Commuting Distances and Gender: A Spatial Urban Model

In any urban center the commuting distances are a function of the spatial structure of the center and of the characteristics of the commuters. In this paper theoretical relationships between commuting distances and distances of residences to city centers are derived for monocentric and polycentric cities. These relationships are then linked to the sociological determinants of commuting distances. An econometric model encompassing both spatial structure variables and social variables is constructed and estimated using data for sixteen urban centers. Gender differences are focused upon. The expansion method is used.     

flowAMOEBA: Identifying Regions of Anomalous Spatial Interactions

This study aims at developing a data‐driven and bottom‐up spatial statistic method for identifying regions of anomalous spatial interactions (clusters of extremely high‐ or low‐value spatial flows), based on which it creates a spatial flow weights matrix. The method, dubbed flowAMOEBA, upgrades a multidirectional optimum ecotope‐based algorithm (AMOEBA) from areal data to spatial flow data through a proper spatial flow neighborhood definition. The method has the potential to dramatically change the way we study spatial interactions. First, it breaks the convention that spatial interaction data are always collected and modeled between spatial entities of the same granularity, as it delineates the OD region of anomalous spatial interactions, regardless of the size, shape, scale, or administrative level. Second, the method creates an empirical spatial flow weights matrix that can handle network autocorrelation embedded in spatial interaction modeling, thus improving related policy‐making or problem‐solving strategies. flowAMOEBA is tested and demonstrated on a synthetic data set as well as a county‐to‐county migration data set.     

A Model of Contiguity for Spatial Unit Allocation

We consider a problem of allocating spatial units (SUs) to particular uses to form "regions" according to specified criteria, which is here called "spatial unit allocation." Contiguity—the quality of a single region being connected—is one of the most frequently required criteria for this problem. This is also one that is difficult to model in algebraic terms for algorithmic solution. The purpose of this article is to propose a new exact formulation of contiguity that can be incorporated into any mixed integer programming model for SU allocation. The resulting model guarantees to enforce contiguity regardless of other included criteria such as compactness. Computational results suggest that problems involving a single region and fewer than about 200 SUs are optimally solved in fairly reasonable time, but that larger problems must rely on heuristics for approximate solutions. It is also found that a problem of any size can be formulated in a more tractable form when a fixed number of SUs are to be selected or when a certain SU is selected in advance.     

A Spatial Logit Association Model for Cluster Detection

In this paper, I propose to set out a logit spatial association model for binary spatial events and develop a scan algorithm to search for spatial associations. I extend the traditional logit model with a spatial autocorrelated component so that the model includes not only known risk factors, but also spatially autocorrelated regions as control or explanatory factors. The case study of West Virginia lung cancer shows that the model effectively captures cool and hot spots in lung cancer mortality.     

A Model for Mental Health Needs and Resourcing in Small Geographic Areas: A Multivariate Spatial Perspective

This paper considers how small area variations in a set of psychiatric referral outcomes in a London health authority of 750,000 people may inform health need assessment and health resourcing for mental illness based on true need. As well as adopting a multivariate perspective, the spatial interdependence of the outcomes is included in the modelling approach outlined. By contrast, existing studies on mental health need tend to focus on single outcomes, and may not include spatial dependence. The analysis relates to three hospital referral outcomes for psychiatric conditions, and to total community mental health referrals across sixty‐seven electoral wards in East London.     

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。     

A Local Model for Multivariate Analysis: Extending Wartenberg’s Multivariate Spatial Correlation

Local analysis can provide specific information about individual observations that is often useful in understanding nonstationary interactions among variables. This paper extends the application of Wartenberg’s Multivariate Spatial Correlation (MSC) method to a local setting. The original MSC can be considered as an adaptation of Principal Component Analysis for spatial effects with respect to spatial autocorrelation. The extended MSC method described in this paper, however, further incorporates another spatial effect, spatial heterogeneity, by the addition of geographic weights in standardizing the data and in calculating the spatial association weight matrix. The extension allows more local analysis and facilitates additional visualization of the results. The geographically weighted MSC is illustrated and justified using the classic dataset collected by André-Michel Guerry on moral statistics in 1830s France.     

Beyond Moran's I: Testing for Spatial Dependence Based on the Spatial Autoregressive Model

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.     

A Dynamic Location-Allocation Model for Evaluating the Spatial Impacts for Just-in-Time Planning

This paper presents an interperiod network storage location-allocation (INSLA) model to solve the just-in-time production planning problem. The model is extended to a multiobjective problem in which trade-offs between delivery time and transportation costs are analyzed. The results for a hypothetical problem show that in an attempt to reduce inventories on the part of the primary purchaser of raw materials, the possibility exists for less than optimal behavior in the system.     

A Spatial Search-Location Model of Retail Centers

Central place theory can be modeled using two types of optimization problems. Location-allocation models have been widely applied to operationalize central place theory as an aggregate optimization problem. This paper constructs a spatial search-location model to formulate central place theory as an individual optimization problem.     

A Spatial Mixture Model of Innovation Diffusion

The diffusion of new product or technical innovation over space is here modeled as an event‐based process in which the likelihood of the next adopter being in region r is influenced by two factors: (i) the potential interactions of individuals in r with current adopters in neighboring regions, and (ii) all other attributes of individuals in r that may influence their adoption propensity. The first factor is characterized by a logit model reflecting the likelihood of adoption due to spatial contacts with previous adopters, and the second by a logit model reflecting the likelihood of adoption due to other intrinsic effects. The resulting spatial diffusion process is then assumed to be driven by a probabilistic mixture of the two. A number of formal properties of this model are analyzed, including its asymptotic behavior. But the main analytical focus is on statistical estimation of parameters. Here it is shown that standard maximum‐likelihood estimates require large sample sizes to achieve reasonable results. Two estimation approaches are developed which yield more sensible results for small sample sizes. These results are applied to a small data set involving the adoption of a new Internet grocery‐shopping service by consumers in the Philadelphia metropolitan area.     

An Anisotropic Model for Spatial Processes

One of the key assumptions in spatial econometric modeling is that the spatial process is isotropic, which means that direction is irrelevant in the specification of the spatial structure. On the one hand, this assumption largely reduces the complexity of the spatial models and facilitates estimation and interpretation; on the other hand, it appears rather restrictive and hard to justify in many empirical applications. In this article a very general anisotropic spatial model, which allows for a high level of flexibility in the spatial structure, is proposed. This new model can be estimated using maximum likelihood and its asymptotic properties are derived at length. When the model is applied to the well-known 1970 Boston housing prices data, it significantly outperforms the isotropic spatial lag model. It also provides interesting additional insights into the price determination process in the properties market. Finally, a Monte Carlo simulation study is used to confirm the optimal properties of the model.     

Bayesian Model Averaging for Spatial Econometric Models

We extend the literature on Bayesian model comparison for ordinary least-squares regression models to include spatial autoregressive and spatial error models. Our focus is on comparing models that consist of different matrices of explanatory variables. A Markov Chain Monte Carlo model composition methodology labeled MC ³ by Madigan and York is developed for two types of spatial econometric models that are frequently used in the literature. The methodology deals with cases where the number of possible models based on different combinations of candidate explanatory variables is large enough such that calculation of posterior probabilities for all models is difficult or infeasible. Estimates and inferences are produced by averaging over models using the posterior model probabilities as weights, a procedure known as Bayesian model averaging. We illustrate the methods using a spatial econometric model of origin–destination population migration flows between the 48 U.S. states and the District of Columbia during the 1990–2000 period.     

A Simulation Study on Specifying a Regression Model for Spatial Data: Choosing between Autocorrelation and Heterogeneity Effects

In this simulation study, regressions specified with autocorrelation effects are compared against those with relationship heterogeneity effects, and in doing so, provides guidance on their use. Regressions investigated are: (1) multiple linear regression, (2) a simultaneous autoregressive error model, and (3) geographically weighted regression. The first is nonspatial and acts as a control, the second accounts for stationary spatial autocorrelation via the error term, while the third captures spatial heterogeneity through the modeling of nonstationary relationships between the response and predictor variables. The geostatistical‐based simulation experiment generates data and coefficients with known multivariate spatial properties, all within an area‐unit spatial setting. Spatial autocorrelation and spatial heterogeneity effects are varied and accounted for. On fitting the regressions, that each have different assumptions and objectives, to very different geographical processes, valuable insights to their likely performance are uncovered. Results objectively confirm an inherent interrelationship between autocorrelation and heterogeneity, that results in an identification problem when choosing one regression over another. Given this, recommendations on the use and implementation of these spatial regressions are suggested, where knowledge of the properties of real study data and the analytical questions being posed are paramount.     

Applying Local Indicators of Spatial Association to Analyze Longitudinal Data: The Absolute Perspective

Local Indicators of Spatial Association (LISA) are a class of spatial statistical methods that have been widely applied in various scientific fields. When applying LISA to make longitudinal comparisons of spatial data, a common way is to run LISA analysis at each time point, then compare the results to infer the distributional dynamics of spatial processes. Given that LISA hinges on the global mean value that often varies across time, the LISA result generated at time T_i reflects the spatial patterns strictly with respect to T_i. Therefore, the typical comparative cross-sectional analysis with LISA can only characterize the relative distributional dynamics. However, the relative perspective alone is inadequate to comprehend the full picture, as the patterns are not directly associated with the changes of the spatial process’s intensity. We argue that it is important to obtain the absolute distribution dynamics to complement the relative perspective, especially for tracking how spatial processes evolve across time at the local level. We develop a solution that modifies the significance test when implementing LISA analysis of longitudinal data to reveal and visualize the absolute distribution dynamics. Experiments were conducted with Mongolian livestock data and Rwanda population data.