regions, mean increase in pseudo R2 of 6.7% and mean decrease in RMSE of 1.7% TCC) and (2) harmonic regression coefficients (one harmonic, from NDVI, SWIR1, and SWIR2), when added to the full suite of median composite and terrain variables used for the NLCD 2011 product, improve the quality of TCC models for every time/region (mean increase in pseudo R2 of 3.6% and mean decrease in RMSE of 1.0% TCC). The harmonic regression NDVI constant was always one of the top four most important predictors across times/regions, and is more correlated with TCC than the NDVI median composite focal mean. Eigen analysis revealed that there is little to no additional information in the full suite of predictor variables (47 bands) when compared to the harmonic regression coefficients alone (using NDVI, SWIR1, and SWIR2; 9 bands), a finding echoed by both model fit statistics and the resulting maps. We conclude that harmonic regression coefficients derived from Landsat (or, by extension, other comparable earth resource satellite data) can be used to map TCC, either alone or in combination with other TCC-related variables.  相似文献   

16.
This study deals with the issue of extreme coefficients in geographically weighted regression (GWR) and their effects on mapping coefficients using three datasets with different spatial resolutions. We found that although GWR yields extreme coefficients regardless of the resolution of the dataset or types of kernel function: (1) GWR tends to generate extreme coefficients for less spatially dense datasets; (2) coefficient maps based on polygon data representing aggregated areal units are more sensitive to extreme coefficients; and (3) coefficient maps using bandwidths generated by a fixed calibration procedure are more vulnerable to the extreme coefficients than adaptive calibration.  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.
The rapid growth of megacities requires special attention among urban planners worldwide, and particularly in Mumbai, India, where growth is very pronounced. To cope with the planning challenges this will bring, developing a retrospective understanding of urban land-use dynamics and the underlying driving-forces behind urban growth is a key prerequisite. This research uses regression-based land-use change models – and in particular non-spatial logistic regression models (LR) and auto-logistic regression models (ALR) – for the Mumbai region over the period 1973–2010, in order to determine the drivers behind spatiotemporal urban expansion. Both global models are complemented by a local, spatial model, the so-called geographically weighted logistic regression (GWLR) model, one that explicitly permits variations in driving-forces across space. The study comes to two main conclusions. First, both global models suggest similar driving-forces behind urban growth over time, revealing that LRs and ALRs result in estimated coefficients with comparable magnitudes. Second, all the local coefficients show distinctive temporal and spatial variations. It is therefore concluded that GWLR aids our understanding of urban growth processes, and so can assist context-related planning and policymaking activities when seeking to secure a sustainable urban future.  相似文献   

19.
Geographically weighted regression (GWR) is a popular technique to deal with spatially varying relationships between a response variable and predictors. Problems, however, have been pointed out (see Wheeler and Tiefelsdorf in J Geogr Syst 7(2):161–187, 2005), which appear to be related to locally poor designs, with severe impact on the estimation of coefficients. Different remedies have been proposed. We propose two regularization methods. The first one is generalized ridge regression, which can also be seen as an empirical Bayes method. We show that it can be implemented using ordinary GWR software with an appropriate choice of the weights. The second one augments the local sample as needed while running GWR. We illustrate both methods along with ordinary GWR on an example of housing prices in the city of Bilbao (Spain) and using simulations.  相似文献   

20.
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   

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