POISSON GRAVITY MODELS OF SPATIAL FLOWS*

ABSTRACT The purpose of this paper is to bring together a number of results on spatial flow models, and to reformulate them within a unified probability framework based on Poisson frequencies. To do so, a class of discrete stochastic processes, designated as independent flow processes, is developed which not only yields a complete characterization of Poisson flow frequencies, but also allows a wide range of gravity-type flow models to be formulated within this distributional framework. In particular, a hierarchical classification of 12 model types is developed, and each model type is shown to be characterizable directly in terms of behavioral axioms on independent flow processes.     

Spatial Point Processes Applied to the Distribution of River Junctions

The notion of randomness has been extensively applied to topological (nondimensional) properties of drainage networks. The spatial (dimensional) organization of five fluvial hierarchies is examined herein through the application of quadrat analysis to random and clustered spatial probability models. The Poisson, Polya-Aeppli, and negative binomial models are compared with point-pattern distributions of river junction location for three basins in Indiana and two fossil systems on an erosion surface in semiarid Australia. The negative binomial model best fits all five networks, suggesting that the branching behavior of fluvial systems follows the mathematical precepts leading to clusteredness of junctions. The degree to which the Polya-Aeppli model fits the data suggests the imposition of a temporally limited set of environmental conditions optimally suited for network growth. Only for the two fossil systems does the Poisson model agree. It is speculated that the effect of prolonged subaerial erosion may be to shift a clustered distribution towards the random state as the surface approaches a pediplained state.     

A Dynamic Analysis of Interaction Data: U.S. Rail Freight Flows, 1972-81

The purpose of this paper is to extend Poisson regression to the analysis of spatial interactions over time. The methodology involves derivation of models using information methods and calibration using Poisson regression. Poisson regression is then used to analyze interannual variation in U.S. rail freight flows, 1972-81. Findings indicate that import and export variability is less important than is flow variability. Import and export variability is highest for the northeastern United States, but flow variability is highest for the southern and western United States. This has implications for the specification of dynamic models of commodity flow.     

Fitting Constrained Poisson Regression Models to Interurban Migration Flows

This paper demonstrates the effects of fitting singly and doubly constrained spatial interaction models using the Poisson regression approach. A large data set containing migration flows between labor market areas in Great Britain in 1970–71 is used. The results of fitting unconstrained, singly constrained, and doubly constrained models are compared with respect to goodness of fit and the interpretability of parameter estimates. The addition of other explanatory variables to the model is also explored.     

Analyzing Space–Time Crime Incidents Using Eigenvector Spatial Filtering: An Application to Vehicle Burglary

Poisson models generally are utilized in analyzing spatial patterns of crime count data. When spatial autocorrelation is present, these models are extended to account for it. Among various methods, eigenvector spatial filtering (ESF) furnishes an efficient means of analysis. However, because space–time crime data have temporal components as well as spatial components, Poisson models need to be further adjusted to reflect the two types of components simultaneously. This article discusses how the ESF method can be utilized to model space–time crime data, extending the generalized linear mixed model specification for it. This approach is illustrated with an application to space–time vehicle burglary incidents in the city of Plano, Texas, during 2004–2009. Los modelos de Poisson generalmente se utilizan en el análisis de los patrones espaciales de los datos de recuento de crimen. Cuando hay autocorrelación espacial, estos modelos son modificados para dar cuenta de ello. Entre los diversos métodos existentes, el método Eigenvector (autovector, vector propio) de filtrado espacial (Eigenvector Spatial Filtering‐ESF) proporciona un medio eficaz para dicho análisis. Sin embargo, dado que los datos de criminalidad espacio‐temporales tienen tanto componentes temporales como espaciales, los modelos tipo Poisson requieren de un ajuste adicional para reflejar ambos tipos de componentes de manera simultánea. El artículo presente expone cómo el método ESF puede ser utilizado para modelar datos espacio‐temporales sobre delitos mediante la modificación del modelo mixto lineal generalizado (Generalized Linear Mixed Model‐GLMM). El procedimiento propuesto se ilustra con el caso de incidentes espacio‐temporales de robos de vehículos en la ciudad de Plano, Texas, durante 2004–2009. 泊松模型一般用于犯罪计数数据的空间模式分析中,当空间自相关关系呈现时,这类模型可扩展以解释潜在的分布特征。在各种模型中,特征向量空间滤波（ESF）提供了一种有效的分析方法。然而,由于时空犯罪数据包含时间和空间组分,因此泊松模型需要进一步调整以同时反映这两种不同类型的数据。本文讨论了如何利用特征向量空间滤波(ESF)模型对时空犯罪数据进行建模,并采用扩展广义线性混合模型(GLMM)进行规范。最后,以德克萨斯州普莱诺市2004‐2009年的车辆盗窃案数据进行了实证验证。     

MIGRATION AS A WAY TO DIVERSIFY: EVIDENCE FROM RURAL TO URBAN MIGRATION IN THE U.S.

This paper extends the utility maximization model of migration by introducing income and unemployment‐related uncertainties as determinants of utility, and analyzes the effects of the informational advantages of migrants. The paper maintains that migration would expand an individual's economic choices and opportunities and allow diversification. Consequently, diversification advantages influence the location decisions of migrants, an effect captured by the correlation of incomes at the origin and potential destinations. We use the discrete choice model based on random utility maximization as the framework for our empirical investigation of migration from the United States rural to urban counties. This paper takes advantage of an equivalent relation between the conditional logit model and Poisson regression to study the migration decisions using aggregate data among a large set of spatial alternatives. The results show that the diversification concerns have significant effects on location decisions of the rural‐urban migrants in the United States.     

Evaluation of the Poisson Approximation To Measures of the Random Pattern in the Square

Theoretical values for spacing between points of the Poisson process are frequently used to evaluate the hypothesis that the locations within a region of pointlike objects have a random pattern. These theoretical spacing values are an approximation to spacing values for a uniform process in which the objects are uniformly and independently located in the region. The adequacy of the Poisson approximation to this uniform process for a square region is evaluated by analytic and numeric methods. The approximation is close for a small number of points when spacing between objects is measured by toroidal distance.     

Who votes alone? The impact of voting by mail on political discussion

Critics of voting by mail express concern over its impact on civil society. For example, Thompson (2004) posits that voting by mail limits electoral civic engagement by preventing the temporal norm of simultaneity on Election Day. I, however, find that the open ballot system of voting by mail promotes deliberation, which encourages civic engagement. This study tests if voting by mail increases political discussion by creating a Poisson regression model of American National Election Survey data. The findings show that voting by mail leads to more political discussion. This evidence supports the theory that voting by mail offers voters a more open and deliberatory system and does not necessarily limit civic engagement.     

A NON-GAUSSIAN TIME SERIES ANALYSIS OF RURAL RETAIL BUSINESS COUNTS*

ABSTRACT. Determinants of the number of retail firms serving a rural area have been investigated by drawing on demand threshold analysis to analyze cross-sectional data. The relevance of such studies to an individual community may be limited if it is characterized by differential levels or unique types of economic activity. Alternatively, conducting the analysis using time-series data on an individual community may lead to problems associated with non-normal and nonstationary data. These problems are addressed by formulating a state-space model of time-series count data. The discrete, nonnegative nature of count data is accommodated by using a conjugate prior for the Poisson location parameter. A guide function is used to link the prior to the state vector and Bayes rules are used for updating.     

Industrial Location Modeling: Extending the Random Utility Framework*

Abstract. Given sound theoretical underpinnings, the random utility maximization‐based conditional logit model (CLM) serves as the principal method for applied research on industrial location decisions. Studies that implement this methodology, however, confront several problems, notably the disadvantages of the underlying Independence of Irrelevant Alternatives (IIA) assumption. This paper shows that by taking advantage of an equivalent relation between the CLM and Poisson regression likelihood functions one can more effectively control for the potential IIA violation in complex choice scenarios where the decision maker confronts a large number of narrowly defined spatial alternatives. As demonstrated here our approach to the IIA problem is compliant with the random utility (profit) maximization framework.     

Analyzing the Relationship Between Smoking and Coronary Heart Disease at the Small Area Level: A Bayesian Approach to Spatial Modeling

We model the relationship between coronary heart disease and smoking prevalence and deprivation at the small area level using the Poisson log-linear model with and without random effects. Extra-Poisson variability (overdispersion) is handled through the addition of spatially structured and unstructured random effects in a Bayesian framework. In addition, four different measures of smoking prevalence are assessed because the smoking data are obtained from a survey that resulted in quite large differences in the size of the sample across the census tracts. Two of the methods use Bayes adjustments of standardized smoking ratios (local and global adjustments), and one uses a nonparametric spatial averaging technique. A preferred model is identified based on the deviance information criterion. Both smoking and deprivation are found to be statistically significant risk factors, but the effect of the smoking variable is reduced once the confounding effects of deprivation are taken into account. Maps of the spatial variability in relative risk, and the importance of the underlying covariates and random effects terms, are produced. We also identify areas with excess relative risk.     

Destination Choice of Athenians: An Application of Geographically Weighted Versions of Standard and Zero Inflated Poisson Spatial Interaction Models

The main aim of this article is to combine recent developments in spatial interaction modeling to better model and explain spatial decisions. The empirical study refers to migration decisions made by internal migrants from Athens, Greece. To achieve this, geographically weighted versions of standard and zero inflated Poisson (ZIP) spatial interaction models are defined and fit. In the absence of empirical studies for the effect of potential determinants on internal migration decisions in Greece and the presence of an excessive number of zero migration flows among municipalities in Greece, this article provides empirical evidence for the power of the proposed Geographically Weighted ZIP regression method to better explain destination choices of Athenian internal migrants. We also discuss statistical inference issues in relation to the application of the proposed regression techniques.     

Bayesian Point Process Modeling to Quantify Geographic Regions of Excess Stillbirth Risk

Motivated by the paucity of high‐quality stillbirth surveillance data and the spatial analysis of such data, we describe the pattern of stillbirth events as a step toward increased understanding of risk factors which can better guide future measures to mitigate these events. A challenge in such an analysis is that some mothers experience stillbirth events from independent pregnancies within a defined study period. To account for these dependencies, we parameterize our model to include a maternal contextual effect and broaden the appeal of Bayesian Poisson point process modeling to quantify excess stillbirth risk while considering a form of a log‐Gaussian Cox process. In the presence of extra unobserved spatial variation in risk, we demonstrate a pragmatic methodologic strategy to model the risk surface in relation to covariates and that there is a variance‐bias trade‐off associated with the use of a maternal contextual effect. We applied our strategy to the spatial distribution of stillbirth in Iowa during the years 2005–2011 using data obtained from an active, statewide public health surveillance program. We identified areas of excess risk for further investigation based on model components that captured important features of the data.     

Mobility-driven cultural transmission along the forager-collector continuum

Hunter-gatherers mobility regimes are often treated as discrete adaptive strategies. Here we present a model of forager mobility which treats collectors and foragers as two ends of a continuous spectrum. We show that a mobility regime can be situated along this spectrum by specifying the number of foraging moves a group makes before returning to its home base. The model allows us to explore the behavioural space between forager (i.e. residential mobility) and collector (logistical mobility) adaptations. We discuss the heuristic value of the model by showing how it can be used to make testable predictions about the impact of mobility strategies on archaeological measures such as occupation intensity and raw-material transportation distance. We then use the model to investigate the impact of mobility on rates of cultural transmission. We show that mobility-driven cultural transmission may be equivalent to a Poisson process and that the time it takes for a cultural behaviour to be transmitted between two mobile groups is optimized when the mobility regime is somewhere between pure forager and pure collectors adaptations. In addition, we find that rates of cultural transmission decline in a very regular way, as the inverse of the square root of the number of moves made before returning to home base. This suggests that there is a mechanistic connection between the mean-squared displacement of hunter-gatherers in space and the transmission of cultural traits.     

International Acquisitions: Host and Home Country Explanatory Characteristics

To better understand what place-specific attributes are most important to foreign direct investors, we consider the pattern of international foreign acquisitions, for the year 1993, from a simultaneous home and host country perspective. It is shown that the world's most prominent buyer and target countries are few in number. Furthermore, with the use of a stepwise-like Poisson regression procedure, we determine that both home and host country conditions are important in explaining the spatial pattern of low-tech and high-tech international acquisitions.
Specifically, international high-tech and low-tech acquisitions are best described by country-specific variables measuring trade, investment risk assessment, patents and tourism and that low-tech acquisitions are also linked with a country's domestic economic strength and government efficiency and stability. The outliers from the Poisson regression equations provide evidence that, in particular, the United States and Canada as well as, other countries geographically adjacent are disproportionately active in this type of foreign direct investment.     

A Spatial Autoregressive Poisson Gravity Model

In this article, a Poisson gravity model is introduced that incorporates spatial dependence of the explained variable without relying on restrictive distributional assumptions of the underlying data‐generating process. The model comprises a spatially filtered component—including the origin‐, destination‐, and origin‐destination‐specific variables—and a spatial residual variable that captures origin‐ and destination‐based spatial autocorrelation. We derive a two‐stage nonlinear least‐squares (NLS) estimator (2NLS) that is hetero‐scedasticity‐robust and, thus, controls for the problem of over‐ or underdispersion that often is present in the empirical analysis of discrete data or, in the case of overdispersion, if spatial autocorrelation is present. This estimator can be shown to have desirable properties for different distributional assumptions, like the observed flows or (spatially) filtered component being either Poisson or negative binomial. In our spatial autoregressive (SAR) model specification, the resulting parameter estimates can be interpreted as the implied total impact effects defined as the sum of direct and indirect spatial feedback effects. Monte Carlo results indicate marginal finite sample biases in the mean and standard deviation of the parameter estimates and convergence to the true parameter values as the sample size increases. In addition, this article illustrates the model by analyzing patent citation flows data across European regions. En el presente artículo, se introduce un modelo de gravedad Poisson, que incorpora la dependencia espacial de la variable explicada, sin apoyarse en presunciones de distribución restrictivas del proceso subyacente de generación de datos. El modelo comprende de un componente espacialmente filtrado, que incluye las variables de origen, destino y origen‐destino específico; y una variable espacial residual que captura la auto‐correlación espacial basada en el origen y destino. Se deriva del calculador (2NLS) de dos etapas no lineales de mínimos cuadrados (NLS), el cual es robusto en heterocedasticidad, y por ello controla el problema de sobre‐dispersión o baja‐dispersión (over and under dispersion), que a menudo se presenta en el análisis empírico de datos discretos; o, en el caso de de sobre‐dispersión, cuando se presenta la auto correlación espacial. Este calculador puede demostrar tener propiedades deseables para diferentes supuestos distribucionales, como los flujos observados un componente (espacialmente) filtrado, ya sea Poisson o binomial negativo. En nuestra especificación de modelo espacial auto regresivo (SAR), las estimaciones de los parámetros resultantes se pueden interpretar como los efectos de impacto total implícitos, definidos como la suma de efectos espaciales, directos o indirectos, de retroalimentación (feedback). Los resultados Monte Carlo indican sesgos marginales de muestras finitas en la media y la desviación estándar de los parámetros estimados, y la convergencia de los valores de los parámetros reales, a medida que aumenta el tamaño de muestra. Este artículo ilustra el modelo mediante el análisis de flujos de datos de citas de patentes, a través de las regiones europeas. 本文提出了一种蕴含空间依赖的泊松引力模型,该模型中解释变量无需依赖潜在数据生成过程的限制性分布假设。该模型由包含起点、终点、起点‐终点特定变量的空间滤波组分和空间残差变量组成,能捕捉到基于起点和终点的空间自相关。我们推导出一个二阶非线性最小二乘（NLS）估计（2NLS）,它对异方差具有鲁棒性,从而可控制对于离散或过离散数据经验性分析中经常出现的过离散和低离散问题。如果空间自相关存在,过离散数据分析就是一个例子。对于不同的分布假设,如或泊松分布或是负二项式分布的观测流或（空间）滤波组分,该估计量显示出令人满意的性能。在本文的空间自回归（SAR）模型设定中,参数估计结果可解释为隐含的全局影响效应,并可被定义为直接和间接的空间反馈效应之和。蒙特卡罗结果给出了参数估计中均值、标准差的临界有限样本偏差,且随样本量增大收敛于真正参数值。此外,本文基于欧洲地区专利引用的流数据进行了模型验证。     

Contact Number Properties in the Study Of Cellular Networks

The purpose of the paper is to determine if different generating processes produce cellular networks with distinctive contact number properties. Properties resulting from patterns produced by three generating processes, the Poisson, the compound negative binomial, and the “Smalley,” are examined in detail. The implications of the findings for the analysis of empirical cellular networks are discussed.     

Characterization of pozzolanic lime mortars used as filling material in shaped grooves for restoring member connections in ancient monuments

This article presents a set of mechanical characteristics for a pozzolanic mortar consisting of hydrated lime and metakaolin, which is used as filler between metallic connectors and marble blocks during restoration activities of ancient monuments in Greece. Mechanical properties include the uniaxial and triaxial compressive strength, the indirect tensile strength, the bending strength, the elastic modulus and Poisson’s ratio, and a shear failure criterion. Cored cylindrical specimens are used for determining the uniaxial and triaxial compressive behavior and the indirect tensile strength of the mortar, thus ensuring the repeatability of the experimental results. The triaxial tests indicated a plastic behavior of the mortars under study, enabling them to perform well in conditions of high shear forces. Calcite and hydraulic components formed in the setting procedure contributed to the plasticity of the final mortar. The mechanical properties that were developed can be utilized to model material behavior and failure under conditions of confined or triaxial loading. The development of a shear failure criterion for a pozzolanic mortar is a substantial accomplishment that has not been previously reported in the international literature.     

How Legislative (In)Activity,Ideological Divergence,and Divided Government Impact Executive Unilateralism: A Test of Three Theories

During the past two decades scholars from a variety of different fields (law, history, journalism, political science) have written extensively about the development and implementation of the Unilateral Presidency. Because several explanations for unilateral action have been posited, we provide a thorough test of three theories of executive unilateral action. Applying a newly-developed methodology to the most comprehensive dataset of unilateral presidential directives to date, results of the Bayesian Poisson Vector Autoregressive model suggest that although executive orders, memoranda, and proclamations are all strategic tools that presidents utilize to unilaterally alter policy, fundamental differences exist between them, as well as the inter-dependence among them. More important, our results show that whereas the percentage of bills passed is related to presidential proclamations, legislative activity actually depends on the number of executive orders issued. However, CQ success scores are related to both executive orders and presidential proclamations. We also find that presidential ideology and congressional ideology are related to executive action, whereas the impact of divided government is at best only weakly related.