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.     

Exploring population spatial concentrations in Northern Ireland by community background and other characteristics: an application of geographically weighted spatial statistics

Information on how populations are spatially concentrated by different characteristics is a key means of guiding government policies in a variety of contexts, in addition to being of substantial academic interest. In particular, to reduce inequalities between groups, it is necessary to understand the characteristics of these groups in terms of their composition and their geographical structure. This article explores the degree to which the population of Northern Ireland is spatially concentrated by a range of characteristics. There is a long history of interest in residential segregation by religion in Northern Ireland; this article assesses population concentration not only by community background (‘religion or religion brought up in’) but also by housing tenure, employment and other socioeconomic and demographic characteristics. The spatial structure of geographical variables can be captured by a range of spatial statistics including Moran's I. Such approaches utilise information on connections between observations or the distances between them. While such approaches are conceptually an improvement on standard aspatial statistics, a logical further step is to compute statistics on a local basis on the grounds that most real-world properties are not spatially homogenous and, therefore, global measures may mask much variation. In population geography, which provides the substantive focus for this article, there are still relatively few studies that assess in depth the application of geographically weighted statistics for exploring population characteristics individually and for exploring relations between variables. This article demonstrates the value of such approaches by using a variety of geographically weighted statistical measures to explore outputs from the 2001 Census of Population of Northern Ireland. A key objective is to assess the degree to which the population is spatially divided, as judged by the selected variables. In other words, do people cluster more strongly with others who share their community background or others who have a similar socioeconomic status in some respect? The analysis demonstrates how geographically weighted statistics can be used to explore the degree to which single socioeconomic and demographic variables and relations between such variables differ at different spatial scales and at different geographical locations. For example, the results show that there are regions comprising neighbouring areas with large proportions of people from the same community background, but with variable unemployment levels, while in other areas the first case holds true but unemployment levels are consistently low. The analysis supports the contention that geographical variations in population characteristics are the norm, and these cannot be captured without using local methods. An additional methodological contribution relates to the treatment of counts expressed as percentages.     

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.     

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...     

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.     

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<...     

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。     

Exploratory analysis of the interrelations between co-located boolean spatial features using network graphs

Visual data mining of spatial data is a challenging task. As exploratory analysis is fundamental, it is beneficial to explore the data using different potential visualisations. In this article, we propose and analyse network graphs as a useful visualisation tool to mine spatial data. Due to their ability to represent complex systems of relationships in a visually insightful and intuitive way, network graphs offer a rich structure that has been recognised in many fields as a powerful visual representation. However, they have not been sufficiently exploited in spatial data mining, where they have principally been used on data that come with an explicit pre-specified network graph structure. This research presents a methodology with which to infer relationship network graphs for large collections of boolean spatial features. The methodology consists of four principal stages: (1) define a co-location model, (2) select the type of co-association of interest, (3) compute statistical diagnostics for these co-associations and (4) construct and visualise a network graph of the statistic from step (3). We illustrate the potential usefulness of the methodology using an example taken from an ecological setting. Specifically, we use network graphs to understand and analyse the potential interactions between potential vector and reservoir species that enable the propagation of leishmaniasis, a disease transmitted by the bite of sandflies.     

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.     

海南省农村多维贫困及影响因素的空间分异

贫困具有多维属性,根据不同社会群体和背景从多维视角定义贫困已成为贫困问题研究的共识。依据Alkire-Foster多维贫困框架,拓展精准扶贫的“两不愁,三保障”识别标准,建立了涵盖教育、健康、居住、生活和收入指标的海南省农户多维贫困评估指标体系,基于海南省70个乡镇、134个贫困村3924户入户调查数据,采用双重临界值法评估了农户及村域多维贫困状况,进而运用地理加权回归(Geographically Weighted Regression,GWR)模型,分析了村域多维贫困影响因素的空间分异。结果显示,调查农户多维贫困率达18.22%,多维贫困程度严重的村多维贫困发生率不一定高,“两不愁、三保障”及收入指标对多维贫困指数的贡献率低。中、西部连片贫困地区多维贫困主要表现为较差的资产状况、不清洁的炊事燃料、较高的家庭成员患病率和较低的家庭成员最高学历。GWR模型分析表明,作为多维贫困最重要的影响因素,户主性别、户主受教育水平、女性劳动力占比和抚养比4个变量估计系数的空间分异明显。总体上,女性户主和低学历户主为主的地区倾向于更易发生多维贫困,二者的影响分别表现为从东到西、从北到南有所增强。女性劳动力占比为负向影响,抚养比为正向影响,呈现出自北向南增强的趋势,体现了海南贫困地区劳动力弱、女性相对更勤劳等典型地域特征。     

呼伦贝尔沙地沙丘砂来源的定量分析— 逐步判别分析(SDA)在粒度分析方面的应用

以呼伦贝尔沙地砂物质的粒度分析资料为基础,利用两组间的逐步判别分析(SDA) 来筛选决定不同沉积物间差异的主导因子,根据主导因子的个数、Mahalanobis距离D2、通过统计学检验的信度琢等3个因素,来定量地确定两个总体间的相似性大小。分析结果表明:呼伦贝尔沙地的风成沙丘砂主要来源于海拉尔组砂(Q3),但河流冲积砂和古土壤也有不可忽视的作用;在嵯岗镇附近及其以西的海拉尔河下游宽阔河谷中,自然条件下河流冲积砂也可以成为风成沙丘砂的主要沙源。     

县域农村贫困化空间分异及其影响因素——以陕西山阳县为例

以国家扶贫开发重点县山阳县为研究区,通过空间自相关分析和分组分析方法探究山阳县农村贫困化的空间格局和类型;利用逐步回归、地理加权回归和地理探测器模型对山阳县农村贫困化影响因素进行分析,讨论影响因素效应水平的空间异质性及其交互作用。研究表明：① 山阳县农村贫困发生率具有较强的空间集聚性,形成6个热点集聚区和4个冷点集聚区;综合考虑农村贫困程度和空间连接性,将山阳县划分为低度贫困区、中度贫困区和高度贫困区。② 水网密度、到最近公路的距离、危房比例、农民人均可支配收入、外出务工人数比例、农户入社比例6个因素是山阳县农村贫困化的主要影响因素,各因素的影响效应具有空间异质性。③ 两因素交互作用要比单因素作用于贫困发生率时影响力更显著,各主要影响因素的交互作用类型有双因子增强型和非线性增强型两种。     

Discrete displacement analysis for geographic linear features and the application to glacier termini

The extent of glacier terminus displacement is instrumental in investigations of natural or artificial geographic changes. Its importance to earth science and engineering is reflected in the considerable efforts that have been devoted to the development of several boundary displacement analysis methods. Among the methods, the buffering-based approach compares favorably with other approaches in objectivity and robustness. However, it does not consider the relative positions of boundaries, because its buffering operation cannot determine features' relative directions. This limitation incurs inaccurate calculation results – underestimation of mean shifts and overestimation of shape variations, especially when the two compared boundaries intersect. Discrete displacement analysis (DDA), an alternative method that considers given geographic objects as a set of a finite number of points, is proposed here. In a series of tests carried out, including Jakobshavn glacier's calving front, DDA was found to correctly calculate mean shift and shape variation even in cases where the conventional buffering-based method failed. Moreover, this approach is independent of the dimension of space in which it is implemented, and thus is expected to be utilized for analysis of 3D geographic object displacement.     

Using rough set theory to identify villages affected by birth defects: the example of Heshun,Shanxi, China

This article uses rough set theory to explore spatial decision rules in neural-tube birth defects and searches for novel spatial factors related to the disease. The whole rule induction process includes data transformation, searching for attribute reducts, rule generation, prediction or classification, and accuracy assessment. We use Heshun as an example, where neural-tube birth defects are prevalent, to validate the approach. About 50% of the villages in Heshun are used as the sample data, from which all of the rules are extracted. Meanwhile, the other villages are used as reference data. The rules extracted from the training data are then applied to the reference data. The result shows that the rules' generalization is reasonably good. Moreover, a novel relationship between the spatial attributes and the neural-tube birth defects was discovered. That is, the villages that lie in Watershed 9 of this district and that are also associated with a gradient of between 16° and 25° are vulnerable to neural-tube birth defects. This result paves the road for predicting where high rates of neural-tube birth defects will occur and can be used as a preliminary step in finding a direct cause for the disease.     

Using spatial analysis and Bayesian network to model the vulnerability and make insurance pricing of catastrophic risk

Vulnerability refers to the degree of an individual subject to the damage arising from a catastrophic disaster. It is affected by multiple indicators that include hazard intensity, environment, and individual characteristics. The traditional area aggregate approach does not differentiate the individuals exposed to the disaster. In this article, we propose a new solution of modeling vulnerability. Our strategy is to use spatial analysis and Bayesian network (BN) to model vulnerability and make insurance pricing in a spatially explicit manner. Spatial analysis is employed to preprocess the data, for example kernel density analysis (KDA) is employed to quantify the influence of geo-features on catastrophic risk and relate such influence to spatial distance. BN provides a consistent platform to integrate a variety of indicators including those extracted by spatial analysis techniques to model uncertainty of vulnerability. Our approach can differentiate attributes of different individuals at a finer scale, integrate quantitative indicators from multiple-sources, and evaluate the vulnerability even with missing data. In the pilot study case of seismic risk, our approach obtains a spatially located result of vulnerability and makes an insurance price at a finer scale for the insured buildings. The result obtained with our method is informative for decision-makers to make a spatially located planning of buildings and allocation of resources before, during, and after the disasters.     

Using autologistic spatial models to simulate the distribution of land-use patterns in Zhangjiajie, Hunan Province

Nowadays, spatial simulation on land use patterns is one of the key contents of LUCC. Modeling is an important tool for simulating land use patterns due to its ability to integrate measurements of changes in land cover and the associated drivers. The conventional regression model can only analyze the correlation between land use types and driving factors, but cannot depict the spatial autocorrelation characteristics. Land uses in Yongding County, which is located in the typical karst mountain areas in northwestern Hunan province, were investigated by means of modeling the spatial autocorrelation of land use types with the purpose of deriving better spatial land use patterns on the basis of terrain characteristics and infrastructural conditions. Through incorporating components describing the spatial autocorrelation into a conventional logistic model, we constructed a regression model (Autologistic model), and used this model to simulate and analyze the spatial land use patterns in Yongding County. According to the comparison with the conventional logistic model without considering the spatial autocorrelation, this model showed better goodness and higher accuracy of fitting. The distribution of arable land, wood land, built-up land and unused land yielded areas under the ROC curves (AUC) was improved to 0.893, 0.940, 0.907 and 0.863 respectively with the autologistic model. It is argued that the improved model based on autologistic method was reasonable to a certain extent. Meanwhile, these analysis results could provide valuable information for modeling future land use change scenarios with actual conditions of local and regional land use, and the probability maps of land use types obtained from this study could also support government decision-making on land use management for Yongding County and other similar areas.     

巢湖西湖岸新石器-商周遗址空间分布规律及其成因

将地理信息系统空间分析方法引入巢湖西湖岸新石器-商周遗址考古工作,通过点密度分析、空间距离分析、三维分析、缓冲区分析等方法研究遗址空间分布规律及其影响因素。研究表明自新石器至商周时期研究区内遗址时空分布呈现:随时间推移由湖岸边逐渐向西北部扩展,后迁移至南部,再均匀扩散的遗址迁移轨迹;先民多选择靠近水源、地势平坦、土壤肥沃的自然岗地、河谷阶地、山麓面居住,导致古遗址空间上大致呈线状、团聚状、分散状等分布特征,具有明显的河谷谷地指向性、阶地岗地指向性、土壤指向性等规律。提出遗址分布在早期可能主要受到气候水文、地貌、植被土壤等自然因素影响,后期生产力发展水平、经济生活方式等人文因素影响加重。本研究为GIS支持下区域考古研究提供了合适的研究实例,同时GIS方法得到一些推论假设仍需要田野考古调查与发掘等进一步佐证。     

The residential segregation of San Antonio,Texas in 1910: an analysis of ethno-racial and occupational spatial patterns with the colocation quotient

The segregation of cities can be traced to a time when the compartmentalization of space and people was based on factors other than race. In segregation research, one of the limiting factors has always been the geographic scale of the data, and the limited knowledge that exists of segregation patterns when the household is the unit of analysis. Historical census data provides the opportunity to analyze the disaggregated information, and this paper does so with San Antonio during 1910. A spatial analysis of residential segregation based on race, ethnicity, and occupations is carried out with the colocation quotient to map and measure the attraction of residents. Results reveal the presence of residential segregation patterns on different sectors of the city based on households’ ethno-racial and occupational attributes; therefore, providing evidence of the existence of residential segregation prior to the commonly cited determinants of segregation of the 20th century.     

Measuring the accessibility of different household income groups to basic community services in upland Misamis Oriental,Northern Mindanao,Philippines

Improving household accessibility to basic community services can help reduce poverty in upland areas. In this study, spatial analysis with GIS was used to measure the accessibility of different household income groups to community services in the landlocked upland municipality Claveria in Northern Mindanao, the Philippines. Important community services were identified through villagers' participation in a matrix‐scoring activity. Travel information was derived from key informant interviews while the geographical coordinates of sample households and important services were collected using GPS receivers. The Flowmap GIS software (version 7.2) was used to compute accessibility to services along the road network by habal‐habal (two‐wheel motorcycle). Outcomes from the participatory data gathering activities revealed that agricultural, educational and health facilities, as well as government services are important to the community to achieve sustainable livelihoods. Because local people perceive accessibility in terms of monetary costs, rather than distance, road distance measurements were converted into fare costs. Results of the accessibility analysis show that higher‐income household groups generally incur lower mean one‐way travel costs to reach important community services than poorer households. However, almost all households spend more than the daily per capita poverty threshold for the province to reach basic community services. A scenario to improve accessibility to services in the study area was investigated to emphasize the potential of GIS‐based accessibility analysis in rural service planning.     

Spatial analysis of water quality and its suitability in farming giant freshwater prawn (Macrobrachium rosenbergii) in Negeri Sembilan region,Peninsular Malaysia

Finding potential sites for resilient prawn production in the tropical environment that also prevents wastage of natural resources is not an easy task. The purpose of this study is to evaluate water quality suitability for prawn farming in Negeri Sembilan of Peninsular Malaysia based on Geographic Information System (GIS). To achieve this goal, numerous criteria including sources of water, water temperature, water pH, sources of pollution, salinity, soil texture and availability of phytoplankton criteria were considered for the modelling process. Analytic Hierarchy Process (AHP) technique was performed to standardize the criteria and the weighting process. The weighted overlay of indicators and results were accomplished by applying the Multi‐Criteria Decision Analysis (MCDA) method in GIS. It was indicated that the Negeri Sembilan area has potential for prawn farming. The results showed that about 25 per cent (163 056.93 ha) of the area was most suitable for prawn farming, about 58 per cent (384 656.88 ha) was considered moderately suitable, while 18 per cent (117 633.49 ha) was regarded as least suitable. The study concluded that the multi‐criteria decision analysis of water quality for prawn farming is vital for regional economic planning in the Negeri Sembilan area and also significant when establishing a model for aquaculture development.