一种基于主成分分析的时空地理加权回归方法

针对时空地理加权回归模型(GTWR)进行预测时,输入变量较多导致计算复杂度高,而输入变量较少引起预测精度降低这一问题,提出了一种基于主成分分析的时空地理加权回归方法(PCA-GTWR)。该方法采用非线性主成分分析方法,先对影响PM2.5浓度的若干相关变量降维处理得到几个综合指标,并将其作为GTWR模型的输入变量进行预测。为验证该方法的有效性,采用北京市2014-04—2017-03的PM2.5数据,利用Pearson相关系数法选取与PM2.5浓度具有较高相关性的影响因素作为常规的GTWR模型的输入变量,在变量个数相同的前提下,与本文方法进行对比。结果表明应用非线性主成分分析方法对相关变量进行预处理后,有效地解决了变量之间的共线性,保留了原始影响因素主要信息,提高了运算效率,且该方法的MAE、RMSE、AIC均低于常规的GTWR模型,拟合优度GF最高达到88.11%。     

一种协同时空地理加权回归PM2.5浓度估算方法

针对PM2.5浓度估算中时空特征考虑不足和样本量较少的问题,该文将协同训练和时空地理加权回归相结合,提出了协同时空地理加权回归。采用两个不同参数的时空地理加权回归模型作为回归器,利用一个回归器训练另一个回归器的未标注样本,选择最优结果作为标注样本加入标注样本,通过不断学习扩大标注样本量提升模型的回归性能。以京津冀地区2015年3-7月的PM2.5浓度数据为实验数据,利用气溶胶光学厚度产品、温度、风速和相对湿度进行建模,采用不同核函数的时空地理加权回归作为对比方法进行实验。结果显示,协同时空地理加权回归性能比基于Gauss核函数时空地理加权回归提升了10%,比基于bi-square核函数时空地理加权回归提升了6.25%,证明该文方法能够提升时空样本数量不足时的PM2.5浓度估算精度。     

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。     

混合地理加权回归模型算法研究

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。     

逐步回归的时空地理加权变量选取方法

针对当前建立时空地理加权回归模型采用一般的变量选择方法不考虑时间和空间因素的问题,该文提出一种基于逐步回归的时空地理加权变量选取方法。通过引入Akaike信息法则为变量的取舍准则,基于逐步回归,利用陕甘宁地区影响人口分布的变量与人口分布关系进行实际性能的实验验证。实验结果表明:该方法优于传统逐步回归法、向前引入法和向后剔除法。     

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。     

贪心算法的地理加权回归特征变量选择方法

针对建立地理加权回归(GWR)模型时,无法直接应用普通线性回归(OLR)常用的特征变量选择方法,且计算过程较复杂的问题,该文基于贪心算法原理,通过引入Akaike信息法则,设计了适用于GWR的特征变量选择方法:逐个引入或删除特征变量,判断该变量对模型置信水平影响程度,根据评价准则决定该变量的取舍,最终实现模型外没有关系强的变量、模型内没有关系弱的变量。实验结果表明,比较基于OLR的逐步回归、向前引入法和向后删除法3种方法选择变量建立模型,向前引入法优于向后剔除法,两者都优于基于OLR的逐步回归法,更适用于GWR分析。     

SuperMap GIS地理加权回归模型研究与实现

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.     

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。     

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.     

Geographically weighted regression and multicollinearity: dispelling the myth

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.     

Geographically weighted regression with the integration of machine learning for spatial prediction

Journal of Geographical Systems - Conventional methods of machine learning have been widely used to generate spatial prediction models because such methods can adaptively learn the mapping...     

多尺度GTWR城市住宅价格建模与分析

尺度、时间、空间距离一直是制约地理时空加权回归模型求解精度的关键.本文基于欧氏距离约束和路网距离约束,将多尺度扩展到时空地理加权回归方法的建模中,以检验多尺度GTWR模型的改进性能,同时验证路网距离约束在多尺度GTWR模型中的优越性.以2015—2018年成都市主城区商品房社区作为案例对象,将多尺度GTWR与GTWR在拟合优度(R2)、残差平方和(RSS)及AIC等方面进行比较.试验结果表明,与GTWR相比,多尺度GTWR对影响住宅价格的自变量提供了更有效的解释,同时路网距离的使用也提高了模型的合理性.在基于欧氏距离约束和路网距离约束方面拟合优度分别提升了0.123和0.208,RSS和AIC值得到了有效的降低.相比于使用欧氏距离约束的GTWR与多尺度GTWR模型,路网距离约束的GTWR(RD)模型的拟合优度提高了0.007,多尺度GTWR(RD)模型的拟合优度提高了0.092,基于路网距离的计算结果进一步证实了多尺度GTWR模型的正确性,也进一步证明了综合考虑尺度、时空距离后的多尺度GTWR具有很好的通用性.     

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.     

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.     

非线性约束下的超短基线模糊度搜索方法

针对超短基线的模糊度固定问题,该文提出了一种改进方法。该方法在长基线非线性约束模型的基础上,采用附加基线长度约束的模糊度搜索模型,该搜索满足基线长度的搜索函数最优解。实验结果表明,该文的算法与无基线约束模型、基线长线性约束模型的LAMBDA方法相比,模糊度成功率明显提高。     

Geographically weighted regression‐based determinants of malaria incidences in northern China

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.