A comment on geographically weighted regression with parameter-specific distance metrics

A recent paper in this journal proposed a form of geographically weighted regression (GWR) that is termed parameter-specific distance metric geographically weighted regression (PSDM GWR). The central focus of the PSDM generalization of the GWR framework is that it allows the kernel function that weights nearby data to be specified with a distinct distance metric. As with the recent paper on Multiscale GWR (MGWR), the PSDM framework presents a form of GWR that also allows for parameter-specific bandwidths to be computed. As a result, a secondary focus of the PSDM GWR framework is to reduce the computational overhead associated with searching a massive parameter space to find a set of optimal parameter-specific bandwidths and parameter-specific distance metrics. In this comment, we discuss several concerns with the PSDM GWR framework in terms of model interpretability, complexity, and computational efficiency. We also recommend some best practices when using these models, suggest how to more holistically assess model variations, and set out an agenda to constructively focus future research endeavors.     

Geographically neural network weighted regression for the accurate estimation of spatial non-stationarity

ABSTRACT

Geographically weighted regression (GWR) is a classic and widely used approach to model spatial non-stationarity. However, the approach makes no precise expressions of its weighting kernels and is insufficient to estimate complex geographical processes. To resolve these problems, we proposed a geographically neural network weighted regression (GNNWR) model that combines ordinary least squares (OLS) and neural networks to estimate spatial non-stationarity based on a concept similar to GWR. Specifically, we designed a spatially weighted neural network (SWNN) to represent the nonstationary weight matrix in GNNWR and developed two case studies to examine the effectiveness of GNNWR. The first case used simulated datasets, and the second case, environmental observations from the coastal areas of Zhejiang. The results showed that GNNWR achieved better fitting accuracy and more adequate prediction than OLS and GWR. In addition, GNNWR is applicable to addressing spatial non-stationarity in various domains with complex geographical processes.     

邻避设施空间分布特征及其与周边住宅价格的关系——广州案例

随着中国城镇的快速发展以及市民环境意识的提高,由邻避设施引发的矛盾日益增多。合理规划邻避设施,是促进环境正义、推动社会和谐的重要课题。论文从“规划云平台”获取广州主城区邻避设施的地理信息数据,通过Python语句编码收集广州主城区小区平均房价数据,运用克里金插值法分析邻避设施的空间分布特征,构建多元线性回归模型和地理加权回归模型研究邻避设施与周边住宅价格的关系。研究发现,广州主城区邻避设施的布局与低收入住宅区的分布在空间上具有一致性,邻避设施主要分布在房价较低的住宅区周边;邻避设施对周边小区房价的影响与邻避设施的类型和所在区位相关,城市边缘区的邻避设施对房价造成了显著的负面影响,而城市中心良好的区位条件、基础设施与公共服务配套一定程度上抵消了邻避设施的负外部性;污名化类的邻避设施对房价的影响程度明显小于污染类、风险聚集类和心理不悦类邻避设施。本研究对有关城市邻避设施的科学规划布点具有一定的借鉴和指导意义。     

基于多光谱和地理加权回归模型的石嘴山城市土壤有机碳空间分布研究

城市土壤有机碳(SOC)分布受城市建设、工业发展等人为因素的影响表现出明显的空间差异。为揭示石嘴山市SOC受城市化、工业化等人类活动的影响,分别利用普通克里格法(OK)、多元线性回归克里格法(RK)、遥感反演方法(RS)和遥感-地理加权回归克里格法(RGWRK)预测石嘴山市SOC空间分布。结果表明:石嘴山市SOC含量在1.31～66.92 g·kg^-1之间变化,其平均值为17.61 g·kg^-1。石嘴山市不同功能区SOC含量存在显著差异(p<0.05),具体表现为工业区>医疗区>商业区>道路>住宅区>公园>农田>科教区;SOC含量变异系数为66.27%,呈中等程度变异;其最佳拟合模型为高斯模型,C₀/(C₀+C)为0.02,属于强空间自相关。SOC与遥感影像波段DN值的差值(B1-B7、B3-B7、B4-B7)和地形因子(高程、坡度、起伏度)之间存在着极显著的相关性(p<0.01);通过对4种方法的结果进行对比可知以各波段DN值差值与地形因子为输...     

Multiscale geographically and temporally weighted regression: exploring the spatiotemporal determinants of housing prices

Understanding scale effects is important and indispensable for geography studies. However, spatial and spatiotemporal statistical tools for measuring the operational scales of different processes are rather limited. This article extends the popular geographically and temporally weighted regression (GTWR) model to consider operational scale effects by proposing multiscale GTWR (MGTWR), which offers a flexible and scalable framework for identifying and analysing multiscale processes by specifying flexible bandwidths for various covariates. Then, MGTWR is employed to explore spatiotemporal variations and how influential factors are associated with housing prices in Shenzhen. This article attempts to extend GTWR to MGTWR in consideration of scale effects, thereby highlighting the importance of different levels of spatiotemporal heterogeneity. Furthermore, the empirical results of this study can provide valuable policy implications for real estate development in areas where urban planning should address multiscale effects in both temporal and spatial dimensions.     

基于空间扩展模型和地理加权回归模型的城市住房价格空间分异比较

鉴于已有研究主要集中探讨住房价格的空间依赖性,较少涉及空间异质性对住房特征价格的影响,也很少尝试构建不同计量模型来比较模型间刻画住房价格影响因素空间分异的准确性,以长沙市中心城区为研究区,采用空间扩展模型和地理加权回归模型比较分析城市住房价格影响因素的空间分异,结果表明：① 空间扩展模型和地理加权回归模型都表明,长沙市中心城区的住房属性边际价格随着区位的变化而变化,揭示住房价格影响因素具有显著的空间异质性;小区环境、交通条件、教育配套、生活设施等因素对住房价格的影响强度存在明显的空间分异。② 地理加权回归模型和空间扩展模型都能对传统特征价格模型进行改进,但地理加权回归模型在解释能力和精度方面都超过空间扩展模型;对属性系数估计空间模式的分析,地理加权回归模型形成的结果比采用坐标多义扩展的空间扩展模型更为复杂和直观。     

Application of geographically weighted regression model in the estimation of surface air temperature lapse rate

The surface air temperature lapse rate(SATLR)plays a key role in the hydrological,glacial and ecological modeling,the regional downscaling,and the reconstruction of high-resolution surface air temperature.However,how to accurately estimate the SATLR in the regions with complex terrain and climatic condition has been a great challenge for re-searchers.The geographically weighted regression(GWR)model was applied in this paper to estimate the SATLR in China's mainland,and then the assessment and validation for the GWR model were made.The spatial pattern of regression residuals which was identified by Moran's Index indicated that the GWR model was broadly reasonable for the estimation of SATLR.The small mean absolute error(MAE)in all months indicated that the GWR model had a strong predictive ability for the surface air temperature.The comparison with previous studies for the seasonal mean SATLR further evidenced the accuracy of the estimation.Therefore,the GWR method has potential application for estimating the SATLR in a large region with complex terrain and climatic condition.     

Spatial non-stationary characteristics between grass yield and its influencing factors in the Ningxia temperate grasslands based on a mixed geographically weighted regression model

Spatial models are effective in obtaining local details on grassland biomass, and their accuracy has important practical significance for the stable management of grasses and livestock. To this end, the present study utilized measured quadrat data of grass yield across different regions in the main growing season of temperate grasslands in Ningxia of China (August 2020), combined with hydrometeorology, elevation, net primary productivity (NPP), and other auxiliary data over the same period. Accordingly, non-stationary characteristics of the spatial scale, and the effects of influencing factors on grass yield were analyzed using a mixed geographically weighted regression (MGWR) model. The results showed that the model was suitable for correlation analysis. The spatial scale of ratio resident-area index (PRI) was the largest, followed by the digital elevation model, NPP, distance from gully, distance from river, average July rainfall, and daily temperature range; whereas the spatial scales of night light, distance from roads, and relative humidity (RH) were the most limited. All influencing factors maintained positive and negative effects on grass yield, save for the strictly negative effect of RH. The regression results revealed a multiscale differential spatial response regularity of different influencing factors on grass yield. Regression parameters revealed that the results of Ordinary least squares (OLS) (Adjusted R² = 0.642) and geographically weighted regression (GWR) (Adjusted R² = 0.797) models were worse than those of MGWR (Adjusted R² = 0.889) models. Based on the results of the RMSE and radius index, the simulation effect also was MGWR > GWR > OLS models. Ultimately, the MGWR model held the strongest prediction performance (R² = 0.8306). Spatially, the grass yield was high in the south and west, and low in the north and east of the study area. The results of this study provide a new technical support for rapid and accurate estimation of grassland yield to dynamically adjust grazing decision in the semi-arid loess hilly region.     

收缩城市住宅价格空间分异及影响机制——以鹤岗市为例

收缩城市的经济社会问题逐渐凸显,住宅市场发展呈现出消极态势,房价变化成为社会关注的焦点。在此背景下,论文以典型收缩城市——黑龙江省鹤岗市为例,基于住宅小区、夜间灯光、POI数据,利用Kriging插值和多尺度地理加权回归模型等方法,结合鹤岗市空间增长与收缩情况分析住宅价格空间分异特征及影响机制。结果显示：① 鹤岗市住宅价格呈圈层模式分布,核心—外围分异程度强。高水平住宅价格小区集聚在核心区内且分布规模小,中高值圈层扩散态势弱;外围工矿型辖区收缩情况相对严重,住宅价格水平低且波动小。② 城市发展状态与住宅价格水平存在空间相关性。不同收缩程度区域经济发展态势、居民收入水平、人口减少与老龄化、保障房建设规模等宏观因素差异影响着住宅价格总体空间分异格局。③ 城市内部区域的增长或收缩状态影响微观设施的作用效果。发展中心的区位优势对增长型区域住宅价格的正向作用更强,高水平公共服务对核心区和城市北部收缩区域住宅价格的增长有明显积极效应,企业工厂的分布对增长型区域住宅价格的负向影响更突出,各因素相互联系、交互影响,共同作用于住宅价格空间分异。     

Urban Expansion and Spatiotemporal Relationships with Driving Factors Revealed by Geographically Weighted Logistic Regression

Urbanization improves our lives but also threatens human health and sustainable development. Revealing the spatiotemporal pattern of urban expansion and spatiotemporal relationships with driving forces, especially in terms of the ubiquitous and fast growing small city, is a crucial prerequisite to solving these problems and realizing sustainable development. Kunshan, China was used as a case study here. Eleven variables from four aspects covering physical, socioeconomic, accessibility and neighborhood were selected, and logistic regression and geographically weighted logistic regression modeling were employed to explore spatiotemporal relationships from 1991-2014. Results reveal that urban expansion in Kunshan shows an accelerating tendency with annual expansion from 2000-2014 four times higher than for 1991-2000. More importantly, the annual expansion rate of Kunshan of 28.42% in 2000-2014 is higher than that of a large city. Urban expansion and related factors have spatiotemporal varying relationships. From a global perspective, the closer to a city, town, main road and the higher the GDP, the more likely a region will undergo urbanization. Interestingly, the effect of population on urban expansion is decreasing, especially in developed areas, and the effect of distance to lake is enhanced. From a local perspective, the magnitude and even the sign of the coefficients vary across the study area. However, the range of the coefficient of GWLR is around that of the corresponding variable in LR, and the sign of most variables in GWLR is consistent with that of corresponding variables in LR. GWLR surpasses LR with the same explanatory variables in revealing regional differences and improving model reliability. Based on these findings, more attention should be given to small cities in China. Promoting the connotation of city culture and public services to realize New-type Urbanization and regional diversity policy in order to manage urban expansion scientifically are also recommended.     

A bootstrap test for constant coefficients in geographically weighted regression models

Statistical tests for whether some coefficients really vary over space play an important role in using the geographically weighted regression (GWR) to explore spatial non-stationarity of the regression relationship. In view of some shortcomings of the existing inferential methods, we propose a residual-based bootstrap test to detect the constant coefficients in a GWR model. The proposed test is free of the assumption that the model error term is normally distributed and admits some useful extensions for identifying more complicated spatial patterns of the coefficients. Some simulation with comparison to the existing test methods is conducted to assess the test performance, including the accuracy of the bootstrap approximation to the null distribution of the test statistic, the power in identifying spatially varying coefficients and the robustness to collinearity among the explanatory variables. The simulation results demonstrate that the bootstrap test works quite well. Furthermore, a real-world data set is analyzed to illustrate the application of the proposed test.     

路网形态与住宅价格的多尺度空间关系研究——基于空间网络分析与多尺度地理加权回归模型

针对以往住宅价格影响因素分析中忽略城市路网形态参数的问题,该文基于空间网络分析,将不同搜索半径下道路接近度与穿行度纳入住宅价格特征变量,构建空间计量模型,探究成都市路网形态对住宅价格的驱动效应。结果表明:1)相比享乐回归模型和地理加权回归模型,多尺度地理加权回归模型揭示了不同变量的空间影响尺度,更适用于探究成都市路网形态对住宅价格的影响;2)路网的局部接近度、局部穿行度核心位于二环内,全局接近度核心主要分布在四环内,全局穿行度核心主要分布在交通干道上;3)不同搜索半径下对住宅价格具有显著驱动效应的接近度均为全局尺度变量,该效应在空间上相对平稳,而穿行度作为局部变量,其在空间上的影响尺度随搜索半径的变化而存在差异,具有一定的空间异质性,其中,路网接近度对住宅价格产生正向影响,其系数空间格局呈跨尺度相似特征,而穿行度产生负向影响,其系数空间格局呈跨尺度变异特征;4)各搜索半径下路网形态变量的差异可在一定程度上改变消费者对其他影响因素的偏好程度。     

成渝经济圈生态效率时空动态演变及其影响因素（英文）

为了响应国家十四五规划,更好地探索促进区域协调绿色发展的新战略,本文采用super-SBM模型和马尔可夫链对成渝经济圈2004–2018年的生态效率值进行了测算与时序分析,同时,利用地理加权回归模型对生态效率进行了空间分析。虽然成渝经济圈生态效率在研究期间有所提高,但其经济发展仍然是生态无效的,这意味着成渝迫切需要提高资源利用效率,促进技术创新。在研究期间,成渝经济圈的生态效率的演变呈现为“π”字形状,并伴随着“俱乐部趋同”的现象,此现象表明生态效率有保持原状的强烈趋势,说明生态效率缺乏足够的改善动力,因此很难实现跨越式转移。从空间上看,生态效率从西北向东南呈高–低–高效率分布,生态效率的时空差异缩小,但集聚效应相对较弱且呈现两极分化趋势。进一步的研究表明,城镇化发展水平、对外开放水平、技术水平、环境规制和产业结构高级化是导致生态效率空间差异的原因。成渝经济圈应针对各自弱点相应采取改善措施提高生态效率,从而促进整个区域的绿色发展。     

基于地理探测器和GWR模型的中国重点镇布局定量归因

重点镇是小城镇发展的龙头,形成科学合理的重点镇布局对优化中国城市化战略格局有重要意义。论文以2004年和2014年分别公布的1887个和3675个全国重点镇为样本,对其分布及效应的变动特征进行探究,进而在地级尺度对重点镇布局的影响因子及其作用进行地理探测和局部空间回归。结果表明：① 经增补调整,中国重点镇布局及建设效应的均衡性增强,主要集聚区西移北扩,冷热点的分布突破“胡焕庸线”,经济辐射效应的分化程度减弱,体现出政策因素的有力影响。除县际均衡和区域倾斜政策外,重点镇的分布还受到海拔高度、公路网密度、常住人口城镇化率等因子的显著作用。② 因子探测器、GWR模型和交互作用探测器的结合能更精准地刻画影响因子的作用方式、方向、路径和强度。中国重点镇的布局不是5个显著性因子均匀、独立、直接作用的结果,而是影响均具空间异质性的各因子两两交互作用后增效的产物。③ 县际均衡政策与其他因子的协同作用是形成现有重点镇分布格局的主导力量;区域倾斜政策的效果总体较好,但目标区域还需更准确。     

基于3种地理加权回归方法的安徽省土壤pH空间预测制图对比研究

基于安徽省140个采样点的土壤pH数据,综合考虑土壤、地形、气候、生物等因子对土壤pH的影响,采用地理加权回归(Geographically Weighted Regression, GWR)、主成分地理加权回归(Principal Component Geographically Weighted Regression, PCA-GWR)和混合地理加权回归(Mixed Geographically Weighted Regression, M-GWR)3种模型对安徽省土壤pH空间分布进行建模预测,揭示环境因子对土壤pH的影响在空间上的差异,最后以多元线性回归模型(Multiple Linear Regression, MLR)为基准比较3种GWR模型的精度。研究表明：(1)安徽省土壤pH具有空间异质性,且集聚特征明显。(2) 3种GWR模型中M-GWR模型略优,GWR、PCA-GWR和M-GWR的建模集调整后决定系数(R_adj²)分别为0.59、0.62和0.63;对比MLR模型,3种GWR模型的R_adj^2<...     

Modelling spatial heterogeneity and anisotropy: child anaemia,sanitation and basic infrastructure in sub-Saharan Africa

Public interventions in support of public health and housing in developing countries could benefit from better understanding of spatial heterogeneity and anisotropy. Estimation of directional variation within geographically weighted regression (GWR) faces problems of local parameter instability, border effects and, if extended to non- spatial attributes, potential endogeneity. This study formulates a GWR model where anisotropy is filtered out based on information from directional variograms. Along with classical regressions, the approach is applied to investigate child anaemia and its associations with household characteristics, sanitation and basic infrastructure in 173 regions of sub-Saharan Africa. Based on ordinary least squares (OLS) results, anaemia prevalence rates are up to three times more responsive to child morbidity (related to malaria and other diseases) than to other covariates. GWR estimates provide similar indications, but also point to poor sanitation facilities as a cofactor of severe anaemia particularly in east and southern Africa. The anisotropy-adjusted GWR is spatially stationary in residuals, and its estimated local parameters are less collinear than GWR with no adjustment. However, similar explanatory power and lack of significant bias in parameters estimated by the latter suggest that directional variation is largely captured by modelled co-movements among the variables.     

高质量发展耦合协调时空格局演化及影响因素——以浙江省县域为例

综合运用耦合协调、空间关联分析和地理加权回归模型,对浙江省县域高质量发展耦合协调水平进行测度,进一步分析其空间演化特征及影响因素.结果 表明:①浙江省县域高质量发展整体上呈现出“东高西低、北高南低”的空间分异特征,高质量发展耦合空间格局以良好耦合为主,高质量发展协调水平以中级协调为主.②高质量发展耦合协调空间结构呈现出...     

基于重心-GTWR模型的京津冀城市群研究

Research into urban expansion patterns and their driving forces is of great significance for urban agglomeration development planning and decision-making.In this paper,we reveal the multi-dimensional characteristics of urban expansion patterns,based on the intensity index of the urban expansion,the differentiation index of the urban expansion,the fractal dimension index,the land urbanization rate,and the center of gravity model,by taking the Beijing-Tianjin-Hebei(Jing-Jin-Ji)urban agglomeration as an example.We then build the center of gravity-geographically and temporally weighted regression(GTWR)model by coupling the center of gravity model with the GTWR model.Through the analysis of the temporal and spatial patterns and by using the center of gravity-GTWR model,we analyze the driving forces of the urban land expansion and summarize the dominant development modes and core driving forces of the Jing-Jin-Ji urban agglomeration.The results show that:1)Between 1990 and 2015,the expansion intensity of the Jing-Jin-Ji urban agglomeration showed a down-up-down trend,and the peak period was in 2005-2010.Before 2005,high-speed development took place in Beijing,Tianjin,Baoding,and Langfang;after 2005,rapid development was seen in Xingtai and Handan.2)Although the barycenter of cities in the Jing-Jin-Ji urban agglomeration has shown a divergent trend,the local interaction between cities has been enhanced,and the driving forces of urban land expansion have shown a characteristic of spatial spillover.3)The spatial development mode of the Jing-Jin-Ji urban agglomeration has changed from a dual-core development mode to a multi-core development mode,which is made up of three functional cores:the transportation core in the northern part,the economic development core in the central part,and the investment core in the southern part.The synergistic development between each functional core has led to the multi-core development mode.4)The center of gravity-GTWR model combines the analysis of spatial and temporal nonstationarity with urban spatial interaction,and analyzes the urban land expansion as a space-time dynamic system.The results of this study show that the model is a feasible approach in the analysis of the driving forces of urban land expansion.     

中国高新技术企业分布影响因素的空间异质性与尺度效应

影响高新技术企业分布的因素往往具有空间非平稳性,然而既有研究对其关注尚少。基于2017—2019年间认定的215791家高新技术企业数据,运用多尺度地理加权回归模型（MGWR）,刻画了中国高新技术企业的空间分布格局,识别了其影响因素的空间异质性与尺度效应,结果表明：① 2019年中国高新技术企业的空间分布呈现出在以“北上广深”为首位中心,以成渝与区域性中心城市为次位中心的高度集聚特征。② 企业内部因素、城市知识创造水平、技术创新水平、创新环境水平和外部连通水平共同影响了高新技术企业的空间分布。③ 影响高新技术企业分布的因素存在空间异质性,公司年龄、高校学生数量、互联网的影响呈现出“东-西”向空间分异格局,专利申请数、高新区、生活设施的正向影响呈现出“南-北”向空间分异格局,高铁的正向影响呈现出“东南-西北”向空间分异格局,研发费用投入对东北地区影响最大,市场化水平对京津冀和珠三角城市群地区影响最大。④ 影响因素存在尺度效应,靠近创新末端的变量具有更大的作用空间尺度。最后,本研究提出相关的政策建议,以期为高新技术产业的发展提供借鉴与参考。     

Using multilevel modeling and geographically weighted regression to identify spatial variations in the relationship between place-level disadvantages and obesity in Taiwan

Objectives

We examined whether and to what extent the relationship between township disadvantages and obesity varied across geographical areas.

Methods

A cross-sectional analysis of a population-based sample of Taiwanese adults (N = 25,985) from the 2005 Social Development Trend Survey on Health and Safety was performed. Multilevel models integrated with geographically weighted regressions were employed to analyze the spatially varying association between area disadvantages and obesity. The dependent variable was body mass index calculated from respondents’ self-reported weight and height. The key explanatory variable was a township disadvantage index made of poverty level, minority composition, and social disorder. Other individual socio-demographic characteristics were included to account for the compositional effect.

Results

The association between township disadvantages and elevated obesity risk in Taiwan was found to be area-specific. In contrast to results from the commonly used global regression, geographically weighted regression model showed that township disadvantages elevated obesity level only in certain areas.

Conclusions

We found heterogeneity of place-level determinants of obesity across geographical areas. Adoption of population approach to curb obesity would require area-specific strategies for most needed areas.