一种局部多项式时空地理加权回归方法

基于加权最小二乘估计的时空地理加权回归方法,在随机项方差相同且最小的假设条件下估计回归参数和拟合值,由于没有考虑时空分析中异方差影响而导致估计结果存在一定偏差。局部多项式估计是一种消除异方差影响的非参数估计方法。本文在局部多项式估计原理基础上,提出了局部多项式时空地理加权回归方法。它是采用三元一阶泰勒级数展开式重构时空回归系数和自变量矩阵,进而建立满足高斯-马尔可夫独立同分布假定要求的新模型,利用新模型回归系数估计值、拟合值以及新模型与原模型的关系,可得到原模型回归系数估计值和拟合值。本文采用模拟数据和真实数据进行试验,以GTWR与局部线性地理加权回归作为对比方法,从方法适用性、整体估计效果、回归系数估计偏差和拟合优度、整体估计偏差等方面分析了LPGTWR方法性能,有效证明了LPGTWR方法能消除异方差影响提升估计精度。     

地理加权回归建模结果不确定性度量与约束方法EI北大核心CSCD

作为一种经典局部加权最小二乘方法,地理加权回归建模一直受样本空间稀疏及预测变量局部共线性等因素困扰,导致建模结果不确定性呈现空间异质。通过协方差传播定律构建后验标准差精度评价指标,本文提出了一种地理加权回归建模结果不确定性度量与约束方法,并基于地表PM 2.5浓度遥感制图实例开展了验证。试验结果表明:不确定性约束后,不同参数下地理加权回归模型的拟合精度、基于样本/站点/区域的十折交叉验证精度均有改善;局部共线性导致的模型回归系数符号偏差问题得到了改正;模型预测结果奇异值及负值能被有效甄别,有效提升了地表PM 2.5浓度制图结果的可靠性。该不确定性度量与约束方法可有效保证地理加权回归模型估算结果的稳定性和有效性。     

地理加权回归模型的多重共线性诊断方法

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。     

地理加权回归分析技术综述

空间数据关系中的异质性或非平稳性特征是近期空间统计或相关应用领域的研究热点之一,而局部空间统计分析技术的提出与发展是其关键环节。地理加权回归分析技术(geographically weighted regression,GWR)通过关于位置的局部加权回归分析模型求解,以随着空间位置不同而变化的参数估计结果,量化反映空间数据关系中的异质性或非平稳性特征。GWR技术已在众多领域内广泛应用,逐渐成为重要的空间关系异质性建模工具之一。针对GWR模型解算、结果解读、模型检验等基础技术环节进行了系统总结,分别分析回顾了其对应的相关研究进展以及应用过程中存在的问题。同时,系统梳理了近年来GWR技术的主要拓展与延伸,重点阐述了其在采用灵活的距离度量选择、参数的多尺度估计以及时空数据建模方面的GWR技术扩展研究。此外,还简要介绍了现有的主要GWR技术软件工具,以期为读者和用户提供相对全面的GWR技术信息参考与知识总结。     

地理加权回归的城市道路时空运行态势空间网格计算方法

随着城市化加速发展,交通拥堵已成为全球大城市面临的共同难题。高效、准确地分析与发现交通状态与影响因素的空间变化关系是优化道路交通要素配置的重要基础。提出了城市道路交通空间地理加权（road grid geographically weighted regression,RG-GWR）模型,首先以两种尺寸网格嵌套的九宫格计算区域路网承载力比率,识别出路网配置不均衡区域;然后结合实况交通态势,以地理加权回归模型计算单元网格的交通时空运行态势影响异质性参数及其回归关系,得到基于网格的邻近区域路网交通要素配置配比,实现以九宫格为单元的路网要素优化配置。以成都市核心区为例,构建了3种尺寸的空间网格,形成多级叠加的九宫格模型,计算提取了两种级别九宫格模型区域承载力参数,结果与高德实际路况匹配度分别达到62.5%与87.5%;RG-GWR模型在不同时段交通态势拟合度达到80%以上。结果表明,从空间角度分析道路交通均衡配置高效、可行,具有服务于智能化平台的广阔前景。     

GBGWR模型在降水量空间分布模拟中的应用

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。     

局部加权线性回归模型的PM2.5空间插值方法

针对传统空间插值方法对影响PM2.5的插值因素考虑不全面和局部加权线性回归模型中近邻个数选择困难等问题,该文基于局部加权线性回归模型提出了一种引入正则化项的空间插值方法。以北京市3个月的PM2.5数据为例,选取SO_2、NO_2、O_3、CO作为观测指标,通过正则化进行权重系数修正、L曲线法确定正则化系数,提高了该插值模型的稳定性与自适应性。交叉验证结果显示,本文方法相对于普通Kriging,3个月的平均绝对误差(MAE)与均方根误差(RMSE)分别降低28.44%、26.25%;相对于反距离加权插值法的MAE、RMSE分别降低18.07%、17.02%。研究结果表明,基于局部加权线性回归模型的PM2.5空间插值相对于传统方法有一定提升。     

GF-6影像下的南方路域针叶植被LAI反演研究

为了更好应用国产高分辨率遥感影像监测评价南方路域植被环境,研究南方路域针叶植被叶面积指数遥感反演.该文以长益高速研究区域的高分六号影像(GF-6)为基础,提出了可适用于针叶叶片的LIBERTY+ SAIL耦合模型并结合多元线性回归、局部加权回归反演路域植被针叶LAI的方法.研究中以耦合模型模拟的冠层光谱反射率、GF-6影像和野外实测生化参数为数据源,通过相关性分析,将与LAI相关性较高的SAVI、RVI和EVI 3种植被指数作为反演因子,结合组合模型反演LAI并评定模型的反演精度.结果 表明,耦合模型对南方路域针叶植被LAI的估算精度整体较高,对比分析两种叶面积指数的组合预测模型,耦合模型结合局部加权回归组合反演LAI具有优越性,可更好地反演路域植被针叶LAI.     

顾及空间异质性的自回归模型应用研究北大核心CSCD

针对传统的空间自回归模型拟合精度较低且无法顾及空间异质性的问题,该文提出了改进的地理加权自回归模型。并以北京市住宅小区特征价格数据为例,利用探索式空间数据分析方法分析住宅价格数据的空间自相关性,探讨其时空演变特征;建立了空间自回归模型、地理加权回归模型和地理加权自回归模型,并在模型之间进行精度对比和分析。实验结果表明:北京市住宅价格具有明显的空间相关性与空间集聚特征;由于综合考虑了空间自相关性和空间异质性,地理加权自回归模型不仅能大幅度提高模型的拟合优度和解释能力,还能更好地揭示住宅价格的空间变化规律,为数据的空间探索提供了新的方向。     

市域尺度货物运输碳排放时空变化及因素分析

针对货物运输导致碳排放成为温室气体主要来源之一的问题,该文综合货物运输车辆的微观温室气体排放及时空变化,从市域尺度分析货物运输碳排放的时空变化规律。利用微观排放模型计算了2000年、2005年、2010年和2015年全国286个城市货物运输碳排放的空间分布及其变化,并应用地理加权回归模型探究城市化不同层面因素对碳排放时空分布变化的影响。结果表明:货物运输碳排放具有显著的空间集聚特征,且高排放地区的集聚规律更加显著;地理加权回归模型精度明显高于普通线性回归模型,经济变量、人口变量、货运强度变量与货物运输碳排放存在显著正相关关系。该研究可为中国各市级区域制订节能减排政策提供量化的科学依据。     

Mapping local regression for spatial object-pairs

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.     

Modeling Urban Growth Using GIS and Remote Sensing

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.     

中国区域加权平均温度的时空分析及模型研究

加权平均温度(T_m)是全球卫星导航系统技术反演大气可降水量的关键参数,影响着水汽反演的精度。针对传统的Bevis模型运用在中国区域精度不高的问题,该文提出新的增加时空参数的T_m多元线性回归模型。根据2013—2015年中国86个探空站点的探空资料,分析了T_m的时空特征;然后根据2013年站点资料,利用线性回归建模方法建立了中国区域的T_m单因子回归模型和增加了时空参数的T_m多因子回归模型,并利用2014—2015年的探空数据进行验证。T_m单因子回归模型和T_m多因子回归模型的精度分别为3.1 K和2.6 K,比Bevis模型(精度3.3 K)分别提高了约6.0%和21.2%。考虑到季节对T_m的影响,将T_m多因子回归模型按季节分段,得到按季节分段的T_m多因子回归模型,其精度与T_m多因子回归模型大致相当,但能更细致表达出不同季节T_m的精度情况。结果表明增加了时空参数的T_m多因子回归模型更加适合中国区域的加权平均温度T_m的计算。     

Geographically weighted elastic net logistic regression

This paper develops a localized approach to elastic net logistic regression, extending previous research describing a localized elastic net as an extension to a localized ridge regression or a localized lasso. All such models have the objective to capture data relationships that vary across space. Geographically weighted elastic net logistic regression is first evaluated through a simulation experiment and shown to provide a robust approach for local model selection and alleviating local collinearity, before application to two case studies: county-level voting patterns in the 2016 USA presidential election, examining the spatial structure of socio-economic factors associated with voting for Trump, and a species presence–absence data set linked to explanatory environmental and climatic factors at gridded locations covering mainland USA. The approach is compared with other logistic regressions. It improves prediction for the election case study only which exhibits much greater spatial heterogeneity in the binary response than the species case study. Model comparisons show that standard geographically weighted logistic regression over-estimated relationship non-stationarity because it fails to adequately deal with collinearity and model selection. Results are discussed in the context of predictor variable collinearity and selection and the heterogeneities that were observed. Ongoing work is investigating locally derived elastic net parameters.     

Analysing regional industrialisation in Jiangsu province using geographically weighted regression

 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     

Multicollinearity and correlation among local regression coefficients in geographically weighted regression

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.     

地形因子与小微地震相关度的空间异质性分析

针对传统最小二乘回归未能顾及数据的空间特性,且无法度量模型自变量与因变量相关性的空间变异特性的问题,本文提出利用地理加权回归方法分析小微地震频次与地形因子相关度的空间异质性。以四川地区的地震监测资料、DEM为实验数据,选取地形复杂度、坡度变率、坡向变率和地面曲率为自变量,地震发生频次为因变量,构建地理加权回归模型,并进行回归系数的空间变异分析。实验分析发现,地震频次与地形因子具有一定的相关性:地形复杂度与地震频次相关性最强;坡度变率、沟壑密度、剖面曲率与地震频次的相关性依次减弱;不同空间位置的地形因子和地震频次的相关性具有较明显的空间异质性。实验结果表明,地理加权回归可以有效地度量分析地震频次与地形因子相关度的空间异质性,研究结果可为地震及次生灾害的分析与预报提供辅助决策参考。     

Examining the influences of air quality in China's cities using multi‐scale geographically weighted regression

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.