Bidimensional Regression

Since its invention by Francis Galton in 1877 regression analysis has been found useful in almost all disciplines. Comparison of geographic phenomena requires a two-dimensional extension of this technique. In this manner geographic maps can be compared with each other. Possible applications include geometric comparison of ancient and modern maps, or of “mental” maps, or for rubber-sheeting as used in Geographic Information Systems and in remote sensing. Other applications, for example, in biology for the comparison of shapes of leaves, fish, faces, or skulls after the manner of D'Arcy W. Thompson are also possible, as are higher-dimensional and multivariate cases. The method implements, and puts into this new context, existing models from the field of cartography. The linear case yields an easy definition of a Pearsonian-like correlation coefficient. The bidimensional case is richer in mathematical options than is the usual unidimensional version. The curvilinear case is of even greater utility. Here the regression coefficients constitute a spatially varying, but coordinate invariant, second-order tensor field defined by the matrix of partial derivatives of the transformation. This can be shown to be essentially equivalent to Tissot's Indicatrix, used in cartography to determine the properties of a map projection. In a computer implementation a nonparametric approach allows visualization of the regression by automatically plotting the pair of scatter diagrams, drawing of the displacement field, differentiable smooth interpolation of the warped coordinates and predicted image, by a diagram of the principal strains, and with contour maps of the estimated local angular, areal, and total distortion.     

认知地图空间分析的地理学研究进展

认知地图是环境意象构成要素、要素间的距离和方向信息最为完全的表现形式,综合反映了居民对城市的认知和城市对居民的影响,是行为地理学核心研究内容之一。论文基于认知地图空间分析的视角,全面梳理了国内外的手绘地图研究、认知地图扭曲研究、地名认知/距离认知/城市空间结构认知、认知地图居民属性研究,提出了国内努力的方向。     

Bayesian Updating of Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents

Probabilistic models have been developed in a previous study by the authors to estimate the seismic deformation demands on structural components of reinforced concrete (RC) bridges with two-column bents. However, such models should be updated to reflect the latest laboratory of field data. Using a Bayesian approach, this article updates a currently available probabilistic model for the deformation demands of columns in bridges with two-column RC bents. The updated model incorporates information from newly available experimental data from shake table tests conducted based on a record of the 1994 Northridge Earthquake for a structural system with three bents with two columns per bent. The updated model is more accurate than the previous one in predicting the deformation demand of bridges with two-column RC bents and reduces the statistical uncertainty due to the addition of new data. As an application, fragility estimates for an example bridge are computed using the updated model both at the component (column) and system (bridge) levels.     

Some Notes on Parametric Significance Tests for Geographically Weighted Regression

The technique of geographically weighted regression (GWR) is used to model spatial 'drift' in linear model coefficients. In this paper we extend the ideas of GWR in a number of ways. First, we introduce a set of analytically derived significance tests allowing a null hypothesis of no spatial parameter drift to be investigated. Second, we discuss 'mixed' GWR models where some parameters are fixed globally but others vary geographically. Again, models of this type may be assessed using significance tests. Finally, we consider a means of deciding the degree of parameter smoothing used in GWR based on the Mallows C_p statistic. To complete the paper, we analyze an example data set based on house prices in Kent in the U.K. using the techniques introduced.     

Weighted Bidimensional Regression. 加权二维回归

Shape analysis is useful for a wide variety of disciplines and has many applications. One of the many approaches to shape analysis focuses on shapes that are represented by predefined landmarks on an object. Some landmarks may be measured with greater precision, exhibit more natural variation, or be more important than others to an analysis. This article introduces a method for including this information when estimating mapping relations or assessing the degree of similarity between two objects that are represented by a set of two‐dimensional landmarks. Weighted bidimensional regression combines aspects of weighted least squares regression and bidimensional regression as a way to weight variables that are represented by a set of two‐dimensional spatial coordinates. One possible weighting scheme is suggested, and the effect of weighting is demonstrated through a face‐matching application. Results indicate that appropriate weighting increases the ability to correctly match two faces and that weighting has the largest effect when used with a projective transformation.     

A Route Map for Successful Applications of Geographically Weighted Regression

Geographically Weighted Regression (GWR) is increasingly used in spatial analyses of social and environmental data. It allows spatial heterogeneities in processes and relationships to be investigated through a series of local regression models rather than a single global one. Standard GWR assumes that relationships between the response and predictor variables operate at the same spatial scale, which is frequently not the case. To address this, several GWR variants have been proposed. This paper describes a route map to decide whether to use a GWR model or not, and if so which of three core variants to apply: a standard GWR, a mixed GWR or a multiscale GWR (MS-GWR). The route map comprises 3 primary steps that should always be undertaken: (1) a basic linear regression, (2) a MS-GWR, and (3) investigations of the results of these in order to decide whether to use a GWR approach, and if so for determining the appropriate GWR variant. The paper also highlights the importance of investigating a number of secondary issues at global and local scales including collinearity, the influence of outliers, and dependent error terms. Code and data for the case study used to illustrate the route map are provided.     

地图投影与全球地缘政治分析:一种空间认知的视角

地缘政治分析离不开地图。在全球地缘政治分析中,作为世界地图基本空间框架的地图投影通过变形为人们架起了一座"认知的桥梁"--一种空间认知的视角,包括结构、中心方位、距离和面积四种认知。它们在人脑中组合成世界意象地图,为全球地缘政治分析营造了一个多维的空间思维条件。世界观念研究、地缘动态研究,地区研究和全球性问题研究都离不开全球地图投影。总之,地图投影对于国际关系研究具有重要价值。     

Evaluating inputs to models of hominin raw material selection: map resolution and path choices

Selection of an appropriate scale is an important decision in study design in many branches of science, since perceived patterns often change with the scales of spatial extent or resolution of an analysis. In previously published work, we created a resource selection model to determine the importance of several independent variables for the selection of lithic materials by hominins at a Middle Palaeolithic site in southern France. Two of these independent variables (calories exerted and difficulty of the terrain covered in travel from source to site) were calculated using elevation data extracted from maps. In the present paper, we examine the differences in model performance when the variables ‘Calories’ and ‘Difficulty’ are calculated using 1) three base maps for elevation that differed in map resolution (from finest to coarsest: a 1:25,000 topographic base map, SPOT DEM, and SRTM DEM), and 2) two different methods for determining the route from source to site (straight-line route and least-cost route; both methods exclude areas with slopes >60% from travel). Our best model was the one that used data calculated using the topographic base map; however, the SRTM DEM-based data produced models of essentially equal quality. Regardless of map scale, models that used data calculated using a straight-line route always outperformed models that used data calculated using a least-cost route. This supports our previous finding that a straight-line route is a more appropriate measure for the path from lithic source to site than a least-cost route. We conclude that the map resolution of each of the base maps used here is appropriate for analyses involving spatial data pertaining to Neandertal activity because this type of data is essentially always coarse-grained.     

Experimental Study and Numerical Model Calibration for Earthquake-Induced Collapse of RC Frames with Emphasis on Key Columns,Joints, and the Overall Structure

A thorough investigation of earthquake-induced collapse of reinforced concrete frames is presented. The inherent correlation between the nonlinear behavior of key components and the collapse mechanism of overall frame is examined through concurrent collapse tests of both frame and key components. Important issues in the component models are investigated through calibration against experiments, leading to a comprehensive structural system model. Both test and simulation indicate that the seismic performance are predominately governed by the key columns, whereas the energy dissipation capacity is somewhat affected by the joints. This study offers systematic experimental data and numerical models for future collapse assessments.     

社区尺度认知地图扭曲的空间分析——基于首师大和北林大的个案研究

以首都师范大学和北京林业大学为例,利用标准方差椭圆方法讨论社区尺度上认知地图的扭曲分析,有四点结论:①社区尺度上的认知地图均为原始地图的缩小认知。但主导缩小方向与社区内部的主要道路网结构密切相关。②社区主干道和社区边界对认知地图的方向扭曲施加重要影响,发挥着定位基准线的作用。③社区尺度上各认知地点标准方差椭圆的长轴方向与空间定位基准线方向基本一致。④反映空间认知被试者差异性的各地点认知的标准方差椭圆面积与被试者对地点的熟悉程度有负向关系。     

The battle of London (1554) – reconstructing a renaissance battlefield

Abstract

The confrontation outside London (7 February 1554) between the rebel army of Sir Thomas Wyatt and forces loyal to Queen Mary Tudor has been frequently characterized as a bloodless contest of will rather than a military conflict. This view, however, fails to account for the action’s wider significance in the study of Tudor warfare, a field arguably distorted by the limited number of battles fought within the sixteenth-century British Isles. Furthermore, the encounter is unusually well-documented by written narratives, while its location ensures that the battlefield is depicted on several near-contemporary and subsequent maps, providing opportunities for more detailed investigation through terrain reconstruction. This article will use methodologies of map regression to define the historic landscape of the battle, permitting tactical-level consideration of the engagement and helping to discern the site’s archaeological potential. By doing so, it will also facilitate a reassessment of the battle’s key events and implications.     

Comparison of Plane Forms

Nonlinear two-dimensional grid transformations are used to compare plane figures. The method is based on the identification of homologous points, and thus can be considered as a bidimensional extension of ordinary curvilinear regression, but is here approached from the point of view of cartography. All of the techniques illustrated by Thompson in 1917 can be mimicked by the computer program. Extensions of the method, based on the derivatives of the transformations, permit the determination of the axes of principal change, and also suggest numerical measures for the degree of similarity of topologically equivalent figures. Applications are illustrated in biology and geography, and more general uses are suggested.     

SPATIAL DEPENDENCE AND SPATIAL STRUCTURAL INSTABILITY IN APPLIED REGRESSION ANALYSIS*

The stability of regression coefficients over the observation set (“regional homogeneity”) is typically assessed by means of a Chow test or within a seemingly unrelated regression (SUR) framework. When spatial error autocorrelation is present in cross-sectional equations the traditional tests are no longer applicable. I evaluate this both in formal terms as well as empirically. I introduce a taxonomy of spatial effects in models for structural instability, and discuss its implication for testing. I compare the performance of traditional tests, robust approaches, maximum-likelihood procedures and pretest techniques by means of a series of simple Monte Carlo experiments.     

Identifying the Impacts of Land-Use Spatial Patterns on Street-Network Accessibility Using Geospatial Methods

While the land use-street network nexus is well acknowledged, evidence for the one-way impacts of land-use patterns on street accessibility is still inadequate. The measurements of land-use patterns and street accessibility lack systematic knowledge. Their empirical correlations also lack geographical variability, constraining site-specific land-use practices. Therefore, this study overcame the aforementioned limitations by examining the two-level spatial models to formulate accessibility-oriented land plans, using a well-developed Chinese city as an example. Firstly, two landscape metrics—Euclidean Nearest-Neighbor Distance (ENN) and Similarity Index (SIMI)—were used to quantify the intra- and inter-land-use configurations, respectively. Both city-level and local accessibility were measured using spatial design network analysis. Performing both ordinary least squares (OLS) and geographically weighted regression (GWR) models, results identified the statistically significant effects of inter-land-use patterns on two-level street accessibility. An exception was that land-use configurations within residential and industrial regions were irrelevant to street accessibility. We also found GWR was a better-fitting model than OLS when estimating locally-varied accessibility, suggesting hierarchical multiscale land-use planning. Overall, locally heterogeneous evidence in this study can substantialize land use-street network interactions and support the decision-making and implementation of place-specific accessibility-oriented land use.     

A Hybrid Approach for Mass Valuation of Residential Properties through Geographic Information Systems and Machine Learning Integration

Geographic Information Systems (GIS) and Machine Learning methods are now widely used in mass property valuation using the physical attributes of properties. However, locational criteria, such as as proximity to important places, sea or forest views, flat topography are just some of the spatial factors that affect property values and, to date, these have been insufficiently used as part of the valuation process. In this study, a hybrid approach is developed by integrating GIS and Machine Learning for mass valuation of residential properties. GIS-based Nominal Valuation Method was applied to carry out proximity, terrain, and visibility analyses using Ordnance Survey and OpenStreetMap data, than land value map of Great Britain was produced. Spatial criteria scores obtained from the GIS analyses were included in the price prediction process in which global and spatially clustered local regression models are built for England and Wales using Price Paid Data and Energy Performance Certificates data. Results showed that adding locational factors to the property price data and applying a novel nominally weighted spatial clustering algorithm for creating a local regression increased the prediction accuracy by about 45%. It also demonstrated that Random Forest was the most accurate ensemble model.     

INCORPORATING TECHNOLOGY DIFFUSION,FACTOR MOBILITY AND STRUCTURAL CHANGE INTO CROSS‐REGION GROWTH REGRESSION: AN APPLICATION TO CHINA*

ABSTRACT This paper advocates a spatial dynamic model that introduces technology diffusion, factor mobility, and structural change into the cross‐region growth regression. The spatial setting is derived from theory rather than spatial statistical tests. An application of this model to the study of cross‐province growth in China over the period 1980–2005 indicates that incomes are spatially correlated, which highlights the significance of technology diffusion and factor mobility. Furthermore, the integration of neoclassical growth empirics and the structural change perspective of development economics provide a much improved account of interprovincial variations in income levels and economic growth.     

Who votes alone? The impact of voting by mail on political discussion

Critics of voting by mail express concern over its impact on civil society. For example, Thompson (2004) posits that voting by mail limits electoral civic engagement by preventing the temporal norm of simultaneity on Election Day. I, however, find that the open ballot system of voting by mail promotes deliberation, which encourages civic engagement. This study tests if voting by mail increases political discussion by creating a Poisson regression model of American National Election Survey data. The findings show that voting by mail leads to more political discussion. This evidence supports the theory that voting by mail offers voters a more open and deliberatory system and does not necessarily limit civic engagement.     

Fremont Hunting and Resource Intensification in the Eastern Great Basin

Empirical tests of resource-intensification models argue for diminishing foraging efficiency among hunter–gatherers in California over the past 2000 years (Basgall, 1987,Research in Economic Anthropology9,21–52; Broughton, 1994aJournal of Archaeological Science21,501–514; 1994bJournal of Anthropological Anthropology13, 371–401). The evidence for this long-term trajectory consists of decreases in the abundance of large, high-ranked prey in archaeofaunal assemblages. This paper presents faunal data from Fremont structural sites in the eastern Great Basin and Northern Colorado Plateau as an additional empirical test of resource intensification patterns and compares them to trends in California and the American Southwest. The measure of resource efficiency used is the artiodactyl index (following Broughton, 1994ab), a tool derived from prey choice models of optimal foraging. Faunal data from Fremont structural sites argue that (1) foraging efficiency declined during the Fremont period, and (2) this decline was due to population growth.     

从地理学视角看城市历史文化景观集体记忆的研究

通过对国内外文献的分析,总结了景观、记忆与地理学的研究进展,指出景观、记忆与地方认同联系密切,而且景观与记忆的研究大多与历史文化景观相关。由于集体记忆所体现出的社会性,通过物质的和象征性的城市历史文化景观,去探究其集体记忆的认知空间和情感空间更具有现实意义。文章探讨了GIS和认知地图方法在城市集体记忆研究中的应用,并对佛山城市历史文化景观的集体记忆进行了实证研究。认为在全球化、城市化趋势下,从地理学视角,透过对历史文化景观集体记忆的分析,将有助于城市历史文化遗产持续性地保护和塑造城市地方感。     

基于旅华美国游客手绘认知地图的中国旅游目的地意象研究

手绘认知地图是典型的非结构化的研究方法,以旅游为主题的手绘认知地图能够深入的探索旅游者对目的地人、地方或事物所持有的意象,尤其在跨文化的研究中独具意义.本研究通过客流跟踪的调研方式,获得了我国八个主要入境旅游城市美国团队游客的手绘认知地图。在此资料基础上从空间认知元素和空间认知结构两方面对跨文化旅游者目的地意象进行了分析,并讨论了其相对于居民城市意象的共性和个性。最后,发现跨文化旅游者目的地意象认知元素因旅游主题性而超越了城市的一般物质形态,空间认知符号化特征显著,并且呈现出明显的尺度差异。