Showing papers in "Geographical Analysis in 2010"

Local Indicators of Spatial Association—LISA

Abstract: The capabilities for visualization, rapid data retrieval, and manipulation in geographic information systems (GIS) have created the need for new techniques of exploratory data analysis that focus on the “spatial” aspects of the data. The identification of local patterns of spatial association is an important concern in this respect. In this paper, I outline a new general class of local indicators of spatial association (LISA) and show how they allow for the decomposition of global indicators, such as Moran's I, into the contribution of each observation. The LISA statistics serve two purposes. On one hand, they may be interpreted as indicators of local pockets of nonstationarity, or hot spots, similar to the Gi and G*i statistics of Getis and Ord (1992). On the other hand, they may be used to assess the influence of individual locations on the magnitude of the global statistic and to identify “outliers,” as in Anselin's Moran scatterplot (1993a). An initial evaluation of the properties of a LISA statistic is carried out for the local Moran, which is applied in a study of the spatial pattern of conflict for African countries and in a number of Monte Carlo simulations.

The Analysis of Spatial Association by Use of Distance Statistics

Abstract: Introduced in this paper is a family of statistics, G, that can be used as a measure of spatial association in a number of circumstances. The basic statistic is derived, its properties are identified, and its advantages explained. Several of the G statistics make it possible to evaluate the spatial association of a variable within a specified distance of a single point. A comparison is made between a general G statistic and Moran’s I for similar hypothetical and empirical conditions. The empirical work includes studies of sudden infant death syndrome by county in North Carolina and dwelling unit prices in metropolitan San Diego by zip-code districts. Results indicate that G statistics should be used in conjunction with I in order to identify characteristics of patterns not revealed by the I statistic alone and, specifically, the G i and G i ∗ statistics enable us to detect local “pockets” of dependence that may not show up when using global statistics.

Local Spatial Autocorrelation Statistics: Distributional Issues and an Application

Abstract: The statistics Gi(d) and Gi*(d), introduced in Getis and Ord (1992) for the study of local pattern in spatial data, are extended and their properties further explored. In particular, nonbinary weights are allowed and the statistics are related to Moran's autocorrelation statistic, I. The correlations between nearby values of the statistics are derived and verified by simulation. A Bonferroni criterion is used to approximate significance levels when testing extreme values from the set of statistics. An example of the use of the statistics is given using spatial-temporal data on the AIDS epidemic centering on San Francisco. Results indicate that in recent years the disease is intensifying in the counties surrounding the city.

Geographically Weighted Regression: A Method for Exploring Spatial Nonstationarity

Abstract: Spatial nonstationarity is a condition in which a simple “global” model cannot explain the relationships between some sets of variables. The nature of the model must alter over space to reflect the structure within the data. In this paper, a technique is developed, termed geographically weighted regression, which attempts to capture this variation by calibrating a multiple regression model which allows different relationships to exist at different points in space. This technique is loosely based on kernel regression. The method itself is introduced and related issues such as the choice of a spatial weighting function are discussed. Following this, a series of related statistical tests are considered which can be described generally as tests for spatial nonstationarity. Using Monte Carlo methods, techniques are proposed for investigating the null hypothesis that the data may be described by a global model rather than a non-stationary one and also for testing whether individual regression coefficients are stable over geographic space. These techniques are demonstrated on a data set from the 1991 U.K. census relating car ownership rates to social class and male unemployment. The paper concludes by discussing ways in which the technique can be extended.

Space-time and integral measures of individual accessibility: a comparative analysis using a point-based framework

Abstract: Conventional integral measures of accessibility, although valuable as indicators of place accessibility, have several limitations when used to evaluate individual accessibility. Two alternatives for overcoming some of the difficulties involved are explored in this study. One is to adapt these measures for evaluating individual accessibility using a disaggregate, nonzonal approach. The other is to develop different types of measures based on an alternative conceptual framework. To pursue the former alternative, this study specifies and examines eighteen gravity-type and cumulative-opportunity accessibility measures using a point-based spatial framework. For the latter option, twelve space-time accessibility measures are developed based on the construct of a prism-constrained feasible opportunity set. This paper compares the relationships and spatial patterns of these thirty measures using network-based GIS procedures. Travel diary data collected in Columbus, Ohio, and a digital data set of 10,727 selected land parcels are used for all computation. Results of this study indicate that space-time and integral indices are distinctive types of accessibility measures which reflect different dimensions of the accessibility experience of individuals. Since space-time measures are more capable of capturing interpersonal differences, especially the effect of space-time constraints, they are more “gender sensitive” and helpful for unraveling gender/ethnic differences in accessibility. An important methodological implication is that whether accessibility is observed to be important or different between individuals depends heavily on whether the measure used is capable of revealing the kind of differences the analyst intends to observe.

Lagrange Multiplier Test Diagnostics for Spatial Dependence and Spatial Heterogeneity

Abstract: Several diagnostics for the assessment of model misspecification due to spatial dependence and spatial heterogeneity are developed as an application of the Lagrange Multiplier principle. The starting point is a general model which incorporates spatially lagged dependent variables, spatial residual autocorrelation and heteroskedasticity. Particular attention is given to tests for spatial residual autocorrelation in the presence of spatially lagged dependent variables and in the presence of heteroskedasticity. The tests are formally derived and illustrated in a number of simple empirical examples.

Properties of Tests for Spatial Dependence in Linear Regression Models

Abstract: 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).

Generating Models by the Expansion Method: Applications to Geographical Research*

Abstract: Analytical research in the social sciences and elsewhere calls for construct- ing models, and then testing and modifying them through a recursive open- ended process. While a great deal of attention has been placed on ways and means for the quantitative testing of models, the segments of the research process that are concerned with generating and modifying them has by and large been left unexplored. Certainly, there is a great deal of merit in the widely held belief that the selection of the right variables and their combina- tion into suitable models is ultimately due to a creative flair that cannot be decomposed into modules and routinized. Nevertheless it might prove use- ful to identify recurring procedures for generating, modifying and mending models that have been or could have been applied in unrelated contexts and that can be decomposed into a sequence of clearly identifiable steps. There can be no guarantee that useful models will ever be arrived at through the application of such procedures. On the other hand they might provide useful guidelines and frames of reference, and perhaps could stimulate a greater awareness of “how” creative research is carried out.

Specification of the World City Network

Abstract: World cities are generally deemed to form an urban system or city network but these are never explicitly specified in the literature. In this paper the world city network is identified as an unusual form of network with three levels of structure: cities as the nodes, the world economy as the supranodal network level, and advanced producer service firms forming a critical subnodal level. The latter create an interlocking network through their global location strategies for placing offices. Hence, it is the advanced producer service firms operating through cities who are the prime actors in world city network formation. This process is formally specified in terms of four intercity relational matrices—elemental, proportional, distance, and asymmetric. Through this specification it becomes possible to apply standard techniques of network analysis to world cities for the first time. In a short conclusion the relevance of this world city network specification for both theory and policy-practice is briefly discussed.

Systems Approach to a Theory of Rural‐Urban Migration

Abstract: Few of the theoretical models provided thus far have considered migrations especially rural urban migration as a spatial process whose dynamics and spatial impact must form part of any comprehensive understanding of the phenomenon. It is the main contention of this discussion that this can best be realized within the framework of general systems theory. This approach requires that a particular complex of variables be recognized as a system possessing certain properties which are common to many other systems. It has the fundamental advantage of providing a conceptual framework within which a whole range of questions relevant to an understanding of the structure and operation of other systems can be asked of the particular phenomenon under study. Emphasis is on a verbal analysis of the ways in which the system operates. A systems approach to rural urban migration is concerned with why people migrate and with all the implications and ramifications of the process. The approach is designed to answer such questions as: why and how does an essentially rural person become a permanent city resident; what changes does he/she undergo in the process; and what effects have these changes both on the rural area from which he/she comes and on the city to which the individual moves. The basic elements in the system of migration are shown in a figure which identifies first the potential migrant who is being encouraged to migrate by stimuli from the environment. Within the systems framework attention is focused not only on the migrant but also on the various institutions (subsystems) and the social economic and other relationships (adjustment mechanisms) which are an integral part of the process of the migrants transformation. The 2 most important subsystems are the rural and urban control subsystems. A system comprises not only matter (the migrant the institutions the various organizations) but also energy. In the physical sense energy is simply the capacity of a given body to do work. 2 forms of energy are relevant here: potential energy and kinetic energy. In a theory of rural urban migration potential energy can be likened to the stimuli acting on the rural individual to move. Once a person has been successfully dislodged from the rural area it can be assumed that he/she is translating potential energy into its kinetic form. The major issues concern not only the act of moving but also the cost distance and the direction of the movement. Rural urban migration is an open system involving not only an exchange of energy but also of matter (in this case persons) with the environment. 1 of the concomitants of the continued interaction between the system and its environment will be the phenomenon of growth in the system.

Maximum‐Difference Barriers: An Alternative Numerical Regionalization Method*

Abstract: Regionalization is the primary classification problem in geography, although other typologies are sometimes demanded by specific research endeavors. Groupings of area units can produce either contiguous or fragmented patterns. Discontiguous regionalizations may have the advantage of placing truly alike areal units in the same category and are obviously necessary when the similarity of distant places is sought. The same number of contiguous regions, on the other hand, will most likely produce a more regular map pattern, thereby facilitating the transferral of the printed map into a more coherent and more lasting mental image.' Furthermore, many problems, particularly those partitioning space for administrative purposes, demand contiguity. Although some within-group homogeneity is often lost by imposing contiguity, this is a difficulty only for situations with relatively low spatial consistency.a This loss of homogeneity may well be offset by the perceptual advantage of simplicity. Previous quantitative approaches to regional clustering have largely achieved contiguity by prohibiting linkages from occurring unless the two places abut. This contiguity restriction has been employed most often with hierarchical grouping procedures in which the clustering of N places proceeds through N 1 levels of classification to the ultimate aggregation of all units into a single group? At

Spatial Empirics for Economic Growth and Convergence

Abstract: This paper suggests some new empirical strategies for analyzing the evolution of regional income distributions over time and space. These approaches are based on extensions to the classical Markov transition matrices that allow for a more comprehensive analysis of the geographical dimensions of the transitional dynamics. This is achieved by integrating some recently developed local spatial statistics within a Markov framework. Insights to not only the frequency with which one economy may transition across different classes in the income distribution, but also how those transitions may or may not be spatially dependent are provided by these new measures. A number of indices are suggested as ways to characterize the space-time dynamics and are illustrated in a case study of U. S. regional income dynamics over the 1929–1994 period.

Local Forms of Spatial Analysis

Abstract: Local forms of spatial analysis focus on exceptions to the general trends represented by more traditional global forms of spatial analysis. There is currently a rapid expansion in the development of such techniques but their history almost exactly parallels that of Geographical Analysis, with the first examples of local analysis appearing in the late 1960s. Indeed, Geographical Analysis has published many of the significant contributions in this field. This paper reviews the development of local forms of spatial analysis and assesses the current situation. Following a discussion on the nature and importance of local analysis, examples are given of local forms of point pattern analysis; local graphical approaches; local measures of spatial dependency; the spatial expansion method; adaptive filtering; multilevel modeling; geographically weighted regression; random coefficients models; autoregressive models; and local forms of spatial interaction models.

Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models

Abstract: A Gibbs sampling (Markov chain Monte Carlo) method for estimating spatial autoregressive limited dependent variable models is presented. The method can accommodate data sets containing spatial outliers and general forms of non-constant variance. It is argued that there are several advantages to the method proposed here relative to that proposed and illustrated in McMillen (1992) for spatial probit models.

The Formation of a Composite Urban Image

Abstract: Since image formation depends on the cognitive organization of perceptions, a change in the individual's available cognitive structure may affect his or her perceptual selectivity. This, in turn, might lead to a reconstruction of the image through selected fields of attention. Although this process is widely accepted, little is known of its neurophysiology, and the formation of an image, therefore, is drawn inferentially from introspective reports. This paper presents, accordingly, a conception of image formation and tests it with a model presenting paths among locational and nonlocational environmental stimuli and an introspective measure of a composite urban image. Changes in the paths due to information and personal attributes that reflect different realms (for example, fields of attention) are further examined with an expanded version of the model. Across the realms, the perceived residential appeal and the perceived level of activities are the main determinants of the composite urban image. Information and personal attributes not only affect the mix of image determinants, but also rearrange their relative effects on the emerging image.

Assessing the Significance of a Spatial Correlogram

Abstract: Simulations comparing the power of the Q-test to the power of several other techniques under several alternative hypotheses reveal the following. The decision rule involving inspection of only the lag-1 autocorrelation coefficient is insensitive to certain forms of spatial dependence, for example, dependence involving interactions that are strongest at high-order lags. A modified Kooijman's (1976) technique is roughly equal in power to the other methods investigated, but requires a simulation for each correlogram tested. Kooijman's original recommendation for estimating the variance of I/max/ can lead to negative variance estimates and should therefore not be used. The Sidak (1967) and Bonferroni methods, which are computationally very simple, are preferable to the Q-test when there are few distance classes and weak spatial pattern. As pattern intensity and number of distance classes increase, the Q-test becomes more powerful.

A Procedure to Generate Thiessen Polygons

Abstract: An algorithm to generate Thiessen diagrams for a set of n points defined in the plane is presented. First, existing proximal polygon computation procedures are reviewed and terms are defined. The algorithm developed here uses a rectangular window within which the Thiessen diagram is defined. The computation of Thiessen polygons uses an iterative walking process whereby the processing starts at the lower left corner of the diagram and proceeds toward the right top corner. The use of a sorted point sequence and dynamical core allocation provide for efficient processing. The presentation is concluded by the discussion of an implementation of the algorithm in a FORTRAN program.

Dynamic models in space and time

Abstract: This paper presents a first-order autoregressive distributed lag model in both space and time. It is shown that this model encompasses a wide series of simpler models frequently used in the analysis of space-time data as well as models that better fit the data and have never been used before. A framework is developed to determine which model is the most likely candidate to study space-time data. As an application, the relationship between the labor force participation rate and the unemployment rate is estimated using regional data of Germany, France and the UK derived from Eurostat, 1983-1993.

Quick Computation of Spatial Autoregressive Estimators

Abstract: Spatial estimators usually require the manipulation of n2 relations among n observations and use operations such as determinants, eigenvalues, and inverses whose operation counts grow at a rate proportional to n3. This paper provides ways to quickly compute estimates when the dependent variable follows a spatial autoregressive process, which by appropriate specification of the independent variables can subsume the case when the errors follow a spatial autoregressive process. Since only nearby observations tend to affect a given observation, most observations have no effect and hence the spatial weight matrix becomes sparse. By exploiting sparsity and rearranging computations, one can compute estimates at low cost. As a demonstration of the efficacy of these techniques, the paper provides a Monte Carlo study whereby 3,107 observation regressions require only 0.1 seconds each when using Matlab on a 200 Mhz Pentium Pro personal computer. In addition, the paper illustrates these techniques by examining voting behavior across U.S. counties in the 1980 presidential election.

A Model of Pedestrian Route Choice and Demand for Retail Facilities within Inner-City Shopping Areas

Abstract: There are still only a few operational models of pedestrian movement. In particular, the gravity /entropy-maximizing model has received most attention. In this paper a descriptive model of pedestrian movement is presented. It can be considered as an extension of O'Kelly's model of the demand for retail facilities in the presence of multistop, multipurpose trips. The model basically consists of three submodels: one for destination choice, one for route choice, and one for impulse stops. Together, these submodels describe/predict the total demand for retail facilities within inner-city shopping areas. The model is applied to data from the city of Maastricht, The Netherlands.

A Dynamic Model of Growth in a Central Place System

Abstract: A model is developed in which the change in the population distribution of a region is linked to the employment pattern, and this latter in turn to the population distribution through the concepts of central place theory. The result is a dynamic model of interacting urban centers in which the fluctuations (the exact history) of the system play a vital role, and with which the effect of an infrastructure decision can be estimated in the long term.

The K-Function Method on a Network and Its Computational Implementation

Abstract: This paper proposes two statistical methods, called the network K-function method and the network cross K-function method, for analyzing the distribution of points on a network. First, by extending the ordinary K-function method defined on a homogeneous infinite plane with the Euclidean distance, the paper formulates the K-function method and the cross K-function method on a finite irregular network with the shortest-path distance. Second, the paper shows advantages of the network K-function methods, such as that the network K-function methods can deal with spatial point processes on a street network in a small district, and that they can exactly take the boundary effect into account. Third, the paper develops the computational implementation of the network K-functions, and shows that the computational order of the K-function method is O(n2Q log nQ) and that of the network cross K-function is O(nQ log U3Q), where nQ is the number of nodes of a network.

The Effects of Data Aggregation in Statistical Analysis

Abstract: The problem of ecological correlation is now widely recognized but detailed analyses of the effects of aggregation on correlation and regression coefficients are rare. A short review of the aggregation problem is followed by an analysis of the specific effect of proximity aggregation on the slope coefficient of a bivariate linear model using data drawn from the Los Angeles Metropolitan region. The evidence suggests that changes in the slope coefficient are best related to the manner in which the covariation between the independent and dependent variables changes with increased aggregation.

Modeling the Uncertainty of Slope and Aspect Estimates Derived from Spatial Databases

Abstract: Estimates of slope and aspect are commonly made from digital elevation models (DEMs), and are subject to the uncertainty present in such models We show that errors in slope and aspect depend on the spatial structure of DEM errors We propose a general-purpose model of DEM errors in which a spatially auto-regressive random field is added as a disturbance term to elevations In addition, we propose a general procedure for propagating such errors through GIS operations In the absence of explicit information on the spatial structure of DEM errors, we demonstrate the potential utility of a worst-case analysis A series of simulations are used to make general observations about the nature and severity of slope and aspect errors

Activity Levels at Hub Facilities in Interacting Networks

Abstract: Hubs are a special type of central facility which are designed to act as switching points for intemodal flows. For instance, a set of ten interacting cities might all be connected to one of two major hubs. All flows between the cities would then be routed via the hubs. There is an obvious saving in the number of routes necessary to interconnect the cities when hubs are utilized, with a concomitant high level of activity at the facilities. This paper takes a heuristic approach to the evaluation of networks and hub locations to find locally optimal designs. It is shown that minimization of transportation costs may require assignment of nodes to a facility other than the nearest. A discount on the interhub transportation costs promotes a wider spacing of facilities. In a system with several hubs, minimization of total hub usage tends to concentrate demand very heavily into one central facility.