Geographical Analysis

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).

Some earth surface systems apparently exhibit deterministic chaos, where small differences in initial conditions produce increasingly divergent results. This casts doubt on the venerable concept of equifinality, whereby surface features converge to similar forms. However, chaotic systems exhibit a broader‐scale order, and their complex patterns occur within well‐defined limits. This broad‐scale order arising from smaller‐scale chaos produces simplexity, where simple rules and regularities emerge from underlying complexity, when the broad‐scale structures are independent of the fine‐scale details. Chaos precludes equifinality, sensu stricto, at certain scales, but simplexity produces equifinality at others. Simplexity is illustrated in a case study of soil‐landform relationships.

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.

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least‐squares dummy estimator, the models are first‐differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first‐differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre‐sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.

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.

Analytical methods for evaluating accessibility have been based on a spatial logic through which the impedance of distance shapes mobility and urban form through processes of locational and travel decision making. These methods are not suitable for understanding individual experiences because of recent changes in the processes underlying contemporary urbanism and the increasing importance of information and communications technologies (ICTs) in people's daily lives. In this paper we argue that analysis of individual accessibility can no longer ignore the complexities and opportunities brought forth by these changes. Further, we argue that the effect of distance on the spatial structure of contemporary cities and human spatial behavior has become much more complicated than what has been conceived in conventional urban models and concepts of accessibility. We suggest that the methods and measures formulated around the mid‐twentieth century are becoming increasingly inadequate for grappling with the complex relationships among urban form, mobility, and individual accessibility. We consider some new possibilities for modeling individual accessibility and their implications for geographical analysis in the twenty‐first century.

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.

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.