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.     

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.     

Mapping the Results of Geographically Weighted Regression

Abstract

Geographically weighted regression (GWR) is a local spatial statistical technique for exploring spatial nonstationarity. Previous approaches to mapping the results of GWR have primarily employed an equal step classification and sequential no-hue colour scheme for choropleth mapping of parameter estimates. This cartographic approach may hinder the exploration of spatial nonstationarity by inadequately illustrating the spatial distribution of the sign, magnitude, and significance of the influence of each explanatory variable on the dependent variable. Approaches for improving mapping of the results of GWR are illustrated using a case study analysis of population density–median home value relationships in Philadelphia, Pennsylvania, USA. These approaches employ data classification schemes informed by the (nonspatial) data distribution, diverging colour schemes, and bivariate choropleth mapping.     

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.     

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。     

地形因子与小微地震相关度的空间异质性分析

针对传统最小二乘回归未能顾及数据的空间特性,且无法度量模型自变量与因变量相关性的空间变异特性的问题,本文提出利用地理加权回归方法分析小微地震频次与地形因子相关度的空间异质性。以四川地区的地震监测资料、DEM为实验数据,选取地形复杂度、坡度变率、坡向变率和地面曲率为自变量,地震发生频次为因变量,构建地理加权回归模型,并进行回归系数的空间变异分析。实验分析发现,地震频次与地形因子具有一定的相关性:地形复杂度与地震频次相关性最强;坡度变率、沟壑密度、剖面曲率与地震频次的相关性依次减弱;不同空间位置的地形因子和地震频次的相关性具有较明显的空间异质性。实验结果表明,地理加权回归可以有效地度量分析地震频次与地形因子相关度的空间异质性,研究结果可为地震及次生灾害的分析与预报提供辅助决策参考。     

Spatiotemporal variability of urban growth factors: A global and local perspective on the megacity of Mumbai

The rapid growth of megacities requires special attention among urban planners worldwide, and particularly in Mumbai, India, where growth is very pronounced. To cope with the planning challenges this will bring, developing a retrospective understanding of urban land-use dynamics and the underlying driving-forces behind urban growth is a key prerequisite. This research uses regression-based land-use change models – and in particular non-spatial logistic regression models (LR) and auto-logistic regression models (ALR) – for the Mumbai region over the period 1973–2010, in order to determine the drivers behind spatiotemporal urban expansion. Both global models are complemented by a local, spatial model, the so-called geographically weighted logistic regression (GWLR) model, one that explicitly permits variations in driving-forces across space. The study comes to two main conclusions. First, both global models suggest similar driving-forces behind urban growth over time, revealing that LRs and ALRs result in estimated coefficients with comparable magnitudes. Second, all the local coefficients show distinctive temporal and spatial variations. It is therefore concluded that GWLR aids our understanding of urban growth processes, and so can assist context-related planning and policymaking activities when seeking to secure a sustainable urban future.     

The pyrogeography of sub-Saharan Africa: a study of the spatial non-stationarity of fire–environment relationships using GWR

This study analyses the relationship between fire incidence and some environmental factors, exploring the spatial non-stationarity of the phenomenon in sub-Saharan Africa. Geographically weighted regression (GWR) was used to study the above relationship. Environment covariates comprise land cover, anthropogenic and climatic variables. GWR was compared to ordinary least squares, and the hypothesis that GWR represents no improvement over the global model was tested. Local regression coefficients were mapped, interpreted and related with fire incidence. GWR revealed local patterns in parameter estimates and also reduced the spatial autocorrelation of model residuals. All the covariates were non-stationary and in terms of goodness of fit, the model replicates the data very well (R ² = 87%). Vegetation has the most significant relationship with fire incidence, with climate variables being more important than anthropogenic variables in explaining variability of the response. Some coefficient estimates exhibit locally different signs, which would have gone undetected by a global approach. This study provides an improved understanding of spatial fire–environment relationships and shows that GWR is a valuable complement to global spatial analysis methods. When studying fire regimes, effects of spatial non-stationarity need to be incorporated in vegetation-fire modules to have better estimates of burned areas and to improve continental estimates of biomass burning and atmospheric emissions derived from vegetation fires.     

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%。     

顾及局部与结构特征的稀疏多项式逻辑回归高光谱图像分类方法

稀疏多项式逻辑回归在分类中仅利用图像光谱信息,导致分类效果不太理想.本文提出了一种顾及局部与结构特征的稀疏多项式逻辑回归高光谱图像分类方法.首先利用加权均值滤波与拓展形态学多属性剖面对原始高光谱图像进行局部与结构特征提取;然后对二者进行加权平均特征级融合以获取更具唯一性的像元特征;最后由稀疏多项式逻辑回归分类器对融合结果进行分类.结果表明,本文方法能有效地提高分类精度,而且具有较强的稳健性.     

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.      

局域差分GPS的数学模型

局域差分GPS中,用户到基准站的距离对定位精度有着决定性影响。利用基准站生成用户误差改正数,其算法很多。文中针对局域差分GPS的数学模型空间相关性,介绍几种常用的内插方法,如加权平均法、线性内插法、低次曲面模型法及三角形内插法,并分析各种方法的内插系数和内插质量因子。利用局域差分GPS进行定位时,只有当用户站位于基准站构成的多边形网内时,才可能得到较高的精度。     

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     

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.     

Non-stationary Approaches for Mapping Terrain and Assessing Prediction Uncertainty

It is well known that terrain may vary markedly over small areas and that statistics used to characterise spatial variation in terrain may be valid only over small areas. In geostatistical terminology, a non-stationary approach may be considered more appropriate than a stationary approach. In many applications, local variation is not accounted for sufficiently. This paper assesses potential benefits in using non-stationary geostatistical approaches for interpolation and for the assessment of uncertainty in predictions with implications for sampling design. Two main non-stationary approaches are employed in this paper dealing with (1) change in the mean and (2) change in the variogram across the region of interest. The relevant approaches are (1) kriging with a trend model (KT) using the variogram of residuals from local drift and (2) locally-adaptive variogram KT, both applied to a sampled photogrammetrically derived digital terrain model (DTM). The fractal dimension estimated locally from the double-log variogram is also mapped to illustrate how spatial variation changes across the data set. It is demonstrated that estimation of the variogram of residuals from local drift is worthwhile in this case for the characterisation of spatial variation. In addition, KT is shown to be useful for the assessment of uncertainty in predictions. This is shown to be true even when the sample grid is dense as is usually the case for remotely-sensed data. In addition, both ordinary kriging (OK) and KT are shown to provide more accurate predictions than inverse distance weighted (IDW) interpolation, used for comparative purposes.     

Dynamic land use change simulation using cellular automata with spatially nonstationary transition rules

The dynamic relationships between land use change and its driving forces vary spatially and can be identified by geographically weighted regression (GWR). We present a novel cellular automata (GWR-CA) model that incorporates GWR-derived spatially varying relationships to simulate land use change. Our GWR-CA model is characterized by spatially nonstationary transition rules that fully address local interactions in land use change. More importantly, each driving factor in our GWR model contains effects that both promote and resist land use change. We applied GWR-CA to simulate rapid land use change in Suzhou City on the Yangtze River Delta from 2000 to 2015. The GWR coefficients were visualized to highlight their spatial patterns and local variation, which are closely associated with their effects on land use change. The transition rules indicate low land conversion potential in the city’s center and outer suburbs, but higher land conversion potential in the inner near suburbs along the belt expressway. Residual statistics show that GWR fits the input data better than logistic regression (LR). Compared with an LR-based CA model, GWR-CA improves overall accuracy by 4.1% and captures 5.5% more urban growth, suggesting that GWR-CA may be superior in modeling land use change. Our results demonstrate that the GWR-CA model is effective in capturing spatially varying land transition rules to produce more realistic results, and is suitable for simulating land use change and urban expansion in rapidly urbanizing regions.     

How many samples are needed? An investigation of binary logistic regression for selective omission in a road network

ABSTRACT

Selective omission in a road network (or road selection) means to retain more important roads, and it is a necessary operator to transform a road network at a large scale to that at a smaller scale. This study discusses the use of the supervised learning approach to road selection, and investigates how many samples are needed for a good performance of road selection. More precisely, the binary logistic regression is employed and three road network data with different sizes and different target scales are involved for testing. The different percentages and numbers of strokes are randomly chosen for training a logistic regression model, which is further applied into the untrained strokes for validation. The performances of using the different sample sizes are mainly evaluated by an error rate estimate. Significance tests are also employed to investigate whether the use of different sample sizes shows statistically significant differences. The experimental results show that in most cases, the error rate estimate is around 0.1–0.2; more importantly, only a small number (e.g., 50–100) of training samples is needed, which indicates the usability of binary logistic regression for road selection.     

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.