Exploring Relationships Between the Global and Regional Measures of Spatial Autocorrelation

Abstract The objective of this research is to investigate dimensions of geographic variation in spatial dependency contained within large multilevel data sets. We calculate 1990 population density by census block group, county, and state for the 48 coterminous states and the District of Columbia of the United States, calculations of interest to a wide variety of spatial scientists. We explore relations between these levels and their variation across the nation. The empirical findings generated by this work furnish implications concerning the Modifiable Areal Unit Problem (MAUP), spatial autocorrelation statistics, scale effects, and resolution.     

Parameter mixing errors within a measuring volume with applications to incoherent scatter

The effect on parameter error estimates resulting from parameter variations within the measuring volume under consideration is studied in the framework of linear statistical inversion theory. It is shown that using estimates for the parameter averages is equivalent to having the theory corrected by the covariances of the variables coupled with the second derivatives of the theory function. If the parameter distributions were known exactly, this would only introduce a bias in the linear theory and hence a systematic error in the parameter centre point estimates. When the distributions are not known exactly, there is another source of error consisting of the uncertainties in the parameter variation estimates. This leads to new error bounds on the allowed parameter variability within the volume under consideration if some prescribed accuracy in the parameter average estimates is required. These considerations are applied to incoherent scatter (IS) radar measurements, where it is important to be able to estimate the effect of integrating both in space and time over a volume with varying parameters in order to obtain spectra or autocorrelation functions. Numerical examples are given in the case of the O⁺ content estimates in measurements with the EISCAT UHF radar, when for example the ion temperature varies over the integration ranges. The results obtained may be used in the design of experiments when high resolution composition measurements are required.     

The Modifiable Areal Unit Problem,in a Regression Model Whose Independent Variable Is a Distance from a Predetermined Point

This paper deals with the modifiable areal unit problem in the context of a regression model where a dependent variable is an attribute value (say, income) of an atomic data unit (say, a household) and an independent variable is a distance from a predetermined point (say, a central business district) to the atomic data unit (a disaggregated model). We apply this disaggregated model to spatially aggregated data in which the dependent variable is the average income over a spatial unit and the independent variable is the average distance from each household in a spatial unit to the predetermined point (an aggregated model). First, estimating the slope coefficient by the least squares method, we prove that the variance of the estimator for the slope coefficient in the aggregated model is larger than that in the disaggregated model. Second, focusing on variations in the variance of the estimator for the slope coefficient in the aggregated model with respect to the number of zones, we obtain the number of zones in which the variance is close to that in the disaggregated model. Third, we obtain the zoning system that has the minimum variance for a fixed number of zones. We also calculate the maximum variance in order to examine the range of the variance.     

Mapping Local‐Scale Ecological Research to Aid Management at Landscape Scales

Natural resource management is typically defined by landscape‐scale management zones, such as the Catchment Management Authority boundaries of the southern Murray‐Darling Basin in Australia. Ecological research generally deals with local‐scale phenomena, with studies at the scale of such landscape management units arising only recently. We developed a method that links local‐scale ecological research to landscape‐scale management zones, which is presented here as a geographical bibliographic database. This research proceeded in four phases. First, we assessed three decades of ecological research in the Goulburn‐Broken Catchment in Victoria, Australia, using this method, revealing the locations where research has taken place across the landscape, and the research themes dominant in different bioregions. Second, we assessed the purposes to which the method could be applied. Third, we tested the method against one of these potential purposes to review ecological research in a subcatchment case study. Last, we interrogated the method to answer an ecological question. This methodological analysis demonstrated that mapping ecological research in this way allows the user to identify geographic gaps in research coverage, assist in limiting search results to a location of interest and to address location‐specific ecological questions. In combination with landscape classification methods, such as biogeographic regionalisation units, this method can be used to evaluate research coverage across similar ecological communities.     

Characteristics of variations of temperature regime and circulation in the upper atmosphere in middle and high latitudes

Statistical characteristics of the variability of meteorological parameters of the stratosphere and mesosphere are reviewed for various latitude belts in the winter and summer seasons. Rocketsonde data were used to calculate mean and median values, variance of the meteorological parameters, excess and asymmetry of empirical distributions, probability of deviations and auto- and mutual correlation functions, which enabled the variability of atmospheric processes in various latitude belts to be characterized. The resolution of a sequence of vertical profiles of temperature, pressure, density and wind components with the help of natural orthogonal components made possible the estimation of the scale of wave perturbations responsible for the variations of the parameters in the middle atmosphere.     

A Surface-Based Approach to Measuring Spatial Segregation

Quantitative indices of residential segregation have been with us for half a century, but suffer significant limitations. While useful for comparison among regions, summary indices fail to reveal spatial aspects of segregation. Such measures generally consider only the population mix within zones, not between them. Zone boundaries are treated as impenetrable barriers to interaction between population subgroups, so that measurement of segregation is constrained by the zoning system, which bears no necessary relation to interaction among population subgroups. A segregation measurement approach less constrained by the chosen zoning system, which enables visualization of segregation levels at the local scale and accounts for the spatial dimension of segregation, is required. We propose a kernel density estimation approach to model spatial aspects of segregation. This provides an explicitly geographical framework for modeling and visualizing local spatial segregation. The density estimation approach lends itself to development of an index of spatial segregation with the advantage of functional compatibility with the most widely used index of segregation (the dissimilarity index D ). We provide a short review of the literature on measuring segregation, briefly describe the kernel density estimation method, and illustrate how the method can be used for measuring segregation. Examples using a simulated landscape and two empirical cases in Washington, DC and Philadelphia, PA are presented.     

School Choice as a Latent Variable: Estimating the “Complier Average Causal Effect” of Vouchers in Charlotte

Randomized field trials of school voucher policy interventions face major statistical hurdles in the measurement of a voucher effect on student achievement. Selection bias undermines the benefits of randomization when the treatment, a random offer of a voucher, is declined by participants who systematically differ from those who accept. This article argues that the complier average causal effect (CACE) is the parameter of interest in voucher evaluations. As an example, the CACE is estimated using data from a small, one‐year field trial of vouchers in Charlotte, NC. In this estimation, voucher impacts in Charlotte are positive, but appear to be moderated by the probability of compliance. For math achievement, maximum likelihood CACE estimates are smaller and insignificant compared to intention to treat and instrumental variable estimates of mean treatment effects.     

幸福地理学研究中的时空间尺度陷阱

尺度是地理学的核心概念,但是在近年兴起的关于幸福地理学研究中对尺度问题的讨论仍属空白。本文在借鉴此前地理学尺度研究成果的基础上,结合现有幸福感的理论和实证研究,分别从现实尺度、分析尺度和实践尺度出发,系统反思了幸福感研究中的尺度陷阱。首先,对区域幸福感水平的度量需要选择汇总尺度和方法,影响幸福感的地理因素本身和地理环境对幸福感的影响也有其特定尺度。第二,分析地理环境对幸福感的影响时,既要合理处理研究结论的尺度变异性和不同时空间尺度上研究结论的整合问题,也要防止出现真实尺度与分析尺度之间出现错位。第三,个人会通过家庭内部成员间取舍、社会比较等尺度重构和尺度政治方式提升幸福感,而政府在试图改善居民幸福感时也需要选择合理的空间干预尺度。幸福感研究必须跳出各类尺度陷阱,探究影响幸福感的地理要素的真实尺度及合理的分析尺度,并妥善解决个人和政府在提升幸福感时面临的尺度政治争端。     

GRAVITY AND SPATIAL STRUCTURE: THE CASE OF INTERSTATE MIGRATION IN MEXICO*

ABSTRACT The estimation of gravity models of internal (aggregate) place‐to‐place migration is plagued with endogeneity (omitted‐variable) biases if the unobserved effects of spatial structure are not accounted for. To address this econometric problem, this paper presents a more general specification of the gravity model, which allows for (bilateral) parameter heterogeneity across individual migration paths—along with (unilateral) origin‐ and destination‐specific effects. The resultant “three‐way fixed‐effects” (3FE) model is applied for an analysis of interstate migration in Mexico based on cross‐sectional data. To overcome parameter‐dimensionality problems (due to limited or incomplete information), the 3FE model is estimated using the Generalized Maximum Entropy (GME) estimator. The empirical implications of this new modeling strategy are illustrated by contrasting the 3FE‐GME estimates with those for the traditional and two‐way fixed‐effects (2FE) models. The former are far more plausible and intuitively interpretable than their traditional and 2FE counterparts, with parameter estimates changing in expected directions. The (average) effect of the migrant stock is markedly smaller than usually estimated, providing a more realistic measure of network‐induced migration. Migration outflows from centrally located origins have significantly steeper distance decay. Path‐specific distance effects exhibit directional asymmetries and spatial similarities.     

ISSUES IN SPATIAL DATA ANALYSIS

ABSTRACT.  Misspecified functional forms tend to produce biased estimates and spatially correlated errors. Imposing less structure than standard spatial lag models while being more amenable to large datasets, nonparametric and semiparametric methods offer significant advantages for spatial modeling. Fixed effect estimators have significant advantages when spatial effects are constant within well-defined zones, but their flexibility can produce variable, inefficient estimates while failing to account adequately for smooth spatial trends. Though estimators that are designed to measure treatment effects can potentially control for unobserved variables while eliminating the need to specify a functional form, they may be biased if the variables are not constant within discrete zones.     

Impacts of Spatial Autocorrelation in Georeferenced Beta and Multinomial Random Variables

The literature is replete with acknowledgments that spatial autocorrelation (SA) inflates the variance of a random variable (RV), and that it also may alter other RV distributional properties. In most studies, impacts of SA have been examined only for the three most commonly used distributions: the normal, Poisson (and its negative binomial counterpart), and binomial distributions; much less is known about its effects on two other RVs that are utilized in GIScience research: the beta and the multinomial. The beta distribution—which is considered to be very flexible because it can mimic a uniform, exponential, sinusoidal, and normal RV—can be utilized to analyze the radiance of a remotely sensed image, for example. The multinomial distribution, a generalization of the binomial distribution, has been widely used for land use classification, and to describe land use change. The literature also suggests that RV impacts of negative SA, a neglected topic in spatial analysis, may differ from those of positive SA, at least for some RVs (e.g., the Poisson RV). The purpose of this article is to extend the investigation of effects of SA to beta and multinomial RVs, with both positive SA and negative SA assessed and contrasted with each other, using simulation experiments. The simulation experiments are designed to support this assessment. One of the major discoveries is that impacts of positive SA and negative SA behave similarly when a RV conforms to a normal distribution; however, maximum negative SA is unable to materialize for asymmetric RV, whereas positive SA always converges upon its maximum.     

Spatial Variability of Controls on Downstream Patterns of Sediment Storage: a Case Study in the Lane Cove Catchment,New South Wales,Australia

This study uses GIS techniques to examine the spatial distribution of stream power along major streamlines in the Lane Cove catchment in northern Sydney, Australia. Channel gradient estimates derived from a 5 m resolution digital elevation model (DEM) are combined with streamflow data to estimate stream power along river courses. Stream power and its constituent components are then related to a detailed field‐based assessment of sediment storage along the trunk stream and primary tributaries. At the catchment scale, sediment storage per unit length decreases as channel gradient and gross stream power increase. However, local controls such as variability in valley width and occurrence of confluence zones exert a greater influence upon sediment storage, disrupting systematic catchment‐wide relationships. The total volume of storage along each streamline has a strong linear relationship to the area of the subcatchment, but the distribution of sediment along streamlines varies between subcatchments. The GIS framework employed in this project allows generation of continuous, empirical data, thereby providing catchment‐specific predictive capacity that can accompany theoretical approaches to stream power modelling.     

RETURNS TO SCALE AND REGIONAL GROWTH: THE STATIC‐DYNAMIC VERDOORN LAW PARADOX REVISITED*

ABSTRACT It has long been an article of faith amongst regional economists that increasing returns to scale are necessary to explain the punctiform location of economic activity and population. However, there is no consensus in the empirical literature over whether returns to scale are constant or increasing. A notable example of this lack of agreement is provided by the static‐dynamic Verdoorn law paradox. While the dynamic Verdoorn law (specified using growth rates) yields estimates of substantial increasing returns to scale, the static Verdoorn law (specified using log‐levels) indicates only the presence of constant returns to scale. In this paper, we explain the static‐dynamic Verdoorn law paradox by showing that estimates of returns to scale obtained using the static law are subject to a spatial aggregation bias, which biases the estimates towards constant returns to scale. We illustrate our arguments by means of simulation exercises. The results obtained hold general lessons for applied economic analysis using spatial data.     

The recognition of multiple spatial patterns: a case study from the French upper paleolithic

A pattern recognition approach to spatial analysis is applied to artifact distributions from the Magdalenian site of Pincevent, Section 36. Patterning is investigated using a κ-means cluster analysis that permits iterative mapping of artifact distributions at several scales of spatial complexity. Multiple scales of patterning are recognized in the Pincevent distributions. These patterns are assessed in terms of those discovered by the excavators through intensive visual inspection of the materials. Basic concordance is seen between these two approaches. Finally, the analysis detects more detailed patterning. A relationship between artifact abundance and location seems to hold constant throughout the site.     

Heterogeneity of Attribute Sampling Error in Spatial Data Sets

This paper considers the standard error of the estimate of the mean of a spatially correlated variable in the case where data are obtained by a process of random sampling. Two distinct mean estimation problems are identified: estimating the area mean and estimating the population mean. Methods are described for obtaining standard error estimates in the two cases and, within the limits of publicly available information, the methods are implemented on average household income data at the census tract scale for Syracuse, New York. The purpose of the paper is to draw attention to issues of data precision in relation to sampled geographic information on averages and in particular to consider the problems of estimating standard errors using such data. The paper also examines the extent to which standard errors vary between census tracts.     

基于可达性与场强模型的中国地级以上城市空间场能测度

空间场能是区域中心城市借助区域联系通道带动腹地发展而产生的"势能差"的抽象表达,可有效刻画区域发展格局与空间差异。采用主成分分析法与指标体系计算城市结节性指数,借助ArcGIS软件平台,采用累积耗费距离法、K阶数据场和ESDA等方法,综合测度了中国287个地级以上城市可达性与空间场能,并分别从省域、市域、县域等单元探讨了中国东中西三大地带与南北场能差异的空间格局与演变特征。结果表明:中国地级以上城市的可达性条件不断改善,平均可达性时间从1991年的246.98min缩短为2010年的193.43min。空间场能显著增长且空间分异性显著,分布结构由单核向多极网络状形态转变。县域场能存在显著的空间极化现象,场能热点区域的分布呈现显著的热点-次热点-次冷点-冷点自东向西带状分布的格局。依据场能分析结果,将全国划分为3个一级经济区和26个二级城市经济区。     

A SPATIAL CLIFF‐ORD‐TYPE MODEL WITH HETEROSKEDASTIC INNOVATIONS: SMALL AND LARGE SAMPLE RESULTS*

ABSTRACT In this paper, we specify a linear Cliff‐and‐Ord‐type spatial model. The model allows for spatial lags in the dependent variable, the exogenous variables, and disturbances. The innovations in the disturbance process are assumed to be heteroskedastic with an unknown form. We formulate multistep GMM/IV‐type estimation procedures for the parameters of the model. We also give the limiting distributions for our suggested estimators and consistent estimators for their asymptotic variance‐covariance matrices. We conduct a Monte Carlo study to show that the derived large‐sample distribution provides a good approximation to the actual small‐sample distribution of our estimators.