Local Indicators of Spatial Association—LISA

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.     

The Saddlepoint Approximation of Moran's I's and Local Moran's Ii's Reference Distributions and Their Numerical Evaluation

Global Moran's I and local Moran's I_i are the most commonly used test statistics for spatial autocorrelation in univariate map patterns or in regression residuals. They belong to the general class of ratios of quadratic forms for whom a whole array of approximation techniques has been proposed in the statistical literature, such as the prominent saddlepoint approximation by Offer Lieberman (1994). The saddlepoint approximation outperforms other approximation methods with respect to its accuracy and computational costs. In addition, only the saddlepoint approximation is capable of handling, in analytical terms, reference distributions of Moran's I that are subject to significant underlying spatial processes. The accuracy and computational benefits of the saddlepoint approximation are demonstrated for a set of local Moran's Ii statistics under either the assumption of global spatial independence or subject to an underlying global spatial process. Local Moran's I_i is known to have an excessive kurtosis and thus void the use of the simple approximation methods of its reference distribution. The results demonstrate how well the saddlepoint approximation fits the reference distribution of local Moran's I_i. Furthermore, for local Moran's I_i under the assumption of global spatial independence several algebraic simplifications lead to substantial gains in numerical efficiency. This makes it possible to evaluate local Moran's I_i's significance in large spatial tessellations.     

Spatial/temporal mismatch: a conflation protocol for Canada Census spatial files

The Canada census is one of the chief sources of demographic and socio-economic data for researchers in this country. Census variables are linked to geography files that allow researchers using geographic information systems (GIS) to view and analyze spatial data. Some of the most useful analysis, however, is based on changes in attribute values over time and space. Analysis of spatio- temporal events such as shifting migration patterns or changes in the distribution of health status permits a more dimensioned perspective than the viewing of static spatial phenomena. The analysis of spatio-temporal phenomena is limited by major changes in the spatial framework (e.g., location of road networks and other spatial entities) between national censuses. This paper addresses this limitation by (i) illustrating the extent of spatial mismatch between the 1996 and the 2001 census; (ii) examining attempts to rectify this problem in other jurisdictions and (iii) presenting a 'made-in-Canada' solution for conflation of census geometries. We believe that this solution will enhance the ability of Canadian researchers to describe and analyze socio-economic, health and demographic shifts across time and space. The research is supported by an ftp site for downloading the census geography rectification software presented in this paper.     

A Cost-Based Ripley’s <Emphasis Type="Italic">K</Emphasis> Function to Assess Social Strategies in Settlement Patterning

Most quantitative approaches to distributional analysis in archaeology assume a homogeneous study surface that is amenable to easy generalisations. This framework has been widely used to describe settlement processes, disregarding the spatial heterogeneity inherent to geographic reality. In other words, researchers have often assumed that the correlation between the elements of a spatial distribution is a function of the Euclidean distance (i.e. straight line distance) between them. Other archaeological studies have tested alternative measures to Euclidean distances, such as cost-based ones, both to describe optimal routes and to assess spatial autocorrelation in a point pattern. Nevertheless, until now there has been no suitable model to introduce these measures into spatial statistical equations. In order to overcome this obstacle, we approach the implementation problem inversely by embedding the spatial pattern under study into a Euclidean frame of reference based on its cost-distance pairwise matrix. This paper describes the application of this methodology on one of the main tools used by archaeologists to assess settlement patterns: Ripley’s K function. We present two case studies, covering both macroscale and mesoscale, with significant variations in the results depending on the use of the Euclidean or cost-based approach. Data, functions and results have been R-packaged for the sake of reproducibility and reusability, allowing other researchers to build upon our methods.     

A Note on the Extremities of Local Moran's Iis and Their Impact on Global Moran's I

By defining local Moran's I_i as a ratio of quadratic forms and making use of its overall additivity to match global Moran's I, we can identify spatial objects with a strong impact on global Moran's I. First, we concentrate on the spatial properties of local Moran's I_i expressed by the local linkage degree. Depending on whether we use the W- or C-coding of the spatial connectivity matrix, the variance of local Moran's I_i for a small local linkage degree will be either large or small. Note that spatial objects associated with a local Moran's I_i with a large variance affect the global statistic much more than spatial objects associated with a local Moran's I_i with a small variance. Counterintuitively, global Moran's I defined in the W-coding is most influenced by spatial objects with a small number of spatial neighbors. In contrast, spatial objects with a large number of spatial neighbors exert more impact on global Moran's I setup in the C-coding. Second, we investigate the impact of the empirical data on local Moran's I_i and show that local Moran's I_i will only be significant for extreme absolute residuals at and around the reference location. Clusters of average regression residuals cannot be detected by local Moran's I_i. Consequently, spatial cliques of extreme residuals contribute more to significance tests on global autocorrelation.     

VARIATIONAL PRINCIPLES AND CONSERVATION CONDITIONS IN VOLTERRA'S ECOLOGY AND IN URBAN RELATIVE DYNAMICS*

ABSTRACT. Relative spatial population dynamics are analyzed in this paper under Volterra-Lotka specifications. At first, the Volterra conservation conditions under absolute growth and their variational principles are reviewed, extended, and interpreted. Then, the relative dynamics are presented which demonstrate the presence of competitive exclusion. The main aim is to derive the variational principles underlying relative population dynamics. It is found that these principles produce an integrand, the stationary value of its integral being the cumulative entropy of the population distribution over a time horizon. Substantive interpretation of these results in accordance with optimization principles in economic theory is presented.     

The Spatial Distribution of French Agricultural Cooperatives: An Exploratory Spatial Data Analysis

Abstract

This paper studies the spatial dynamics of French agricultural cooperatives using the recently developed exploratory spatial data analysis tool. Analysis at the level of French districts in 1995 and 2005 shows strong evidence for global and local spatial autocorrelations in the geographical distribution of agricultural cooperatives. The presence of spatial disparities between French districts is confirmed by the detection of such specific spatial patterns as district clusters, a group of neighbouring districts with the same high or low level of agricultural cooperative activities. A typology of all the different Regions is developed to examine the specific spatial patterns of the agricultural cooperative activities. The results indicate that major organizational changes in cooperatives do not significantly modify the initial dynamics concerning the location of activities.     

Asymmetric incoherent scatter spectra from a relaxation collision model

A relaxation collision model for ion flow through a stationary neutral gas has been used to obtain ion velocity distributions and line-of-sight incoherent scatter spectra for a range of values of collision frequency and electric field. The mean velocity of the line-of-sight ion velocity distribution has been compared with the Doppler shift of the corresponding spectra. The latter is not always a good estimate of the former, because the ion velocity distribution in the plane perpendicular to the magnetic field direction is highly distorted. For ion-neutral collision frequency to ion gyrofrequency ratios 0.1 ≤V_i,/Ω_i≤0.5, the greatest inaccuracies in mean velocity estimation take place along the electric field direction, while for 0.5 ≤ V_i/Ω_i ≤ 1.0 the greatest inaccuracies occur across the electric field direction. These inaccuracies would be reduced but not eliminated in a more realistic model. At F-region altitudes, other processes must be invoked to explain observed asymmetrical spectra, but the comparison of mean line-of-sight ion velocity and spectrum Doppler shift may still have relevance.     

A Geographic Network Automata Approach for Modeling Dynamic Ecological Systems

Landscape connectivity networks are composed of nodes representing georeferenced habitat patches that link together based on a species’ maximum dispersal distance. These static representations cannot capture the complexity in species dispersal where the network of habitat patch nodes changes structure over time as a function of local dispersal dynamics. Therefore, the objective of this study is to integrate geographic information, complexity, and network science to propose a novel Geographic Network Automata (GNA) modeling approach for the simulation of dynamic spatial ecological networks. The proposed GNA modeling approach is applied to the emerald ash borer (EAB) forest insect infestation using geospatial data sets from Michigan, U.S.A. and simulates the evolution of the EAB spatiotemporal dispersal network structures across a large regional scale. The GNA model calibration and sensitivity analysis are performed. The simulated spatial network structures are quantified using graph theory measures. Results indicate that the spatial distribution of habitat patch nodes across the landscape in combination with EAB dispersal processes generate a highly connected small-world dispersal network that is robust to node removal. The presented GNA model framework is general and flexible so that different types of geospatial phenomena can be modeled, providing valuable insights for management and decision-making.     

BAYSIAN INFERENCE FOR ORDERED RESPONSE DATA WITH A DYNAMIC SPATIAL‐ORDERED PROBIT MODEL

ABSTRACT Many databases involve ordered discrete responses in a temporal and spatial context, including, for example, land development intensity levels, vehicle ownership, and pavement conditions. An appreciation of such behaviors requires rigorous statistical methods, recognizing spatial effects and dynamic processes. This study develops a dynamic spatial‐ordered probit (DSOP) model in order to capture patterns of spatial and temporal autocorrelation in ordered categorical response data. This model is estimated in a Bayesian framework using Gibbs sampling and data augmentation, in order to generate all autocorrelated latent variables. It incorporates spatial effects in an ordered probit model by allowing for interregional spatial interactions and heteroskedasticity, along with random effects across regions or any clusters of observational units. The model assumes an autoregressive, AR(1), process across latent response values, thereby recognizing time‐series dynamics in panel data sets. The model code and estimation approach is tested on simulated data sets, in order to reproduce known parameter values and provide insights into estimation performance, yielding much more accurate estimates than standard, nonspatial techniques. The proposed and tested DSOP model is felt to be a significant contribution to the field of spatial econometrics, where binary applications (for discrete response data) have been seen as the cutting edge. The Bayesian framework and Gibbs sampling techniques used here permit such complexity, in world of two‐dimensional autocorrelation.     

An Initial Analysis of River Discharge and Rainfall in Coastal New South Wales,Australia Using Wavelet Transforms

In many coastal catchments of south eastern New South Wales, Australia, changes in river morphology are a response to human impact superimposed on spatial and temporal patterns of variability in precipitation and discharge. Understanding, and preferably quantifying, spatial and temporal patterns of hydrologic variability are essential to understanding natural changes, and to separate these from artificial changes in river systems. Prediction and management of water resources are also dependent upon this understanding. We assess the variability in precipitation and discharge using the wavelet transform which projects the time series of data into a three dimensional surface of frequency, amplitude and time. The analysis reveals that changes across time often reflect changes in individual seasons and may be linked to changes in particular seasonal atmospheric circulation systems. Strong perturbations in the analysis of one catchment are consistent with documented, geomorphically‐effective, flooding sequences. The characteristics of the series in the transformed data reveal interesting differences at certain times and scales which may be a reflection of changes in larger scale atmospheric processes.     

A SPATIO‐TEMPORAL KERNEL METHOD FOR MAPPING CHANGES IN PREHISTORIC LAND‐USE PATTERNS

Archaeologists are accustomed to considering both the spatial distributions of sites and the temporal distributions of dates as means of analysing the dynamics of prehistoric societies. However, spatial and temporal approaches have thus far remained largely separate, rather than being combined within a single, unified framework. A formal methodology is outlined that combines univariate kernel density estimation based on radiocarbon dates with bivariate kernel density estimation based on spatial site coordinates; the approach allows archaeologists to arrive at reconstructed land‐use distributions through time that not only correct for the problematic issue of site contemporaneity, but also reflect the continuous nature of the archaeological record. The model is implemented using as a data set a series of sites from the Mesolithic of Atlantic Iberia; the results demonstrate that it is capable of providing key insights into changing patterns of land use that are not apparent from either the temporal or the spatial perspective alone.     

The Majority Theorem for the Single (p = 1) Median Problem and Local Spatial Autocorrelation

Except for about a half dozen papers, virtually all (co)authored by Griffith, the existing literature lacks much content about the interface between spatial optimization, a popular form of geographic analysis, and spatial autocorrelation, a fundamental property of georeferenced data. The popular p-median location-allocation problem highlights this situation: the empirical geographic distribution of demand virtually always exhibits positive spatial autocorrelation. This property of geospatial data offers additional overlooked information for solving such spatial optimization problems when it actually relates to their solutions. With a proof-of-concept outlook, this paper articulates connections between the well-known Majority Theorem of the 1-median minisum problem and local indices of spatial autocorrelation; the LISA statistics appear to be the more useful of these later statistics because they better embrace negative spatial autocorrelation. The relationship articulation outlined here results in the positing of a new proposition labeled the egalitarian theorem.     

Duration Modeling of Spatial Point Patterns

This paper attempts to further the research by Odland and Ellis (1992) in applying event history methodology to the analysis of spatial point patterns (that is, event patterns). Its empirical focus is the event pattern derived from the adoption of an agricultural innovation, the Harvestore, in southern Ontario, Canada, from 1963 to 1986. Event history analysis involves the use of discrete-state, continuous-time stochastic models to investigate a temporal longitudinal record on discrete variables. Event history models are usually concerned with durations of time between events and the effects of intertemporal time dependencies on future event occurrences. As such, they are often referred to as duration models. Many of the methods used in event history analysis allow the use of other nonnegative interval measurements in place of standard temporal intervals to investigate a series of events. In particular, spatial intervals (or durations) of distances between events may also be accommodated by event history models. Our analysis extends the previous research of Odland and Ellis (1992) by using a wider range of parametric models to explore duration dependence, investigating the role of spatial censoring, and using a more extensive set of explanatory variables. In addition, simulation experiments and graphical tests are used to evaluate the empirical event pattern against one generated from Complete Spatial Randomness. Results indicate that the event pattern formed by the Harvestore adopter farms is clustered (that is, is described by positive duration dependency), the sales agent is a significant factor in the distribution of adopters, and that contrasting results are obtained from the analysis using censored data versus uncensored data.     

Measurements of gradients in ionospheric parameters with a new nine-position experiment at Millstone Hill

A new nine-position experiment is now routinely carried out with the Millstone Hill incoherent scatter radars which allows estimation of spatial gradients in the measured ionospheric scalar parameters N_e, T_e, and T_i, and in the components of the ion velocity vector v_i. Use of this technique results in improved estimates of basic and derived parameters from incoherent scatter data at times of significant gradients. We detail the data analysis method and present the first results from this new experiment. The gradients in N_e and in the components of vi are used to compute the motion term in the ionospheric F region continuity equation ▿ · (Nv), which is then combined with ∂N/∂t to estimate the O⁺ recombination rate β at night. Meridional neutral winds U_mer are computed from the field-aligned ion velocity v_∥ and a calculation of the O⁺ diffusion velocity v_d, and it is found that horizontal gradients in the ion velocity field at times significantly affect the calculation of the neutral winds.     

The political geography of macro-level turnout in American political development

Aggregate turnout rates are among the central indicators of democratic performance in the American polity. Despite the considerable implications of macro turnout, however, most studies of turnout focus instead on the micro level. As a consequence, we know little about how local, political, and historical influences have impacted turnout over the course of American political development. The result is a somewhat impoverished conception of turnout that often removes the political from political participation. In this article, I argue for a new, macro-level perspective that highlights the political dimension of turnout by placing turnout in the local political settings in which it has taken place. I contrast two competing explanations of macro turnout variation across local electorates, a political account and Elazar's cultural thesis, and discuss their implications for the political geography of macro turnout in American electoral history. I then examine this political geography by employing a local indicator of spatial association (a LISA statistic) to identify the spatial structuring of macro turnout in the United States from 1828 through 2000. I demonstrate that a political perspective provides greater leverage than Elazar's cultural perspective in explaining the political geography of macro turnout in the United States.     

Analyzing the Spatial Dynamics of Deforestation in Brazilian Amazon

Historically, development in Brazilian Amazon was promoted by permits of deforestation under soft territory control or supervision. However, due to the importance of this biome for biodiversity and ecosystem balance in a global perspective, Brazilian's government has tightened deforestation control. This work investigates the spatial pattern of deforestation in a cross‐section and time perspective using global and local spatial data analysis. Global results indicate the existence of high spatial correlation and that deforestation holds concentrated across space, despite the efficacy of policy mechanisms adopted for controlling and reducing the level of deforestation in Legal Amazon. Furthermore, local results support the hypothesis of high spillover effects. Considering the spatial analysis results, we highlight some implications for policy design aiming deforestation control.     

我国旅游业技术创新水平的区域空间分布特征——基于专利数据的统计分析

本文基于专利的统计数据,分别采用绝对指标、相对指标和特化系数来评价我国旅游业技术创新水平的空间分布特征。研究结果表明,采用绝对指标评价的旅游业技术创新水平呈现“东高西低”的格局;而采用相对指标（单位人口的旅游业专利申请数量）评价的结果表明,东部地区仍处于领先地位,但与绝对指标评价结果相比,西部地区的排序明显升高;东部地区旅游业发明专利特化系数较高,如北京、天津、上海、广东、海南均在1．1以上,但是全国大多数省市的旅游业专利还属于实用新型和外观设计特化类,说明我国旅游业技术创新结构并不完善。     

Local Spatial Autocorrelation in a Biological Model

We review the recently developed local spatial autocorrelation statistics I_i, c_i, G_i, and G_i*. We discuss two alternative randomization assumptions, total and conditional, and then newly derive expectations and variances under conditional randomization for I_i and c_i, as well as under total randomization for c_i. The four statistics are tested by a biological simulation model from population genetics in which a population lives on a 21 × 21 lattice of stepping stones (sixty-four individuals per stone) and reproduces and disperses over a number of generations. Some designs model global spatial autocorrelation, others spatially random surfaces. We find that spatially random designs give reliable test results by permutational methods of testing significance. Globally autocorrelated designs do not fit expectations by any of the three tests we employed. Asymptotic methods of testing significance failed consistently, regardless of design. Because most biological data sets are autocorrelated, significance testing for local spatial autocorrelation is problematic. However, the statistics are informative when employed in an exploratory manner. We found that hotspots (positive local autocorrelation) and coldspots (negative local autocorrelation) are successfully distinguished in spatially autocorrelated, biologically plausible data sets.     

Picking 'winners' in space: Impact of spatial targeting on firm performance in China

This paper examines the spatial patterns of China's industrial encouragement policy and its distributional impact on firm productivity. To this end, I develop separate proxies to measure three popular policy instruments (subsidies, tax holidays, and preferential access to loans). I first show that China's industrial support policies tend to exhibit a prominent spatial feature of targeting firms located in lagging cities with lower density. Taking into account potential endogeneity of industrial policy, unobserved heterogeneity and firm dynamics, quantile regression techniques show that more intense industrial support leads to: (a) a reduction in the productivity of lower-performing firms, especially in denser cities; and (b) a small productivity gain for better performing firms but only in denser cities. Counterfactual analysis further reveals that pursuing an alternative, space-neutral industrial encouragement policy would increase average productivity by 14–16%, in aggregate, but also contribute to significantly higher regional inequality.