Constructing the Spatial Weights Matrix Using a Local Statistic

Spatial weights matrices are necessary elements in most regression models where a representation of spatial structure is needed. We construct a spatial weights matrix, W , based on the principle that spatial structure should be considered in a two‐part framework, those units that evoke a distance effect, and those that do not. Our two‐variable local statistics model (LSM) is based on the G_i* local statistic. The local statistic concept depends on the designation of a critical distance, d_c, defined as the distance beyond which no discernible increase in clustering of high or low values exists. In a series of simulation experiments LSM is compared to well‐known spatial weights matrix specifications—two different contiguity configurations, three different inverse distance formulations, and three semi‐variance models. The simulation experiments are carried out on a random spatial pattern and two types of spatial clustering patterns. The LSM performed best according to the Akaike Information Criterion, a spatial autoregressive coefficient evaluation, and Moran's I tests on residuals. The flexibility inherent in the LSM allows for its favorable performance when compared to the rigidity of the global models.     

基于高速公路交通流的江苏省城市空间关联特征

在江苏省高速公路网络2012年12月OD流量数据和通行时间数据支撑下,本文从县市尺度出发,在对城市空间关联的节点、路径和组团等要素分析基础上,尝试勾绘关联特征的基本图示。结论如下:①城市节点分布有一定的等级性,且节点重要性本身与其社会经济发展状况或在高速公路的功能定位有关。②单一组团或近邻组团以"中心城市+关联节点"进行关联,且城市间的通行时间基本在1小时内,而中长距离的双核心或多核心的组团则以中心城市作为联系基轴建构,且通行时间在1-3小时之间。③综合节点、路径和组团等要素勾绘的城市关联特征模式包含苏北系统、跨江系统和苏南系统,且该模式昭示以"多板块协同发展"的思路规划区域发展战略可作为优先考虑的方案。     

Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 European regions.     

The Spatiotemporal Evolution of Sydney's Tram Network Using Network Econometrics

This paper examines the evolution of Sydney trams using network econometrics approaches. Network econometrics extends spatial econometrics by developing weight matrices based on the physical structure of the network, allowing for competing and complementary elements to have distinct effects. This research establishes a digitized database of Sydney historical tramway network, providing a complete set of geo-referenced data of the opening and closing year and frequencies by time of day for every line. An autoregressive distributed lag model is specified and reveals that the combination of correlation strength and magnitude of lagged flow change on correlated links is a significant predictor of future tram service. The results indicate that complementary and competitive links play distinct roles in shaping the network structure. A link is more likely to undergo the same structural change highly complementary (upstream or downstream) links underwent previously, where the influence is measured by a combination of correlation strength and link importance, reflected by historical service levels.     

INTERPRETING SPATIAL ECONOMETRIC ORIGIN‐DESTINATION FLOW MODELS

Spatial interaction or gravity models have been used to model flows that take many forms, for example population migration, commodity flows, traffic flows, all of which reflect movements between origin and destination regions. We focus on how to interpret estimates from spatial autoregressive extensions to the conventional regression‐based gravity models that relax the assumption of independence between flows. These models proposed by LeSage and Pace ( 2008 , 2009 ) define spatial dependence involving flows between regions. We show how to calculate partial derivative expressions for these models that can be used to quantify these various types of effect that arise from changes in the characteristics/explanatory variables of the model.     

SPATIAL ECONOMETRIC MODELING OF ORIGIN‐DESTINATION FLOWS*

ABSTRACT Standard spatial autoregressive models rely on spatial weight structures constructed to model dependence among n regions. Ways of parsimoniously modeling the connectivity among the sample of N=n² origin‐destination (OD) pairs that arise in a closed system of interregional flows has remained a stumbling block. We overcome this problem by proposing spatial weight structures that model dependence among the N OD pairs in a fashion consistent with standard spatial autoregressive models. This results in a family of spatial OD models introduced here that represent an extension of the spatial regression models described in Anselin (1988) .     

Spatial Autoregressive Models for Geographically Hierarchical Data Structures

This article discusses how standard spatial autoregressive models and their estimation can be extended to accommodate geographically hierarchical data structures. Whereas standard spatial econometric models normally operate at a single geographical scale, many geographical data sets are hierarchical in nature—for example, information about houses nested into data about the census tracts in which those houses are found. Here we outline four model specifications by combining different formulations of the spatial weight matrix W and of ways of modeling regional effects. These are (1) groupwise W and fixed regional effects; (2) groupwise W and random regional effects; (3) proximity‐based W and fixed regional effects; and (4) proximity‐based W and random regional effects. We discuss each of these model specifications and their associated estimation methods, giving particular attention to the fourth. We describe this as a hierarchical spatial autoregressive model. We view it as having the most potential to extend spatial econometrics to accommodate geographically hierarchical data structures and as offering the greatest coming together of spatial econometric and multilevel modeling approaches. Subsequently, we provide Bayesian Markov Chain Monte Carlo algorithms for implementing the model. We demonstrate its application using a two‐level land price data set where land parcels nest into districts in Beijing, China, finding significant spatial dependence at both the land parcel level and the district level.     

京津冀交通路网结构特征及其演变的分形刻画

交通一体化是京津冀协同发展的基础和前提，合理的交通网络结构对提升城市群整体效能意义重大。本文基于1995-2030年多源交通路网数据，运用分形思想，研究京津冀以城市群为节点体系的交通路网空间结构特征及演化趋势。主要结论如下：①京津冀高等级路网仍有一定扩展潜力，交通网络整体等级结构尚不稳定，未达到一种优化的分形递阶状态。②各级路网空间分布具有自仿射特征，但各向异性扩展强度正在逐渐减弱，城镇化和交通一体化战略的实施正在促进各级路网逐渐向自相似的结构一体化方向演化。③交通路网空间结构演化与城镇用地结构不同步，可能与系统所处城镇化发展阶段有关。④高等级路网分维演化服从次数大于1的logistic模型，按照规划预期，各级路网空间发育将相继在2040年前后达到饱和；但按照规划设计高速公路建设将过度饱和，未来应及时调整规划。     

Evaluating Crash Risk in Urban Areas Based on Vehicle and Pedestrian Modeling

This article presents a method for investigating the spatial distribution of vehicle and pedestrian traffic crashes relative to the volume of vehicle and pedestrian movement in urban areas. This method consists of two phases. First, vehicle and pedestrian traffic volumes on the street network are modeled using a space syntax configurational analysis of the network, land use data, and observed traffic data. Second, crash prediction models are fitted to the traffic crash data, using negative binomial regression models and based on traffic volume estimates and street segment lengths. The method was applied in two areas in Tel Aviv, Israel, which differ in their morphological and traffic characteristics. The case‐studies illustrated the method's capability in identifying hazardous locations on the network and examining relative crash risks. The analysis shows that an increase in vehicle or pedestrian traffic volume tends to be associated with a decrease in relative crash risk. Moreover, the spatial patterns of relative crash risks are associated with the design characteristics of urban space: areas characterized by dense street networks encourage more walking, and are generally safer for pedestrians, while those with longer street segments encourage more driving, are less safe for pedestrians, but safer for vehicles.     

GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*

ABSTRACT The estimation of gravity models of internal (aggregate) place‐to‐place migration is plagued with endogeneity (omitted‐variable) biases if the unobserved effects of spatial structure are not accounted for. To address this econometric problem, this paper presents a more general specification of the gravity model, which allows for (bilateral) parameter heterogeneity across individual migration paths—along with (unilateral) origin‐ and destination‐specific effects. The resultant “three‐way fixed‐effects” (3FE) model is applied for an analysis of interstate migration in Mexico based on cross‐sectional data. To overcome parameter‐dimensionality problems (due to limited or incomplete information), the 3FE model is estimated using the Generalized Maximum Entropy (GME) estimator. The empirical implications of this new modeling strategy are illustrated by contrasting the 3FE‐GME estimates with those for the traditional and two‐way fixed‐effects (2FE) models. The former are far more plausible and intuitively interpretable than their traditional and 2FE counterparts, with parameter estimates changing in expected directions. The (average) effect of the migrant stock is markedly smaller than usually estimated, providing a more realistic measure of network‐induced migration. Migration outflows from centrally located origins have significantly steeper distance decay. Path‐specific distance effects exhibit directional asymmetries and spatial similarities.     

武汉都市圈经济社会要素流的空间分析

都市圈城际经济联系与相互作用空间表现形式为城市间、城市-区域间的人流、物流、信息流、资金流、技术流等经济社会要素流。基于城际功能集散效应影响量建立城市流模型:F=NE,揭示出:武汉都市圈各中心城市经济社会要素流强度空间差异明显,对外经济联系呈现显著规模等级分布,空间结构上已经形成以武汉为中心的"鞍形"圈层结构。通过统计数据,利用SPSS统计软件,从实证角度分析得出:武汉成为圈域经济社会要素流集散中心,城际经济社会要素流不同程度表现出以武汉为中心的"等级放射状"空间格局。     

中国城市群空间结构演化的影响因素分析——基于铁路客运的功能联系视角

以中国13个城市群为研究对象,采用铁路客运班次构造多中心指数来表征基于功能联系的城市群空间结构,在分析城市群空间结构演变基础上重点分析其影响因素。研究发现,基于功能联系视角的城市群空间结构总体呈单中心化趋势,但地区差异化明显,珠三角、山东半岛和闽东南城市群已表现出多中心化特征;城市群空间结构的多中心程度随经济发展水平的提高表现为先单中心后多中心的演变过程;城市群规模的增大和城市间联系加强促进了城市群向多中心方向演化;而面积小、三产比重高的城市群更有利于形成单中心的结构;政府干预作用对城市群空间结构影响并不显著。鉴于不同城市群空间结构演化趋势不同,未来政策取向应该遵从各个城市群自身规律。     

Optimizing the Spatial Structure of the Agricultural Production Function

Important characteristics of spatial agricultural production functions are derived by introducing a non‐negative curvilinear spatial demand function for production input intensities. Given the usual neoclassical rationale assumptions of spatial demand for capital and labor inputs under competitive environment of farming in developing agricultural economies, the optimal production levels are determined by optimizing spatial demand for production inputs. Decreasing price‐to‐transport costs ratio (that is, decrease in the prices of capital goods or increase in freight rates) and increasing wage‐to‐travel costs ratio (that is, increase in labor wages or decrease in the travel rate) expand the limits of the (spatial) optimal boundary of the demand for agricultural capital goods and labor input respectively. These effects occur on account of the operation of (positive) spatial price gradient and (negative) wage‐gradient in the market region. It may be noted that elasticities of demand for production factors are spatially variant and have significant effects on the alterations in the structure of agricultural production. However, the spatial optimal solution of production has a complicated relationship with them. The price elasticity has negative and wage elasticity has positive spatial gradients in the market region. Farmers located in the periphery of the market region are not much affected by the proportionate changes occurring in the prices of agricultural capital goods but are more sensitive to the proportional changes in labor wages. Because of a decreasing trend in capital input demand and increase in labor input with distance from the market, capital‐product diminishes with a decreasing rate and labor‐product increases with an increasing rate in the spatial structure of agricultural production. As a result, capital‐labor ratio falls toward zero, which raises profit rate per unit of capital investment especially in the outer part of the market region. The equilibria of optimal production with price elasticity as well as of capital intensity with labor employment (that is, capital‐labor ratio as unity) determine spatial limits of the optimal production zone which is shifted outward subject to the provision of cheap transportation, stabilizing market prices and/or increasing wage rate at the market center. It will help in extending outwardly the optimal spatial limits of capital investment and will mobilize capital resources of farmers in the periphery for efficient and competitive capital‐dominated farming.     

MODELING SPATIAL STRUCTURES THROUGH EQUILIBRIUM STATES FOR TRANSITION MATRICES*

ABSTRACT. In this paper we present a model for spatial interaction within a network of towns. This interaction is modeled through equilibrium states for certain Markov chains where, in particular, explicit formulas for these states are given. Our model exploits and intertwines ideas from gravity models, the competing destinations model and the intervening opportunities model. The central idea in the paper is to capture the effect of spatial structure in a framework where interaction is determined by the global network configuration.     

WHERE IS THE ECONOMICS IN SPATIAL ECONOMETRICS?*

ABSTRACT Spatial econometrics has been criticized by some economists because some model specifications have been driven by data‐analytic considerations rather than having a firm foundation in economic theory. In particular, this applies to the so‐called W matrix, which is integral to the structure of endogenous and exogenous spatial lags, and to spatial error processes, and which are almost the sine qua non of spatial econometrics. Moreover, it has been suggested that the significance of a spatially lagged dependent variable involving W may be misleading, since it may be simply picking up the effects of omitted spatially dependent variables, incorrectly suggesting the existence of a spillover mechanism. In this paper, we review the theoretical and empirical rationale for network dependence and spatial externalities as embodied in spatially lagged variables, arguing that failing to acknowledge their presence at least leads to biased inference, can be a cause of inconsistent estimation, and leads to an incorrect understanding of true causal processes.     

flowAMOEBA: Identifying Regions of Anomalous Spatial Interactions

This study aims at developing a data‐driven and bottom‐up spatial statistic method for identifying regions of anomalous spatial interactions (clusters of extremely high‐ or low‐value spatial flows), based on which it creates a spatial flow weights matrix. The method, dubbed flowAMOEBA, upgrades a multidirectional optimum ecotope‐based algorithm (AMOEBA) from areal data to spatial flow data through a proper spatial flow neighborhood definition. The method has the potential to dramatically change the way we study spatial interactions. First, it breaks the convention that spatial interaction data are always collected and modeled between spatial entities of the same granularity, as it delineates the OD region of anomalous spatial interactions, regardless of the size, shape, scale, or administrative level. Second, the method creates an empirical spatial flow weights matrix that can handle network autocorrelation embedded in spatial interaction modeling, thus improving related policy‐making or problem‐solving strategies. flowAMOEBA is tested and demonstrated on a synthetic data set as well as a county‐to‐county migration data set.     

Semiparametric Maximum Likelihood Estimates of Spatial Dependence

We semiparametrically model spatial dependence via a combination of simpler weight matrices (termed spatial basis matrices) and fit this model via maximum likelihood. Estimation of the model relies on the intuition that bounds to the log‐determinant term in the log‐likelihood can provide penalties to overfitting both the level and pattern of spatial dependence. By relying on symmetric and doubly stochastic spatial basis matrices that reflect different weight specifications assigned to neighboring observations, we are able to derive a mathematical expression for bounds on the log‐determinant term that appears in the likelihood function. These bounds can be conveniently calculated allowing us to solve for maximum likelihood estimates at the bounds using a simple optimization over two quadratic forms that involve small matrices. An intuitively pleasing aspect of our approach is that the objective function for the bounded log‐likelihoods contains one quadratic form equal to the sum‐of‐squared errors measuring the quality of fit, and another quadratic form reflecting a penalty to overfitting spatial dependence. We apply our semiparametric estimation method to a housing model using 57,647 U.S. census tracts.     

交通路网中心性对土地利用强度的影响研究——以青岛市中心城区为例

采取青岛市交通路网矢量数据和 POI 数据，综合运用核密度估计法、地理加权回归模型和多中心性评价模型，从中心性角度解析了青岛市中心城区交通路网与土地利用强度的相关关系。研究表明：青岛市中心城区交通路网的临近中心性与直线中心性结构呈现“中心—外围”模式，中介中心性具有显著的点轴模式；商业、公共服务以及居住用地布局均呈现多中心结构；交通路网中心性与土地利用强度具有较强的相关性且相关关系具有空间异质性；商业用地和公共服务用地与交通路网中心性的相关性高于居住用地。研究揭示了交通路网与土地利用强度之间具有较强的依赖性，为城市规划提供可靠的理论依据，有助于进一步优化城市空间布局。     

中原城市群城镇网络结构特征分析:基于空间引力与客运联系

以中原城市群县、市区节点为研究单元,基于引力模型与复杂网络模型,根据测定的城镇间引力量与城际直接的客运班次两类数据,对中原城市群空间网络结构特征进行比较与归纳。结果表明:中原城市群空间联系突出了"双中心"与层次结构特征,引力与客运联系网络互为支撑,又各具特色,郑州与洛阳在城市群网络结构中的中心度较高,但对网络并没有绝对的控制力,城市群网络的集团化效应明显。城市群最大联系轴向有序,但空间网络结构并没有呈现较强的"长尾分布",城镇网络结构中心度分布有序性差。城市群引力网络子群体间的联系较弱,内部的联系密切,受行政区划的屏蔽或行政级别差异影响显著;而客运联系网络各子群体之间的联系较强,核心市区功能效应显著。