基于GWR模型的北极滨海平原融冻湖表面温度空间分布模拟

通过分析北极滨海平原融冻湖泊形态和空间特征与湖泊表面温度之间的相关性,选取湖泊面积、形态紧凑系数、平均深度、与楚科齐海岸线距离,与波弗特海岸线距离、纬度等6个影响因素为参数,分别利用普通最小二乘线性回归(OLS)法和地理加权回归(GWR)法构建湖泊表面温度的空间分布模型,并采用主成分分析法消除变量共线性以降低模型估计误差方差。研究结果表明,与OLS模型相比,GWR模型显著提高了模型拟合度(确定系数R~2由0.648增至0.752)和精度(平均绝对误差从0.47K降至0.38K;均方根误差从0.62K降至0.44K),能更好地模拟融冻湖泊表面温度的空间分布,可为极地地区区域性气候变化的研究提供更为可靠的多因素预测模型和统计解释。     

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%。     

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。     

基于空间回归模型的道路交通事故影响因子分析

为分析影响交通事故的主要道路影响因子,选取道路结构、道路附属设施、交通基础设施等方面的16个解释变量,考虑交通事故分布的过度分散性、零膨胀性及空间相关性,构建空间滞后-零膨胀负二项回归模型,并利用赤池信息准则（Akaike information criterion,AIC）和贝叶斯信息准则（Bayesian information criterion,BIC）、模型残差的空间依赖性检验等指标将其与常用的普通最小二乘（ordinary least square,OLS）等回归模型进行对比。结果显示,所提模型的拟合效果最优;车道数、道路宽度、平均车速等因子对交通事故的发生具有显著影响。     

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。     

犯罪案件时空分布模型研究

以社区犯罪案件为主要对象,研究马鞍山市犯罪案件的空间分布特征。结合数据挖掘技术、GIS技术与数学建模,根据犯罪心理学和刑侦学相关理论,建立OLR、GWR和GTWR 3种犯罪地理目标模型,对犯罪活动进行模型拟合。通过对比研究发现,GTWR模型考虑了案件的时间与空间特征,相较于最小二乘回归与地理加权回归在时空平稳性、均方根误差、平均绝对误差、平均绝对百分误差和模型拟合精度都得到了较好的效果。     

南昌市二手房价格影响因子的空间异质性

以安居客网站爬取的2018年10月894个南昌市住宅小区二手房价格为研究对象,利用地理加权回归模型探讨了建筑特征、邻里特征、区位特征等方面各影响因子对住宅价格的作用差异.研究结果表明:1)地理加权回归(GWR)模型的拟合结果优于OLS模型,将回归系数结果空间可视化发现南昌市二手房价格影响因子具有空间异质性.2)不同因子...     

利用主成分分析法及地理加权回归模型分析AOD数据

针对采用地理加权回归模型（GWR）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地理加权回归方法（PCA-GWR）。首先,该方法检验了气溶胶光学厚度（AOD）影响因素之间的共线性;然后,通过非线性主成分分析法（NLPCA）对影响AOD值的若干相关变量进行处理,既消除了相关变量彼此之间的多重共线性,又可以起到降维的作用;最后,利用非线性主成分分析得到较少的几个综合指标,通过地理加权回归模型对AOD值进行分析预测。为验证该方法的有效性,采用京津冀地区的AOD、高程、风速、气温、湿度、气压、坡度、坡向数据,利用Pearson相关系数法选取与AOD浓度具有较高相关性的影响因素作为常规的GWR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。研究结果表明：应用非线性主成分分析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,且该方法所得的MAE、RMSE、AIC及其拟合优度R²均优于常规的GWR模型。     

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。     

顾及空间异质性的自回归模型应用研究

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。     

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.     

Do Factors Causing Wildfires Vary in Space? Evidence from Geographically Weighted Regression

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.     

Using Landsat Imagery and Census Data for Urban Population Density Modeling in Port-au-Prince,Haiti

This research uses the most recent (2003) census data and a Landsat ETM+ image to build a population estimation model for Port-au-Prince, Haiti. The purpose of the study is to establish the linkage of population density with remotely sensed surface reflectance signals of an urban area, and use that to estimate population when census data are not available in a timely fashion. The research begins with deriving subpixel vegetation-impervious surface-soil (VIS) fractions derived from the Landsat ETM+ multispectral bands, and then uses the geographically weighted regression (GWR) model to examine how the variation of population density can be explained by the VIS variables and their derivatives. With comparison to the ordinary least square (OLS) model, the GWR model accounts for spatial non-stationarity in the relationship between population patterns and land characteristics in the study area. The study reveals that three VIS variables are significant in explaining population density: the mean value of houses fraction image, the mean value of vegetation fraction image, and the standard deviation of vegetation fraction image.     

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.     

Exploring the Impact of Non-normality on Spatial Non-stationarity in Geographically Weighted Regression Analyses: Tobacco Outlet Density in New Jersey

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.     

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.     

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.     

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.     

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     

Using Contextualized Geographically Weighted Regression to Model the Spatial Heterogeneity of Land Prices in Beijing,China

Geographically Weighted Regression (GWR) is a method of spatial statistical analysis allowing the modeled relationship between a response variable and a set of covariates to vary geographically across a study region. Its use of geographical weighting arises from the expectation that observations close together by distance are likely to share similar characteristics. In practice, however, two points can be geographically close but socially distant because the contexts (or neighborhoods) within which they are situated are not alike. Drawing on a previous study of geographically and temporally weighted regression, in this article we develop what we describe as contextualized Geographically Weighted Regression (CGWR), applying it to the field of hedonic house price modeling to examine spatial heterogeneity in the land parcel prices of Beijing, China. Contextual variables are incorporated into the analysis by adjusting the geographical weights matrix to measure proximity not only by distance but also with respect to an attribute space defined by measures of each observation's neighborhood. Comparing CGWR with GWR suggests that adding the contextual information improves the model fit.