A General Misspecification Test for Spatial Regression Models: Dependence, Heterogeneity, and Nonlinearity

There is an increasing awareness of the potentials of nonlinear modeling in regional science. This can be explained partly by the recognition of the limitations of conventional equilibrium models in complex situations, and also by the easy availability and accessibility of sophisticated computational techniques. Among the class of nonlinear models, dynamic variants based on, for example, chaos theory stand out as an interesting approach. However, the operational significance of such approaches is still rather limited and a rigorous statistical-econometric treatment of nonlinear dynamic modeling experiments is lacking. Against this background this paper is concerned with a methodological and empirical analysis of a general misspecification test for spatial regression models that is expected to have power against nonlinearity, spatial dependence, and heteroskedasticity. The paper seeks to break new research ground by linking the classical diagnostic tools developed in spatial econometrics to a misspecification test derived directly from chaos theory—the BDS test, developed by Brock, Dechert, and Scheinkman (1987). A spatial variant of the BDS test is introduced and applied in the context of two examples of spatial process models, one of which is concerned with the spatial distribution of regional investments in The Netherlands, the other with spatial crime patterns in Columbus, Ohio.     

Properties of Tests for Spatial Dependence in Linear Regression Models

Based on a large number of Monte Carlo simulation experiments on a regular lattice, we compare the properties of Moran's I and Lagrange multiplier tests for spatial dependence, that is, for both spatial error autocorrelation and for a spatially lagged dependent variable. We consider both bias and power of the tests for six sample sizes, ranging from twenty-five to 225 observations, for different structures of the spatial weights matrix, for several underlying error distributions, for misspecified weights matrices, and for the situation where boundary effects are present. The results provide an indication of the sample sizes for which the asymptotic properties of the tests can be considered to hold. They also illustrate the power of the Lagrange multiplier tests to distinguish between substantive spatial dependence (spatial lag) and spatial dependence as a nuisance (error autocorrelation).     

Estimation Bias in Spatial Models with Strongly Connected Weight Matrices

This article shows that, for both spatial lag and spatial error models with strongly connected weight matrices, maximum likelihood estimates of the spatial dependence parameter are necessarily biased downward . In addition, this bias is shown to be present in general Moran tests of spatial dependency. Thus, positive dependencies may often fail to be detected when weight matrices are strongly connected. The analysis begins with a detailed examination of downward bias for the extreme case of maximally connected weight matrices. Results for this case are then extended by continuity to a broader range of (appropriately defined) strongly connected matrices. Finally, a simulated numerical example is presented to illustrate some of the practical consequences of these biases.     

Graph Theory Interpretation of Flow Matrices: A Note on Maximization Procedures for Identifying Significant Links

A maximization procedure for identifying significant links in a flow matrix is described and its use illustrated. The method appears to have advantages over primary-flow linkage methods and over methods based on flow-combination procedures.     

Tests for Patterns in Geographic Variation

We develop tests of whether a pattern of geographic variation departs significantly from random variation over an area. Localities are vertices in a graph whose edges are connections based on criteria of geographic contiguity. Ranked variables are assigned to each locality. Distributions of absolute differences in rank along edges between vertices yield various statistics of edge length that are compared with expectations developed in the paper. Several typical patterns such as a cline, depression, or a crazy-quilt are generated and their behavior characterized by this method. Computational and graphical methods allocate observed patterns to one of several types. The methods are general; three illustrative examples from biology and one from regional studies are furnished.     

Problems in the Building of Mathematical Models for Geographic Systems

Some basic concepts and principles of general systems theory applicable to geographical systems are formulated. A geosystem is viewed from the point of view of the controllable processes that convert it from one state to another and insure its self-regulation and stability. Since geographical systems derive energy from the surrounding environment and use it for their physical-chemical and biological functions, the structural elements of such systems behave thermodynamically like automata performing irreversible processes, and the laws of thermodynamics can therefore be applied to the functioning of such systems. A mathematical apparatus is demonstrated for the study migratory flows of mass and energy in geographical systems.     

A Family of Location Models for Multiple-Type Discrete Dispersion

One of the defining objectives in location science is to maximize dispersion. Facilities can be dispersed for a wide variety of purposes, including attempts to optimize competitive market advantage, disperse negative impacts, and optimize security. With one exception, all of the extant dispersion models consider only one type of facility, and ignore problems where multiple types of facilities must be located. We provide examples where multiple-type dispersion is appropriate and based on this develop a general class of facility location problems that optimize multiple-type dispersion. This family of models expands on the previously formulated definitions of dispersion for single types of facilities, by allowing the interactions among different types of facilities to determine the extent to which they will be spatially dispersed. We provide a set of integer-linear programming formulations for the principal models of this class and suggest a methodology for intelligent constraint elimination. We also present results of solving a range of multiple-type dispersion problems optimally and demonstrate that only the smallest versions of such problems can be solved in a reasonable amount of computer time using general-purpose optimization software. We conclude that the family of multiple-type dispersion models provides a more comprehensive, flexible, and realistic framework for locating facilities where weighted distances should be maximized, when compared with the special case of locating only a single type of facility.     

Location-Allocation Models for Control of Forest Fires by Air Tankers

Four air tanker location-allocation models are considered as tools for suppression of forest fires. The models are tested and compared using forest fire data for Alberta. The results show that fire location patterns can vary considerably over the short term and that not responding to such variation by optimally relocating air tanker groups could be very costly in terms of losses to fire. We argue that an improved location-allocation model can serve as the heart of an optimal air tanker relocation system and suggest the basic requirements for developing such a model.
Quatre modèles localisation-allocation pour avions-citerne sont considérés comme des outils servant dans la lutte contre les incendies forestiers. Les différents modèles sont mis a l'tpreuve et comparts utilisant des données recuillies lors d'incendies forestiers survenus en Alberta. Les rtsultats obtenus montrent que les modèles de localisation de feu peuvent varier considérablement B court terme et que de ne pas se soucier de telles variations par une relocalisation optimale des groupes d'avions-citerne pourait s'avérer trts couteux en terme de pertes dues aux incendies forestiers. Nous soutenons qu'un modtle localisation-allocation amtliort peut constituer le coeur d'un systtme de relocalisation optimal pour avions-citerne et suggérons les conditions fondamentales requises pour le dèveloppement d'un tel modèle.     

Computational Comparison of Five Maximal Covering Models for Locating Ambulances

This article categorizes existing maximum coverage optimization models for locating ambulances based on whether the models incorporate uncertainty about (1) ambulance availability and (2) response times. Data from Edmonton, Alberta, Canada are used to test five different models, using the approximate hypercube model to compare solution quality between models. The basic maximum covering model, which ignores these two sources of uncertainty, generates solutions that perform far worse than those generated by more sophisticated models. For a specified number of ambulances, a model that incorporates both sources of uncertainty generates a configuration that covers up to 26% more of the demand than the configuration produced by the basic model.     

No passion for Brownlow: Models of staffing the presidency

Post‐Watergate critics of the American presidency have directed much attention to the problem of controlling the White House staff. This paper argues that their proposals have ignored an implicit lesson contained in the Brownlow Report of 1937 and that it is unrealistic to build the Cabinet and department secretaries into any model of white House staff functions, particularly as a constraint mechanism on the staff. Such proposals understate the political role of the staff and approaches to reform must search for a political rather than an institutional response.     

A Classification of Models in Economic Geography

Models used in economic geography are classified on the basis of a general scientific classification of models which distinguishes two broad categories: ideal and material models. Ideal models are further categorized as visual, symbolic, and mathematical models, and material models as natural, physical, and mathematical models. Examples of each type are suggested. Other possible typologies of models can be devised; for example, logical, graphic, and mathematical models, representing a logical progression of scientific research. Models can be divided into general and particular models, depending on whether they treat aggregates or individual aspects. The complete model of a regional territorial-production complex would be a system of general and particular models. In terms of content, models can be classified as structural, functional, or synthetic (structural-functional) models. Finally, there could be a typology distinguishing static and dynamic models, nonoptimized and optimized models, and varying categories of prediction (models of an existing situation, planning models, predictive models).     

Models of Space Searching in Urban Areas

City dwellers occasionally must seek jobs, dwellings, or particular services or goods. Two very different ways exist by which the individual may conduct such a search. Lacking prior information, the person may elect to visit perceived possible locations until an appropriate one is found. Alternatively, an address may first be ascertained and then visited by finding a path to it. Clearly, there is a substantial difference between these two methods in terms of the amount of spatial movement they require in order to satisfy the searcher's needs. In this paper, this difference is modeled for situations that vary in terms of the density of acceptable end points of the search, as well as in characteristics of the signs of these end points, their patterns, and the level of information with which the searcher may begin.     

The Use of Electric Models in Geography

The use of electrical models, such as conducting sheet analogues, in geography is based on the fact that a wide variety of problems, say, the flow of groundwater and an electrical current, are founded on the same set of differential equations. The technique of electrical analogues is found to be useful in the solution of a number of geographical problems that cannot always be handled effectively by electronic computers. For example, conducting sheet analogues can be used to obtain map transformations in which area is proportional to the magnitude of a particular mapped feature, for example, equidemic projections in which countries or continents are mapped on the scale of their population density. Other problems that may be suitable for analogue simulation include those involving population potential as well as those in which optimization calls for least cost or least effort.     

近现代工业遗产保护模式初探

工业遗产的形态多种多样,根据其不同的保护等级、城市发展及环境生态保护的需要,工业遗产的保护模式也有多种,不同模式都有其针对性强、效益明显的保护对象,但也各有利弊。以博物馆模式为例,其对工业遗产的保护与利用都比较到位,也易于建设,但因经济盈利空间有限,往往会造成政府财政的压力。此类问题影响着工业遗产保护的质量与效益,应该引起我们对工业遗产保护与再利用模式的深入思考。     

Symptoms of Instability in Models of Spatial Dependence

In recent years, there has been a growing interest in the problems caused by the existence of instability in cross-sectional regressions. The results about local autocorrelation measures are part of this debate, as are the proposals concerning the concept of geographically weighted regressions. This article also deals with the problem of stability (or the lack thereof), but focusing the discussion on the supposition of constancy in the parameter of spatial dependence. In most cases, this assumption is treated, with the risks that this involves, as a maintained hypothesis, which should be ascertained before continuing with the modeling exercise. In the article, we present a simple heterogeneity test for this type of parameters, based on the Lagrange Multiplier principle. To illustrate its use, we take the distribution of per capita income among the European regions as our discussion case. According to our results, there are clear signs of structural breaks in the spatial distribution of this variable and the scale factor and the autocorrelation coefficient appear to be principal actors.