Geographical Analysis

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 G_i 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.

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.

The statistics G_i(d) and G_i*(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.

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.

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.

Dựa trên một số lượng lớn các thí nghiệm mô phỏng Monte Carlo trên một mạng lưới đều đặn, chúng tôi so sánh các tính chất của kiểm tra Moran's I và kiểm tra nhân tử Lagrange đối với phụ thuộc không gian, tức là đối với cả tự tương quan lỗi không gian và biến phụ thuộc được suy rộng không gian. Chúng tôi xem xét cả độ chệch và sức mạnh của các bài kiểm tra cho sáu cỡ mẫu, từ hai mươi lăm đến 225 quan sát, cho các cấu trúc khác nhau của ma trận trọng số không gian, cho nhiều phân bố lỗi bên dưới, cho các ma trận trọng số được chỉ định sai, và cho tình huống khi có hiệu ứng ranh giới. Kết quả cung cấp chỉ số về các cỡ mẫu mà các tính chất tiệm cận của các bài kiểm tra có thể được xem là có hiệu lực. Chúng cũng minh họa sức mạnh của các bài kiểm tra nhân tử Lagrange để phân biệt giữa phụ thuộc không gian thực chất (trễ không gian) và phụ thuộc không gian như một phiền nhiễu (tự tương quan lỗi).

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.

Hägerstrand's time geography is a powerful conceptual framework for understanding constraints on human activity participation in space and time. However, rigorous, analytical definitions of basic time geography entities and relationships do not exist. This limits abilities to make statements about error and uncertainty in time geographic measurement and analysis. It also compromises comparison among different time geographic analyses and the development of standard time geographic computational tools. The time geographic measurement theory in this article consists of analytical formulations for basic time geography entities and relations, specifically, the space–time path, prism, composite path‐prisms, stations, bundling, and intersections. The definitions have arbitrary spatial and temporal resolutions and are explicit with respect to informational assumptions: there are clear distinctions between measured and inferred components of each entity or relation. They are also general ton‐dimensional space rather than the strict two‐dimensional space of classical time geography. Algebraic solutions are available for one or two spatial dimensions, while numeric (but tractable) solutions are required for some entities and relations in higher dimensional space.

The statistic known as Moran's I is widely used to test for the presence of spatial dependence in observations taken on a lattice. Under the null hypothesis that the data are independent and identically distributed normal random variates, the distribution of Moran's I is known, and hypothesis tests based on this statistic have been shown in the literature to have various optimality properties. Given its simplicity, Moran's I is also frequently used outside of the formal hypothesis‐testing setting in exploratory analyses of spatially referenced data; however, its limitations are not very well understood. To illustrate these limitations, we show that, for data generated according to the spatial autoregressive (SAR) model, Moran's I is only a good estimator of the SAR model's spatial‐dependence parameter when the parameter is close to 0. In this research, we develop an alternative closed‐form measure of spatial autocorrelation, which we call APLE, because it is an approximate profile‐likelihood estimator (APLE) of the SAR model's spatial‐dependence parameter. We show that APLE can be used as a test statistic for, and an estimator of, the strength of spatial autocorrelation. We include both theoretical and simulation‐based motivations (including comparison with the maximum‐likelihood estimator), for using APLE as an estimator. In conjunction, we propose the APLE scatterplot, an exploratory graphical tool that is analogous to the Moran scatterplot, and we demonstrate that the APLE scatterplot is a better visual tool for assessing the strength of spatial autocorrelation in the data than the Moran scatterplot. In addition, Monte Carlo tests based on both APLE and Moran's I are introduced and compared. Finally, we include an analysis of the well‐known Mercer and Hall wheat‐yield data to illustrate the difference between APLE and Moran's I when they are used in exploratory spatial data analysis.

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.