RECURSIVE ALGORITHMS FOR THE ELIMINATION OF REDUNDANT PATHS IN SPATIAL LAG OPERATORS*

ABSTRACT. Recursive algorithms for the elimination of redundant paths in spatial lag operators are introduced. It is shown that these algorithms have superior computational properties in comparison with the cumbersome procedure proposed by Ross and Harary (1952). A rigorous definition of spatial lag operators is given, while a number of mathematical results and properties are derived. Theoretical and empirical results regarding the performance of the proposed algorithms are presented.     

Impacts of Multiple-Period Lags in Dynamic Logit Models

This paper will provide an introduction to a new field of research, viz. the sensitivity of the solution trajectory of a dynamic logit model (belonging to the class of discrete choice models) in the light of a multiperiod lag structure. It is well known from recent advances in the area of chaos and turbulence theory that the stability of a dynamic system is critically dependent on various factors, such as threshold values of parameters, initial conditions, and also the lag structure. This paper aims to identify the consequences of different lag structures in dynamic logit models (including also dynamic spatial interaction models). Various simulation experiments will be used to show that the onset of instability of the solution trajectory tends to decrease as the number of time lags increases (depending also on the growth rate of the system).     

A Model of Contiguity for Spatial Unit Allocation

We consider a problem of allocating spatial units (SUs) to particular uses to form "regions" according to specified criteria, which is here called "spatial unit allocation." Contiguity—the quality of a single region being connected—is one of the most frequently required criteria for this problem. This is also one that is difficult to model in algebraic terms for algorithmic solution. The purpose of this article is to propose a new exact formulation of contiguity that can be incorporated into any mixed integer programming model for SU allocation. The resulting model guarantees to enforce contiguity regardless of other included criteria such as compactness. Computational results suggest that problems involving a single region and fewer than about 200 SUs are optimally solved in fairly reasonable time, but that larger problems must rely on heuristics for approximate solutions. It is also found that a problem of any size can be formulated in a more tractable form when a fixed number of SUs are to be selected or when a certain SU is selected in advance.     

A Zero‐One Programming Model for Contiguous Land Acquisition

The land acquisition problem is a spatial partitioning problem that involves selecting multiple parcels to be acquired for a particular land use. Three selection criteria are considered: total cost, total area, and spatial contiguity. Achieving contiguity or connectivity has been problematic in previous exact methods for land acquisition. Here we present a new zero‐one programming model that enforces necessary and sufficient conditions for achieving contiguity in discrete cell landscapes, independent of other spatial attributes such as compactness. Computational experience with several demonstration problems is reported, and results and extensions are discussed.     

北京市公共服务设施供需协调发展的时空演化特征——以教育医疗设施为例

公共服务设施的优化配置是构建和谐社会、改善民生的内在要求。本文通过构建协调发展度模型,对北京市2001年和2012年16个区县教育医疗设施供需关系及二者协调发展的时空演化特征进行研究。研究认为:①教育设施"供不应需",供需差距增大;协调发展等级总体较低且有下降趋势;协调发展水平由"东高西低"向"南高北低"格局演变,空间差异增大。②医疗设施"供不应需",供需差距缩小;供需协调发展等级较低但有上升趋势,空间格局由"中心集聚"向"南高北低"演变,空间差异减小。     

THE IMPACTS OF TRANSPORTATION INFRASTRUCTURE ON PROPERTY VALUES: A HIGHER-ORDER SPATIAL ECONOMETRICS APPROACH

ABSTRACT.  We evaluate the impacts of enhanced transportation systems on property values for U.S. manufacturing firms, allowing for higher-order spatial error correlation. We use a state-level model of production cost and input demand that recognizes the productive contribution of public transportation infrastructure stocks. Our findings include significant impacts on property shadow values and input composition from both public highway and airport investment. We also find that these effects have a spatial dimension that depends on the proximity of the transport system; at least one and as many as three spatial error lags are significant in our estimating equations. Further, recognizing production growth from transportation system improvements augments the associated incentives for private capital investment.     

Gender, space, and the location changes of jobs and people: a spatial simultaneous equations analysis

This article summarizes a spatial econometric analysis of local population and employment growth in the Netherlands, with specific reference to impacts of gender and space. The simultaneous equations model used distinguishes between population- and gender-specific employment groups, and includes autoregressive and cross-regressive spatial lags to detect relations both within and among these groups. Spatial weights matrices reflecting different bands of travel times are used to calculate the spatial lags and to gauge the spatial nature of these relations. The empirical results show that although population–employment interaction is more localized for women's employment, no gender difference exists in the direction of interaction. Employment growth for both men and women is more influenced by population growth than vice versa. The interaction within employment groups is even more important than population growth. Women's, and especially men's, local employment growth mostly benefits from the same employment growth in neighboring locations. Finally, interaction between these groups is practically absent, although men's employment growth may have a negative impact on women's employment growth within small geographic areas. In summary, the results confirm the crucial roles of gender and space, and offer important insights into possible relations within and among subgroups of jobs and people.     

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.     

Noninferior Bandwidth Line Simplification: Algorithm and Structural Analysis

Digital line simplification operators are an important preprocessing component of a spatial data handling system. Simplification operators are used to generalize digital line files because these files are encoded at one scale but the objects they represent can be displayed at many other scales. Most line simplification algorithms are heuristics that caricaturize lines by eliminating points representing redundant data or conversely retaining the characteristic points of a line that have a high informational content. This paper presents a noninferior simplification algorithm that produces an optimal caricature of an encoded line with respect to the bandwidth criterion that all deleted points must be within a prespecified distance of the simplified line. Results show that it is a practical alternative to existing bandwidth heuristics.     

Shared rivers and interstate conflict

“The previous war in the Middle East was about oil, the next war will be about water.” Such predictions have been made regularly, and particularly with reference to the possibility of upstream–downstream conflicts in major rivers which cross interstate boundaries. A good case can be made that competition over water resources may exacerbate conflict and contribute to interstate violence. More than 200 river systems are shared by two or more countries. Many rivers run between countries with a history of conflict, where water plays an important part in the economic life of the country. The dramatic statements about ‘water wars’, however, have a weaker foundation. As resource optimists have pointed out, there is an abundance of water where it is not subject to wasteful uses, human ingenuity can overcome water shortages, and nations can cooperate rather than fight to resolve international water issues. This study is built on newly generated data on boundary-crossing rivers, which have been added to the Correlates of War contiguity dataset. Our results indicate that a joint river does indeed increase the probability of militarized disputes and armed conflict over and above mere contiguity. This risk factor is comparable in size to standard control variables, but much smaller than the effect of contiguity itself. Water scarcity is also associated with conflict, and the upstream/downstream relationship appears to be the form of shared river most frequently associated with conflict. But these results are not very strong and we do not have any systematic data on the issues involved in the shared-river conflicts.     

Toward a Theory of Spatial Statistics: Another Step Forward

An update is presented to an earlier piece outlining some steps that needed to be taken toward the establishment of a theory of spatial statistics. Findings that have appeared since this first paper are summarized and interpreted, and extensions and suggestions are offered for the further establishment of a basis for a theory of spatial statistics. Topics include boundary considerations, the role of latent spatial dependencies, and small-sample-size issues. These topics embrace the problems of data transformations, edge effect bias, reference sampling distributions, multivariate autocorrelation models, conditional expectations, and higher-order autoregressive structures. In part, a course is charted for the next step to be taken.     

Shared rivers and conflict – A reconsideration

Neomalthusians have regularly predicted "water wars" while cornucopians have argued that there is no inherent water scarcity and liberal institutionalists have seen cooperation as a more likely outcome of competition for limited water resources than violent conflict. Three earlier studies have found a positive statistical relationship between shared rivers and low-level interstate conflict. Based on a more comprehensive dataset, an improved model of conflict, and a more appropriate control for geographical opportunity, we argue that these results are spurious and that we cannot establish a conflict-inducing effect of shared rivers over and beyond contiguity itself. In fact, the new dataset presented here makes it clear that nearly all neighbors in the international system share at least one river. This calls for a different approach to investigating interaction in shared river basins. This notwithstanding, freshwater and other shared resources may still provide a mechanism to explain why contiguity is robustly associated with conflict, so the water-conflict scenario cannot be dismissed. Indeed, our results show that among river-sharing states, basins with an upstream/downstream configuration increase the risk of conflict. The article finally discusses how river interaction should be further investigated based on these results and what new data are needed to enable such research.     

Were Olduvai Hominins making butchering tools or battering tools? Analysis of a recently excavated lithic assemblage from BK (Bed II,Olduvai Gorge,Tanzania)

A new interpretation of early stone-tool use by hominins at Olduvai depicts them as involved in battering activities (using pounding tools) rather than making cutting butchering tools as is commonly inferred in most other Plio-Pleistocene sites where lithics appear associated to faunal remains. The bulk of this interpretation is based on the recognition of the stigma of percussion activities in anvils and detached by-products. Renewed excavations at BK after more than half a century of the beginning of the digging at the site by M. Leakey have produced a new and unbiased lithic assemblage. The taphonomic study of the faunal assemblage has shown that BK is an anthropogenic site where carcass butchery practices were repeatedly performed over a vast amount of time. The present analysis of the lithic artefacts supports this interpretation by showing that the obtainment of flakes was the principal aim in stone knapping. We argue that a number of technical traits observed in the lithic collection of BK can be best interpreted as the result of bipolar loading rather than the by-products of battering activities. Since BK has provided the second largest collection of hominid-modified bones from Olduvai, it is concluded that detached pieces produced in the course of bipolar reduction might have played an active role in bone modification and that active rather than passive percussion behaviors might have been responsible for the formation of the lithic assemblage. The functionality of the Oldowan stone tools are discussed under the light of the new study.     

An Anisotropic Model for Spatial Processes

One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model.     

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.     

The Colocation Quotient: A New Measure of Spatial Association Between Categorical Subsets of Points. 协同区位商：点集分类子集间空间关联性的新度量标准

This article presents a new metric we label the colocation quotient (CLQ), a measurement designed to quantify (potentially asymmetrical) spatial association between categories of a population that may itself exhibit spatial autocorrelation. We begin by explaining why most metrics of categorical spatial association are inadequate for many common situations. Our focus is on where a single categorical data variable is measured at point locations that constitute a population of interest. We then develop our new metric, the CLQ, as a point‐based association metric most similar to the cross‐k‐function and join count statistic. However, it differs from the former in that it is based on distance ranks rather than on raw distances and differs from the latter in that it is asymmetric. After introducing the statistical calculation and underlying rationale, a random labeling technique is described to test for significance. The new metric is applied to economic and ecological point data to demonstrate its broad utility. The method expands upon explanatory powers present in current point‐based colocation statistics.     

A Genetic Approach to Detecting Clusters in Point Data Sets

Spatial analysis techniques are widely used throughout geography. However, as the size of geographic data sets increases exponentially, limitations to the traditional methods of spatial analysis become apparent. To overcome some of these limitations, many algorithms for exploratory spatial analysis have been developed. This article presents both a new cluster detection method based on a genetic algorithm, and Programs for Cluster Detection, a toolkit application containing the new method as well as implementations of three established methods: Openshaw's Geographical Analysis Machine (GAM), case point-centered searching (proposed by Besag and Newell), and randomized GAM (proposed by Fotheringham and Zhan). We compare the effectiveness of cluster detection and the runtime performance of these four methods and Kulldorf's spatial scan statistic on a synthetic point data set simulating incidence of a rare disease among a spatially variable background population. The proposed method has faster average running times than the other methods and significantly reduces overreporting of the underlying clusters, thus reducing the user's postprocessing burden. Therefore, the proposed method improves upon previous methods for automated cluster detection. The results of our method are also compared with those of Map Explorer (MAPEX), a previous attempt to develop a genetic algorithm for cluster detection. The results of these comparisons indicate that our method overcomes many of the problems faced by MAPEX, thus, we believe, establishing that genetic algorithms can indeed offer a viable approach to cluster detection.     

Exploring Spatial Patterns Using an Expanded Spatial Autocorrelation Framework

Spatial autocorrelation (SA) is regarded as an important dimension of spatial pattern. SA measures usually consist of two components: measuring the similarity of attribute values and defining the spatial relationships among observations. The latter component is often represented by a spatial weights matrix that predefines spatial relationship between observations in most measures. Therefore, SA measures, in essence, are measures of attribute similarity, conditioned by spatial relationship. Another dimension of spatial pattern can be explored by controlling observations to be compared based upon the degree of attribute similarity. The resulting measures are spatial proximity measures of observations, meeting predefined attribute similarity criteria. Proposed measures reflect degrees of clustering or dispersion for observations meeting certain levels of attribute similarity. An existing spatial autocorrelation framework is expanded to a general framework to evaluate spatial patterns and can accommodate the proposed approach measuring proximity. Analogous to the concept of variogram, clustergram is proposed to show the levels of spatial clustering over a range of attribute similarity, or attribute lags. Specific measures based on the proposed approach are formulated and applied to a hypothetical landscape and an empirical example, showing that these new measures capture spatial pattern information not reflected by traditional spatial autocorrelation measures.     

SPACE–TIME MEASURES OF DEMAND FOR SERVICE: BRIDGING LOCATION MODELLING AND ACCESSIBILITY STUDIES THROUGH A TIME‐GEOGRAPHIC FRAMEWORK

Demand for service in location modelling is often evaluated based on the spatial proximity of fixed and static reference locations of demand (e.g. home) to a facility, which ignores person‐specific activity–travel patterns and the temporal changes in demand for service throughout the day. To address these limitations, this study draws upon recent developments in space–time measures of individual accessibility to explore the spatial and temporal structures of demand by considering individuals' space–time constraints and impact of existing urban structures. Based on a time‐geographic framework, eight space–time demand measures were developed and compared with three conventional location‐based demand measures for 12 hospitals through an empirical study conducted in Columbus, Ohio. The results show that geographic proximity between clients' home and facilities may not be an effective indicator for service demand, and conventional demand measures tend to underestimate potential demand for service in most situations. The study concludes that space–time demand measures that take into account people's activity‐travel patterns in space–time would lead to better estimation of demand for service in most cases.