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.     

融合地理探测器和地理加权回归的太原市建设用地变化因素研究

准确地识别城市化进程中建设用地的变化情况及其背后的驱动力,对城市后续的可持续发展具有重要意义。本文首先以2000—2020年遥感影像为基础,对太原市建设用地空间分布变化进行研究,然后结合地理探测器模型和地理加权回归模型,对研究区建设用地的空间分布影响驱动力因子进行研究,得到以下结论:除政策因素外,现有的城市建设用地空间分布变化还受到高程、交通、GDP、人口等因素的显著作用。太原市城市建设用地变化的布局不单是GDP变化、人口变化、海拔高度、公路网密度4个显著性因子均匀、独立、直接作用的结果,而是具有空间异质性的各因子两两交互作用后增效的产物。本文成果有望为城市建设用地驱动力研究提供一种新思路。     

Exploring relation of land surface temperature with selected variables using geographically weighted regression and ordinary least square methods in Manipur State,India

In the present study, relationship between Land surface temperature and selected indices, vegetation index (VARI), built-up index (BUI) and elevation (DEM) is investigated. Ordinary least square method and geographically weighted regression are used to analyse the spatial correlation between the indices with surface temperature. Subsequently, temporal trends (2001–2015) in surface temperature and vegetation are explored after every two years of interval. LANDSAT image and ASTER DEM are used to extract LST and additional indices. The selected variables (Built-up, vegetation and topography) explain 69% of the variation in surface temperature. The OLS and GWR revealed that topography and vegetation are the significant factor of LST in Manipur State. Topography being a constant parameter, its effect is constant over time. The changing scenario of vegetation is significantly contributing to LST. The surface temperature over a period of 15 years show increasing trend and is negatively and strongly correlated to vegetation cover.     

Modeling the spatial variation of urban land surface temperature in relation to environmental and anthropogenic factors: a case study of Tehran,Iran

ABSTRACT

Spatial variation of Urban Land Surface Temperature (ULST) is a complex function of environmental, climatic, and anthropogenic factors. It thus requires specific techniques to quantify this phenomenon and its influencing factors. In this study, four models, Random Forest (RF), Generalized Additive Model (GAM), Boosted Regression Tree (BRT), and Support Vector Machine (SVM), are calibrated to simulate the ULST based on independent factors, i.e., land use/land cover (LULC), solar radiation, altitude, aspect, distance to major roads, and Normalized Difference Vegetation Index (NDVI). Additionally, the spatial influence and the main interactions among the influential factors of the ULST are explored. Landsat-8 is the main source for data extraction and Tehran metropolitan area in Iran is selected as the study area. Results show that NDVI, LULC, and altitude explained 86% of the ULST °C variation. Unexpectedly, lower LST is observed near the major roads, which was due to the presence of vegetation along the streets and highways in Tehran. The results also revealed that variation in the ULST was influenced by the interaction between altitude – NDVI, altitude – road, and LULC – altitude. This indicates that the individual examination of the underlying factors of the ULST variation might be unilluminating. Performance evaluation of the four models reveals a close performance in which their R² and Root Mean Square Error (RMSE) fall between 60.6–62.1% and 2.56–2.60 °C, respectively. However, the difference between the models is not statistically significant. This study evaluated the predictive performance of several models for ULST simulation and enhanced our understanding of the spatial influence and interactions among the underlying driving forces of the ULST variations.     

中国雾霾分布及其组成相关性分析

雾霾天气由于其对人体健康及交通能见度的极大影响而受到广泛关注。在收集相关污染物与气象数据基础上,基于GIS技术及最小二乘法和地理加权回归模型分析了我国2014年1月雾霾空间分布特征及其组成要素的相关性。研究表明,2014年1月我国各省会城市基本都受到雾霾影响,其中华北地区最为显著,华东、华南沿海城市具有一定的相似性;西南部地区大部雾霾污染明显小于其他地区。从雾霾物质组成上看,PM_(2.5)与PM_(10)、CO、NO_2和SO_2之间存在微妙关系,随着其他污染物的增加,PM_(2.5)数值也会随之增大,其中PM_(10)和CO对PM2.5的影响是显著的。从研究方法上看,利用地理加权回归建模方法对雾霾及其组成成份相关性研究的效果(84%)略好于最小二乘法的分析效果(82.59%)。本研究可为了解雾霾空间分布特征及分析其相关影响因素提供参考。     

Forest inventories by LiDAR data: A comparison of single tree segmentation and metric-based methods for inventories of a heterogeneous temperate forest

Inventories of temperate forests of Central Europe mainly rely on terrestrial measurements. Rapid alterations of forests by disturbances and multilayer silvicultural systems increasingly challenge the use of conventional plot based inventories, particularly in protected areas. Airborne LiDAR offers an alternative or supplement to conventional inventories, but despite the possibility of obtaining such remote sensing data, its operational use for broader areas in Central Europe remains experimental. We evaluated two methods of forest inventory that use LiDAR data at the landscape level: the single tree segment-based method and an area-based method. We compared a set of structural forest attributes modeled by these methods with a conventional forest inventory of the highly heterogeneous forest of the Bavarian Forest National Park (Germany), which partially includes stands affected by severe natural disturbances. Area-based models were accurate for all structural attributes, with cross-validated average root mean squared error ranging from ∼3.4 to ∼13.4 in the best modeling case. The coefficients of variation for the mapped area-based estimations were mostly minor. The area-based estimations were varied but highly correlated (Pearson’s correlations between ∼ 0.56 and 0.85) with single tree segmentation estimations; undetected trees in the single tree segmentat-based method were the main sources of inconsistency. The single tree segment-based method was highly correlated (∼ 0.54 to 0.90) with data from ground-based forest inventories. The single tree-based algorithm delivered highly reliable estimates for a set of forest structural attributes that are of interest in forest inventories at the landscape scale. We recommend LiDAR forest inventories at the landscape scale in both heterogeneous commercial forests and large protected areas in the central European temperate sites.     

Explicitly incorporating spatial dependence in predictive vegetation models in the form of explanatory variables: a Mojave Desert case study

Predictive vegetation modeling is defined as predicting the distribution of vegetation across a landscape based upon its relationship with environmental factors. These models generally ignore or attempt to remove spatial dependence in the data. When explicitly included in the model, spatial dependence can increase model accuracy. We develop presence/absence models for 11 vegetation alliances in the Mojave Desert with classification trees and generalized linear models, and use geostatistical interpolation to calculate spatial dependence terms used in the models. Results were mixed across models and methods, but in general, the spatial dependence terms more consistently increased model accuracy for widespread alliances. GLMs had higher accuracy in general.     

New urban settlements in a perspective of public and private interests. Case study: a Swedish municipality within the hinterland of the Stockholm city

The changes of land use patterns and urban structures could be seen as the dynamic result of the trade off between public and private interests. Thereby the land use change is to some extent unpredictable. The focus in the current study is to measure the importance of spatial location factors regarding new residential and commercial buildings in relation to existing urban amenities and political guidelines. The relative importance of the location factors was studied by multinomial regression analysis. Results from this study reveal that the location profiles of new urban object types attained here indicate strong correspondence with local political land use guidelines and to clustering. The spatial distribution of new urban settlements does not in general correspond to the monocentric urban scheme where firms and residents locate in spatial proximity to urban centres.