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.     

Using Spatial Filters and Exploratory Data Analysis to Enhance Regression Models of Spatial Data

Residual spatial autocorrelation is a situation frequently encountered in regression analysis of spatial data. The statistical problems arising due to this phenomenon are well‐understood. Original developments in the field of statistical analysis of spatial data were meant to detect spatial pattern, in order to assess whether corrective measures were required. An early development was the use of residual autocorrelation as an exploratory tool to improve regression analysis of spatial data. In this note, we propose the use of spatial filtering and exploratory data analysis as a way to identify omitted but potentially relevant independent variables. We use an example of blood donation patterns in Toronto, Canada, to demonstrate the proposed approach. In particular, we show how an initial filter used to rectify autocorrelation problems can be progressively replaced by substantive variables. In the present case, the variables so retrieved reveal the impact of urban form, travel habits, and demographic and socio‐economic attributes on donation rates. The approach is particularly appealing for model formulations that do not easily accommodate positive spatial autocorrelation, but should be of interest as well for the case of continuous variables in linear regression.     

Assessing Spatial Dependence in Count Data: Winsorized and Spatial Filter Specification Alternatives to the Auto-Poisson Model

The auto-Poisson probability model furnishes an obvious tool for modeling counts of geographically distributed rare events. Unfortunately, its original specification can accommodate only negative spatial autocorrelation, which itself is a rare event. More recent alternative reformulations, namely, the Winsorized and spatial filter specifications, circumvent this drawback. A comparison of their performances presented in this article reveals some of their relative advantages and disadvantages.     

Implementing Spatial Data Analysis Software Tools in R

This article reports on work in progress on the implementation of functions for spatial statistical analysis, in particular of lattice/area data in the R language environment. The underlying spatial weights matrix classes, as well as methods for deriving them from data from commonly used geographical information systems are presented, handled using other contributed R packages. Since the initial release of some functions in 2001, and the release of the spdep package in 2002, experience has been gained in the use of various functions. The topics covered are the ingestion of positional data, exploratory data analysis of positional, attribute, and neighborhood data, and hypothesis testing of autocorrelation for univariate data. It also provides information about community building in using R for analyzing spatial data.     

GeoDa : An Introduction to Spatial Data Analysis

This article presents an overview of GeoDa™, a free software program intended to serve as a user-friendly and graphical introduction to spatial analysis for non-geographic information systems (GIS) specialists. It includes functionality ranging from simple mapping to exploratory data analysis, the visualization of global and local spatial autocorrelation, and spatial regression. A key feature of GeoDa is an interactive environment that combines maps with statistical graphics, using the technology of dynamically linked windows. A brief review of the software design is given, as well as some illustrative examples that highlight distinctive features of the program in applications dealing with public health, economic development, real estate analysis, and criminology.     

A Note on the Spatial Analysis of Sets of Highly Disaggregated Data

Abstract

Compared with other North American colonies, little scholarship exists on slave-holding in early Georgia. In this article, the author augments this historiography by examining a remarkable and little-used collection of sources. Data gleaned from analyzing more than 400 wills written by eighteenth-century white settlers reveal that roughly 39 percent of early Georgians owned slaves and that slave distribution was pyramidal, as most slaveholders owned but a few slaves, although some elites held many. While these findings support existing research, data from the wills suggest that early Georgia slaveholders owned, on average, about half as many slaves as other scholars contend. Besides informing an understanding of slavery in the colony, this article provides an overview of the early Georgia wills themselves, which, as sources, are highly accessible and contain a wealth of information for future scholars.     

Nonparametric Estimation of the Spatial Connectivity Matrix Using Spatial Panel Data

We use moments from the covariance matrix for spatial panel data to estimate the parameters of the spatial autoregression model, including the spatial connectivity matrix W. In the unrestricted spatial autoregression model, the parameters are underidentified by one when W is symmetric. We show that a special case exists in which W is asymmetric and its parameters are exactly identified. If the panel data are stationary and ergodic, spatially and temporally, the estimates of W and the spatial autoregression coefficients are consistent. Spatial panel data for house prices in Israel are used to illustrate this methodology. Los autores usan momentos de una matriz de covarianza para datos panel espaciales para estimar los parámetros del modelo de autoregresión espacial (spatial autoregressive model), incluyendo la matriz de conectividad (o de ponderación) espacial W. En el modelo de autoregresión espacial sin restricciones, los parámetros están sub‐identificados por un valor de uno en los casos que la matriz W es simétrica. Los autores demuestran que existe un caso especial en el cual la matriz W es asimétrica y sus parámetros tienen cálculo exacto. Si los datos panel son estacionarios y ergódicos, espacial y temporalmente, los estimados de W y el coeficiente de autoregresión espacial son consistentes. Para ilustrar la metodología propuesta, los autores usan datos‐panel espaciales de precios de vivienda en Israel. 本文通过采用空间面板数据的协方差矩阵对包含空间相关矩阵W的空间自回归模型进行参数的矩估计。在无约束空间自回归模型中,W是对称矩阵时,参数可由其估计得到。本文展示了一种W是对称矩阵且其参数能够被精确估计的特殊情况。如果面板数据在时间与空间特征上具有平稳性和遍历性,那么W和空间自回归参数的估计是一致的。最后,针对以色列住房价格的空间面板数据采用此方法进行实证研究。     

Crime Risk Maps: A Multivariate Spatial Analysis of Crime Data

In crime analyses, maps showing the degree of risk help police departments to make decisions on operational matters, such as where to patrol or how to deploy police officers. This study statistically models spatial crime data for multiple crime types in order to produce joint crime risk maps. To effectively model and map the spatial crime data, we consider two important characteristics of crime occurrences: the spatial dependence between sites, and the dependence between multiple crime types. We reflect both characteristics in the model simultaneously using a generalized multivariate conditional autoregressive model. As a real‐data application, we examine the number of incidents of vehicle theft, larceny, and burglary in 83 census tracts of San Francisco in 2010. Then, we employ a Bayesian approach using a Markov chain Monte Carlo method to estimate the model parameters. Based on the results, we detect the crime hotspots, thus demonstrating the advantage of using a multivariate spatial analysis for crime data.     

Geography, Spatial Data Analysis, and Geostatistics: An Overview

Geostatistics is a distinctive methodology within the field of spatial statistics. In the past, it has been linked to particular problems (e.g., spatial interpolation by kriging) and types of spatial data (attributes defined on continuous space). It has been used more by physical than human geographers because of the nature of their types of data. The approach taken by geostatisticians has several features that distinguish it from the methods typically used by human geographers for analyzing spatial variation associated with regional data, and we discuss these. Geostatisticians attach much importance to estimating and modeling the variogram to explore and analyze spatial variation because of the insight it provides. This article identifies the benefits of geostatistics, reviews its uses, and examines some of the recent developments that make it valuable for the analysis of data on areal supports across a wide range of problems.     

Knowledge Spillovers and Total Factor Productivity: Evidence Using a Spatial Panel Data Model

This article investigates the impact of knowledge capital stocks on total factor productivity (TFP) through the lens of the knowledge capital model proposed by Griliches (1979) , augmented with a spatially discounted cross-region knowledge spillover pool variable. The objective is to shift attention from firms and industries to regions and to estimate the impact of cross-region knowledge spillovers on TFP in Europe. The dependent variable is the region-level TFP, measured in terms of the superlative TFP index suggested by Caves, Christensen, and Diewert (1982) . This index describes how efficiently each region transforms physical capital and labor into output. The explanatory variables are internal and out-of-region stocks of knowledge, the latter capturing the contribution of cross-region knowledge spillovers. We construct patent stocks to proxy annual regional knowledge capital stocks for N =203 regions during 1997–2002. In estimating the effects, we implement a spatial panel data model that controls for spatial autocorrelation as well as individual heterogeneity across regions. The findings provide a fairly remarkable confirmation of the role of knowledge capital contributing to productivity differences among regions and add an important spatial dimension to discussions in the literature by showing that productivity effects of knowledge spillovers increase with geographic proximity.     

Spatial Distribution of Trees and Landscapes of the Past: A Mixed Spatially Correlated Multinomial Logit Model Approach for the Analysis of the Public Land Survey Data

Public Land Survey (PLS) data have been widely used in landscape studies of forest and woodlands in the pre‐ and early‐European‐settled Midwestern and Western United States. We aim to reconstruct presettlement forest vegetation at a finer spatial resolution than available from the PLS data using environmental covariates (slope, aspect, geology, and soil type) and the spatially correlated structure of witness tree data. To accommodate various data obtained from multiple sources while explicitly taking into account their spatial structures, we adopt a mixed spatially correlated multinomial logit model within the framework of a generalized linear mixed model. The application of the proposed model is illustrated using the three most abundant tree taxa from PLS data in the Arbuckle Mountains of south‐central Oklahoma. To assess the influence of each source of information on the spatial prediction, we considered four variant multinomial/spatial models and evaluated their relative predictive power using a validation technique. The probabilistic information about the spatial distribution of tree species obtained from different models reveals the need to integrate information about witness tree data as well as environmental covariates, and the nature of tree species; that is, a tendency to cluster in space to share environmental conditions in the reconstruction of the presettlement forest vegetation surface. Los datos sobre el uso y cobertura de tierras del Public Land Survey (PLS) han sido utilizados ampliamente en estudios de paisaje de bosques y de bosques históricos para periodo previo al asentamiento de migrantes europeos en el medio oeste y oeste de los Estados Unidos. Nuestro objetivo es reconstruir la vegetación forestal previa al asentamiento europeo a una resolución espacial más fina que la disponible actualmente en base a datos del PLS, usando covariables ambientales (pendiente, orientación, geología y tipo de suelo) y la estructura de correlación espacial de los datos de los árboles testigos. Para dar cabida a los diversos datos obtenidos de fuentes múltiples, y a la vez teniendo en cuenta explícitamente sus estructuras espaciales, adoptamos un modelo logit multinomial espacial mixto dentro del marco de los modelos mixtos lineales generalizados (GLMM). La aplicación del modelo propuesto es ilustrada con los tres tipos más abundantes de árboles según los datos del PLS para las montañas de Arbuckle en el centro‐sur de Oklahoma, EEUU. Para evaluar la influencia de cada fuente de información sobre la predicción espacial, se consideraron cuatro variantes de los modelos multinomial y espaciales. El poder predictivo de dichos modelos fue evaluado en relación con una técnica de validación. La información probabilística acerca de la distribución espacial de las especies de árboles obtenidos a partir de los diferentes modelos revela que para la reconstrucción de la superficie de la vegetación forestal histórica, es necesario integrar la información sobre los datos de árboles testigos así como las covariables ambientales y la naturaleza de las especies de árboles: es decir, la tendencia de los arboles a agruparse en el espacio para compartir las mismas condiciones ambientales. 公共土地调查(PLS)数据在欧洲人定居美国中西部和西部地区之前以及早期的森林和林地景观研究中得到广泛应用。本文旨在利用环境协变量（坡度、坡向、地貌和土地类型）证据树数据的空间关联结构,重建比PLS数据中更有效的更精细空间分辨率的前殖民期森林植被。为集成多种来源的各类数据,并明确地考虑数据间的空间结构,本文在广义线性混合模型(GLMM)框架下提出了混合空间关联多项Logit模型。以俄克拉荷马州中南部的阿尔布克尔山脉为研究区,提取PLS数据中三种最丰富的树种对模型进行验证。为估计每种信息来源对模型空间预测准确性的影响,本文考虑了4种变异的多项/空间模型并运用验证技术评估它们的相对预测能力。从不同模型获得的树种空间分布的概率信息表明,需要对证据树数据、环境协变量和树种自然属性信息进行集成,也就是说,在重建前殖民期森林植被曲面时,空间上的集聚趋势共享了环境条件。     

Recursive Estimation of the Spatial Error Model

In this paper, we propose a recursive approach to estimate the spatial error model. We compare the suggested methodology with standard estimation procedures and we report a set of Monte Carlo experiments which show that the recursive approach substantially reduces the computational effort affecting the precision of the estimators within reasonable limits. The proposed technique can prove helpful when applied to real-time streams of geographical data that are becoming increasingly available in the big data era. Finally, we illustrate this methodology using a set of earthquake data.     

Multiscale Continuous and Discrete Spatial Heterogeneity Analysis: The Development of a Local Model Combining Eigenvector Spatial Filters and Generalized Lasso Penalties

Two types of spatial heterogeneity can exist simultaneously: continuous variations across an entire space and significant changes that occur only in specific spatial units. Moreover, each of these can act across multiple spatial scales. To effectively detect both continuous and discrete spatial heterogeneity across different scales, this study proposes a novel approach that combines the random effects eigenvector spatially filtering-based spatially varying coefficient (RE-ESF-SVC) model and the generalized lasso (GL) technique. Additionally, a restricted maximum likelihood estimation (REML)-based two-step iterative algorithm is developed for parameter estimation. Simulation experiments and an empirical application using rental price data confirm the ability of the proposed model to identify multiscale continuous and discrete spatial heterogeneity.     

The Effect on Attribute Prediction of Location Uncertainty in Spatial Data

A datum is considered spatial if it contains location information. Typically, there is also attribute information, whose distribution depends on its location. Thus, error in location information can lead to error in attribute information, which is reflected ultimately in the inference drawn from the data. We propose a statistical model for incorporating location error into spatial data analysis. We investigate the effect of location error on the spatial lag, the covariance function, and optimal spatial linear prediction (that is, kriging). We show that the form of kriging after adjusting for location error is the same as that of kriging without adjusting for location error. However, location error changes entries in the matrix of explanatory variables, the matrix of co‐variances between the sample sites, and the vector of covariances between the sample sites and the prediction location. We investigate, through simulation, the effect that varying trend, measurement error, location error, range of spatial dependence, sample size, and prediction location have on kriging after and without adjusting for location error. When the location error is large, kriging after adjusting for location error performs markedly better than kriging without adjusting for location error, in terms of both the prediction bias and the mean squared prediction error.     

A Generalization of the Utility Theory Approach To the Problem of Spatial Interaction

The derivation of the gravity model from utility theory is reformulated and generalized in order to show (1) how both the number of trips to individual destinations and the total travel budget may be determined simultaneously, and (2) how the effect of both distance and destination quality on trip distribution and total budget may be analyzed. Results are compared with the revealed space preference approach and are found to be superior in dealing theoretically with trip frequency and the effects of spatial context. For empirical applications, however, the revealed preference approach is advantageous.