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.     

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 TRANSLOG APPROACH TO CONSUMER SPATIAL BEHAVIOR*

With the view that travel behavior stems from the principle of utility maximization, in this paper I present a spatial translog demand model that accounts for interdependence among travel alternatives and that handles varying elasticities of substitution for various destination pairs. Using simulation as the mode of inquiry, this model describes the effect of spatial size, spatial configuration, and spatial substitution on spatial interaction. In addition to indicating how varying spatial sizes and configurations affect the average trip length and the trip making pattern, the simulation results also point out the possible effect of having spatially dependent locations in the system. Competing destinations increase the attractiveness of nearby locations, and complementary destinations reduce the impeding effect of space. The model is primarily relevant to the demand for shopping trips.     

Model Uncertainty in Matrix Exponential Spatial Growth Regression Models

This article considers the most important aspects of model uncertainty for spatial regression models, namely, the appropriate spatial weight matrix to be employed and the appropriate explanatory variables. We focus on the spatial Durbin model (SDM) specification in this study that nests most models used in the regional growth literature, and develop a simple Bayesian model‐averaging approach that provides a unified and formal treatment of these aspects of model uncertainty for SDM growth models. The approach expands on previous work by reducing the computational costs through the use of Bayesian information criterion model weights and a matrix exponential specification of the SDM model. The spatial Durbin matrix exponential model has theoretical and computational advantages over the spatial autoregressive specification due to the ease of inversion, differentiation, and integration of the matrix exponential. In particular, the matrix exponential has a simple matrix determinant that vanishes for the case of a spatial weight matrix with a trace of zero. This allows for a larger domain of spatial growth regression models to be analyzed with this approach, including models based on different classes of spatial weight matrices. The working of the approach is illustrated for the case of 32 potential determinants and three classes of spatial weight matrices (contiguity‐based, k‐nearest neighbor, and distance‐based spatial weight matrices), using a data set of income per capita growth for 273 European regions.     

Nonlinear Multivariate Spatial Modeling Using NLPCA and Pair‐Copulas

A novel geostatistical modeling approach is developed to model nonlinear multivariate spatial dependence using nonlinear principal component analysis (NLPCA) and pair‐copulas. In spatial studies, multivariate measurements are frequently collected at each location. The dependence between such measurements can be complex. In this article, a multivariate geostatistical model is developed that can capture both nonlinear spatial dependence across locations and nonlinear dependence between measurements at a particular location. Nonlinear multivariate dependence between spatial variables is removed using NLPCA. Subsequently, a pair‐copula based model is fitted to each transformed variable to model the univariate nonlinear spatial dependencies. NLPCA and pair‐copulas, within the proposed model, are compared with stepwise conditional transformation (SCT) and conventional kriging. The results show that, for the two case studies presented, the proposed model that utilizes NLPCA and pair‐copulas reproduces nonlinear multivariate structures and univariate distributions better than existing methods based on SCT and kriging.     

ACCOUNTING FOR LOCAL SPATIAL HETEROGENEITIES IN HOUSING MARKET STUDIES

We adopt a novel method to deal with omitted spatial heterogeneities in hedonic house price analysis. A Gaussian variant of the conditional autoregressive (CAR) model is used to study the impact of spatial effects. In a general linear modeling framework, we include zone‐specific random effects that are allowed to interact spatially with neighboring zones. The results demonstrate that this estimator accounts for missing spatial information, producing more reliable results on estimated spatially related coefficients. The CAR model is benchmarked against a fixed effects model. Socioeconomic neighborhood characteristics are found to have only modest impact on spatial variation in housing prices.     

现代服务业集聚形成机理空间计量分析

在纳入空间效应前提下,构建现代服务业集聚形成机理空间面板计量模型,对我国28个省域相关数据实证研究表明:我国现代服务业集聚在省域之间有较强的空间依赖性和正的空间溢出效应。技术差异在时间维度上对现代服务业集聚促进作用显著,在空间维度上并不显著;交易费用与现代服务业集聚有显著的负相关性;知识溢出、规模经济、政府行为对现代服务业集聚促进作用显著。     

A Spatial Price Determination Model for Multi‐Market Heterogeneously Distributed Resources: An Application to Forestry Markets in Sweden

The spatial dimension is a key paradigm in price determination, as attested by recent studies in the literature that highlighted the differential in market behavior between spatial and non‐spatial pricing settings. In this paper, we develop a model of spatial pricing for multi‐market heterogeneously distributed resources, with an application to the Swedish forestry sector. The focus of the model is to estimate the impact of spatial interaction on the demand for resources in terms of resource allocation, competition, and pricing. In its core, the pricing mechanism relies on a supply–demand framework. Using disaggregated data at the gridcell level for forest feedstock supply and harvesting costs in Sweden, we construct regional supply curves for each gridcell assuming a maximum transportation distance to delimit the potential market. Demand nodes are exogenously determined and are adjusted using a distance‐decay model to assess demand pressure across locations. We apply the model empirically to assess the impact on forest feedstock prices of a 20 TWh increase in biofuel production.     

Competition in a Repeated Spatial Auction Market with an Application to Timber Sales

In this paper we develop a model of a repeated spatial auction market. The auction model contributes to the literature on spatial competition by considering the sale of goods in a market with spatial and temporal dimensions, and in which goods are sold by an auction institution instead of a posted-price institution. In the Nash equilibrium of the spatial auction model, each bidder is found to have a dominance solvable strategy to bid below his net (of transportation costs) valuation for the first unit of the good because there is an option value to not winning, namely that the following units may be locationally preferred to the first unit. The equilibrium bidding strategies lead to the possibility of non–Pareto-efficient outcomes. The auction model is applied to data from U.S. Forest Service timber sales.     

Measuring potential spatial access to primary health care physicians using a modified gravity model

Ensuring equity of access to primary health care (PHC) across Canada is a continuing challenge, especially in rural and remote regions. Despite considerable attention recently by the World Health Organization, Health Canada and other health policy bodies, there has been no nation-wide study of potential (versus realized) spatial access to PHC. This knowledge gap is partly attributable to the difficulty of conducting the analysis required to accurately measure and represent spatial access to PHC. The traditional epidemiological method uses a simple ratio of PHC physicians to the denominator population to measure geographical access. We argue, however, that this measure fails to capture relative access. For instance, a person who lives 90 minutes from the nearest PHC physician is unlikely to be as well cared for as the individual who lives more proximate and potentially has a range of choice with respect to PHC providers. In this article, we discuss spatial analytical techniques to measure potential spatial access. We consider the relative merits of kernel density estimation and a gravity model. Ultimately, a modified version of the gravity model is developed for this article and used to calculate potential spatial access to PHC physicians in the Canadian province of Nova Scotia. This model incorporates a distance decay function that better represents relative spatial access to PHC. The results of the modified gravity model demonstrate greater nuance with respect to potential access scores. While variability in access to PHC physicians across the test province of Nova Scotia is evident, the gravity model better accounts for real access by assuming that people can travel across artificial census boundaries. We argue that this is an important innovation in measuring potential spatial access to PHC physicians in Canada. It contributes more broadly to assessing the success of policy mandates to enhance the equitability of PHC provisioning in Canadian provinces.     

Cellular Automata for Studying Historical Spatial Process of Traditional Settlements Based on Gaussian Mixture Model: A Case Study of Qiaoxiang Village in Southern China

ABSTRACT

The spatial evolution of traditional rural settlements is a natural process that occurs without professional development planning. With rural spatial organization now being stimulated by China’s economic structure adjustment, making top-down plans match bottom-up spatial principles is important for the continuity of rural communities. In this research, a Cellular automaton based model was introduced to describe the historical spatial rules of rural settlements based on a traditional village in Southern China. In order to reproduce the rural spatial characteristics and laws that were close to the actual situation truthfully and distinctly, in this model, we refined the growth process into three cyclical steps, and used a Multivariate Gaussian Mixture Model for the evaluation of spatial transition potential. Through historical simulation, evaluation of the current status, and future spatial predictions, results showed that: (1) the growth during the whole spatial process maintained logical consistency for optimal selection; (2) certain houses in the southeast region should be carefully protected as a core living culture exhibit, while the best utilization of other homes should be considered; and (3) the most probable region of growth for tourist services or new housing estates is scattered along the river in the central area of the village.     

A Spatial Prior for Bayesian Vector Autoregressive Models

In this paper we develop a Bayesian prior motivated by cross-sectional spatial autoregressive models for use in time-series vector autoregressive forecasting involving spatial variables. We compare forecast accuracy of the proposed spatial prior to that from a vector autoregressive model relying on the Minnesota prior and find a significant improvement. In addition to a spatially motivated prior variance as in LeSage and Pan (1995) we develop a set of prior means based on spatial contiguity. A Theil-Goldberger estimator may be used for the proposed model making it easy to implement.     

THE SLX MODEL

We provide a comprehensive overview of the strengths and weaknesses of different spatial econometric model specifications in terms of spillover effects. Based on this overview, we advocate taking the SLX model as point of departure in case a well‐founded theory indicating which model is most appropriate is lacking. In contrast to other spatial econometric models, the SLX model also allows for the spatial weights matrix W to be parameterized and the application of standard econometric techniques to test for endogenous explanatory variables. This starkly contrasts commonly used spatial econometric specification strategies and is a complement to the critique of spatial econometrics raised in a special theme issue of the Journal of Regional Science (Volume 52, Issue 2). To illustrate the pitfalls of the standard spatial econometrics approach and the benefits of our proposed alternative approach in an empirical setting, the Baltagi and Li (2004) cigarette demand model is estimated.     

MODELING SPATIAL STRUCTURES THROUGH EQUILIBRIUM STATES FOR TRANSITION MATRICES*

ABSTRACT. In this paper we present a model for spatial interaction within a network of towns. This interaction is modeled through equilibrium states for certain Markov chains where, in particular, explicit formulas for these states are given. Our model exploits and intertwines ideas from gravity models, the competing destinations model and the intervening opportunities model. The central idea in the paper is to capture the effect of spatial structure in a framework where interaction is determined by the global network configuration.     

Analysis of Dynamic Spatial Interaction Models by Means of Optimal Control

This paper deals with the design of general classes of dynamic spatial interaction models. On the basis of a general (well-behaved) multiperiod objective function and of a dynamic model representing the evolution of a spatial interaction system, an optimal control model is constructed. Particular attention is given to the equilibrium and stability conditions. It turns out that it is possible to identify steady-state solutions for a dynamic spatial interaction model. Furthermore, it can also be demonstrated that the entropy model is a specific case of this spatial interaction system. A simple illustration for urban dynamics is given as well.     

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.     

Exploring Spatial Process Dynamics Using Irregular Cellular Automaton Models

Cellular automaton models have enjoyed popularity in recent years as easily constructed models of many complex spatial processes, particularly in the natural sciences, and more recently in geography also. Most such models adopt a regular lattice (often a grid) as the basis for the spatial relations of adjacency that govern evolution of the model. A number of variations on the cellular automaton formalism have been introduced in geography but the impact of such variations on the likely behavior of the models has not been explored. This paper proposes a method for beginning to explore these issues and suggests that this is a new approach to the investigation of the relationships between spatial structure and dynamics of spatial processes. A framework for this exploration is suggested, and details of the required methods and measures are provided. In particular, a measure of spatial pattern—spatial information—based on entropy concepts is introduced. Initial results from investigation along the proposed lines are reported, which suggest that a distinction can he made between spatially robust and fragile processes. Some implications of this result and the methodology presented are briefly discussed.     

Designs for Detecting Spatial Dependence

The aim of this article is to find optimal or nearly optimal designs for experiments to detect spatial dependence that might be in the data. The questions to be answered are: how to optimally select predictor values to detect the spatial structure (if it is existent) and how to avoid to spuriously detect spatial dependence if there is no such structure. The starting point of this analysis involves two different linear regression models: (1) an ordinary linear regression model with i.i.d. error terms—the nonspatial case and (2) a regression model with a spatially autocorrelated error term, a so-called simultaneous spatial autoregressive error model. The procedure can be divided into two main parts: The first is use of an exchange algorithm to find the optimal design for the respective data collection process; for its evaluation an artificial data set was generated and used. The second is estimation of the parameters of the regression model and calculation of Moran's I , which is used as an indicator for spatial dependence in the data set. The method is illustrated by applying it to a well-known case study in spatial analysis.     

Does Policy Diffusion Need Space? Spatializing the Dynamics of Policy Diffusion

For decades, scholars in multiple disciplines have examined spatial diffusion, or the spatiotemporal properties associated with the diffusion of innovations. These properties include contagious, hierarchical, and relocation diffusion. Each of these refers to a spatial model that epitomizes how innovations spread among geographic locations. Policy diffusion, a separate but homologous research tradition, had its theoretical underpinnings in spatial diffusion. However, contemporary policy diffusion has focused largely on mechanism‐based diffusion. This article demonstrates how exploratory spatial data analysis can be used to uncover spatial policy diffusion properties. In this study, municipal smoking regulation adoptions, religious‐based initiatives, and bag ban and bag fees are examined. This study finds evidence that for each policy more than one property is occurring; therefore, this study proposes that a hybrid model best explains diffusion. This article demonstrates how examining spatial diffusion properties, in addition to diffusion mechanisms, can improve the conceptualization of diffusion theories, enhance mechanism or theory‐based specification of diffusion models, and unravel the specific regional or neighboring causal pathways linking policies between adopting jurisdictions.     

The Zone Definition Problem in Location-Allocation Modeling

Location-allocation modeling is a frequently used set of techniques for solving a variety of locational problems, some of which can be politically sensitive. The typical application of a location-allocation model involves locating facilities by selecting a set of sites from a larger set of candidate sites, with the selection procedure being a function of “optimality” in terms of the allocation of demand to the selected sites. In this paper we examine the sensitivity of one particular type of location-allocation model, the p-median procedure, to the definition of spatial units for which demand is measured. We show that a p-median solution is optimal only for a particular definition of spatial units and that variations in the definition of spatial units can cause large deviations in optimal facility locations. The broad implication of these findings is that the outcome of any location-allocation procedure using aggregate data should not be relied upon for planning purposes. This has important implications for a large variety of applications.