北京PM2.5浓度空间分布的贝叶斯地理加权回归模拟北大核心CSCD

针对地理加权回归(GWR)模型无法克服小样本数据下异常值影响的问题,该文利用贝叶斯地理加权回归(BGWR)模型对北京地区2016年10月1日至12月29日长达90d的PM2.5监测数据进行了浓度模拟。该方法通过加入贝叶斯先验信息,选取不同的平滑函数,在局部空间样本稀少的情况下,有效降低了异常值和"弱数据"对回归结果的影响,更加真实地反映了PM2.5浓度空间分布。实验结果表明,基于不同平滑函数的3种BGWR模型校正决定系数分别达到了0.799、0.801和0.867。平均比GWR模型提升了28%,比OLS模型提升了32%,证实了BGWR模型在模拟PM2.5浓度分布时具有更好的适用性。     

稳健度量选权迭代的地理加权回归研究

针对地理加权回归参数估计采用最小二乘方法,最小二乘估计易受离群值影响,导致地理加权回归模型并不稳健的问题,该文提出基于稳健度量选权迭代的地理加权回归分析方法,核心思想是通过标准化残差构造权重函数,通过迭代加权降低离群值对回归模型参数估计的影响。利用模拟数据与真实数据进行试验,分别与GWR、RGWR进行对比分析,以MSE、MAE为指标进行性能评价。模拟数据试验中,RMIWGWR模型比RGWR模型的MSE、MAE指标分别提升9.29%和8.34%;真实数据试验中,RMIWGWR模型比RGWR模型的MSE、MAE指标分别提升63.88%和38.45%。试验表明:该方法可改善粗差存在环境下地理加权回归模型参数估计精度,提升模型拟合效果。     

基于IGGⅢ的地理加权回归模型研究

针对离群值存在时地理加权回归模型拟合效果较差的问题,本文提出了基于IGGⅢ的地理加权回归方法。核心是采用IGGⅢ方案中的权函数计算权重矩阵,将权因子用于地理加权回归参数估计模型。利用模拟数据和真实数据与GWR、ACV-GWR进行对比试验,以MSE、MAE和R²作为指标对结果进行评价。模拟试验结果显示,IGGⅢ-GWR比GWR性能分别提升了51.14%、23.77%、28.4%,比ACV-GWR分别提升了49.96%、22.57%、27.1%;真实试验结果显示,IGGⅢ-GWR比GWR性能分别提升了12.65%、7.44%、0.37%,比ACV-GWR分别提升了11.85%、6.96%、0.34%。试验结果表明,基于IGGⅢ的地理加权回归可提高模型的抗差能力,拟合效果更好。     

一种基于半监督学习的地理加权回归方法

地理加权回归方法在小样本数据下回归分析精度往往不高。半监督学习是一种利用未标记样本参与训练的机器学习方法,可以有效地提升少量有标记样本的学习性能。基于此本文提出了一种基于半监督学习的地理加权回归方法,其核心思想是利用有标记样本建立回归模型来训练未标记样本,再选择置信度高的结果扩充有标记样本,不断训练,以提高回归性能。本文采用模拟数据和真实数据进行试验,以均方误差提升百分比作为性能评价指标,将SSLGWR与GWR、COREG对比分析。模拟数据试验中,SSLGWR在3种不同配置下性能分别提升了39.66%、11.92%和0.94%。真实数据试验中,SSLGWR在3种不同配置下性能分别提升了8.94%、3.36%和5.87%。SSLGWR结果均显著优于GWR和COGWR。试验证明,半监督学习方法能利用未标记数据提升地理加权回归模型的性能,特别是在有标记样本数量较少时作用显著。     

利用搜索引擎数据模拟疾病空间分布

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。     

一种基于CUDA的大数据量地理加权回归并行加速算法

针对传统地理加权回归（GWR）在大数据量计算中存在的计算效率低、内存占用大、数据规模受限等问题,本文提出了快速并行地理加权回归（FPGWR）算法,基于英伟达CUDA架构实现了GWR的并行加速,将串行过程分解为并行的独立回归计算模块,同时优化了内存使用模型,提高了算法的运行速度。对比FPGWR和传统GWR在不同数量级模拟数据上和真实数据上的运行速度,结果显示,FPGWR能够支持更大规模的样本量计算并有效提升运行效率,数据量越大加速效果越显著。     

顾及PWV的中南4省1区春节期间PM2.5浓度估算

社会经济的发展伴随而来的环境污染问题日渐得到人们的重视.针对中南地区4省1区(河南省、湖北省、湖南省、广东省和广西壮族自治区)春节期间PM2.5的变化情况,结合该区域所属及其相邻探空站获取的大气可降水量PWV数据以及气象监测站获取的风速数据,通过反距离加权插值得到中南4省1区春节期间的PWV和风速值,综合考虑CO、SO2、O3和NO2等大气污染物以及PWV、风速和DEM高程值建立该地区春节期间的地理加权回归(GWR)、地理加权回归克里金(GWRK)以及地理加权回归规则样条(GWRCRS)插值模型,并运用3种模型对中南地区4省1区2017、2018年春节假期期间进行PM2.5浓度估算.研究结果显示,GWRK和GWRCRS模型的估算效果较GWR模型更优,而GWRCRS模型估算精度最高,对中南地区4省1区春节期间的PM2.5监测预警具有一定的实用性参考价值.     

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。     

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。     

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。     

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.     

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。     

Comparing spatially varying coefficient models: a case study examining violent crime rates and their relationships to alcohol outlets and illegal drug arrests

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.      

时序变差函数特征驱动下的月平均降水空间分布模拟

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。     

An assessment of coefficient accuracy in linear regression models with spatially varying coefficients

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.     

顾及空间非平稳特征的遥感干旱监测

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。     

Comparison of Geographically Weighted Regression and Regression Kriging for Estimating the Spatial Distribution of Soil Organic Matter

Soil organic matter (SOM) is an important component of soils, and knowing the spatial distribution and variation of SOM is the premise for sustainably utilizing soils. The objective of this study was to compare geographically weighted regression (GWR) with regression kriging (RK) for estimating the spatial distribution of SOM using field-sample data in SOM and auxiliary data in correlated environmental variables (e.g., elevation, slope, ferrous minerals index, and Normalized Difference Vegetation Index). Results showed that GWR was a relatively better method and could provide promising results for SOM prediction in comparison with RK. The map interpolated by GWR showed similar spatial patterns influenced by environmental variables and the nonapparent effect of data outliers, but with higher accuracies, compared to that interpolated by RK.     

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.