Statistics for Spatial Data.

Emotion and Adaptation

An introduction to spatial econometric models and methods is provided that discusses spatial autoregressive processes that can be used to extend conventional regression models. Estimation and interpretation of these models are illustrated with an applied example that examines the relationship between commuting to work times and transportation mode choice for a sample of 3,110 US counties in the year 2000. These extensions to conventional regression models are useful when modeling cross-sectional regional observations or and panel data samples collected from regions over both space and time can be easily implemented using publicly available software. Use of these models for the case of non-spatial structured dependence is also discussed.

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Introduction to spatial econometrics

Economics and Information Theory

Over the past decade, the field of finite-dimensional variational inequality and complementarity problems has seen a rapid development in its theory of existence, uniqueness and sensitivity of solution(s), in the theory of algorithms, and in the application of these techniques to transportation planning, regional science, socio-economic analysis, energy modeling, and game theory. This paper provides a state-of-the-art review of these developments as well as a summary of some open research topics in this growing field.

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

I Theoretical Development.- 1 Spatial Interaction Processes: An Overview.- 1.1 Introduction.- 1.2 Theoretical Perspectives.- 1.2.1 Macro versus Micro Theories.- 1.2.2 Static versus Dynamic Theories.- 1.2.3 Probabilistic versus Deterministic Theories.- 1.3 Analytical Framework.- 1.3.1 Measures of Spatial Separation.- 1.3.2 Spatial Aggregation Assumptions.- 1.3.3 Structural Independence Assumptions.- 1.4 Spatial Interaction Processes.- 1.4.1 Interaction Patterns.- 1.4.2 General Interaction Processes.- 1.4.3 Independent Interaction Processes.- 1.5 Relaxations of Independence.- 1.5.1 Relaxations of Frequency Independence.- 1.5.2 Relaxations of Locational Independence.- 1.5.3 More Complex Types of Interdependencies.- 2 Gravity Models: An Overview.- 2.1 Introduction.- 2.2 General Gravity Models.- 2.2.1 Model Specifications.- 2.2.2 Illustrative Examples.- 2.2.3 Behavioral Characterizations.- 2.3 Functional Specifications.- 2.3.1 Origin and Destination Functions.- 2.3.2 Deterrence Functions.- 2.4 Exponential Gravity Models.- 2.4.1 Model Specifications.- 2.4.2 Illustrative Examples.- 2.4.3 Behavioral Characterizations.- 2.5 Generalizations of the Gravity Models.- 2.5.1 Generalized Search Processes.- 2.5.2 Interaction Processes with Hierarchical Destinations.- 2.5.3 Interaction Processes with Random Destination Sets.- 3 Spatial Interaction Processes: Formal Development.- 3.1 Introduction.- 3.2 Analytical Preliminaries.- 3.2.1 Measurable Spaces.- 3.2.2 Measurable Functions.- 3.2.3 Probability Spaces.- 3.3 Interaction Probability Spaces.- 3.3.1 Interaction Patterns.- 3.3.2 Locational Attributes of Interactions.- 3.3.3 Interaction Events.- 3.3.4 Frequency Attributes of Interactions.- 3.4 Interaction Processes.- 3.4.1 Separation Configurations.- 3.4.2 General Interaction Processes.- 3.4.3 Independent Interaction Processes.- 3.5 Frequency Processes.- 3.6 Generated Frequency Processes.- 3.6.1 Poisson Frequency Processes.- 3.6.2 Poisson Characterization Theorem.- 3.7 Threshold Interaction Processes.- 3.7.1 Potential Interactions.- 3.7.2 Independent Threshold Interaction Processes.- 3.7.3 Threshold Frequency Processes.- 3.8 Search Processes.- 3.8.1 Search Events.- 3.8.2 Realized-Interaction Frequencies.- 3.8.3 Independent Search Processes.- 3.9 Relaxations of Independence.- 3.9.1 Relaxations of Frequency Independence.- 3.9.2 Relaxation of Locational Independence.- 3.9.3 More Complex Types of Interdependencies.- 3.10 Notes and References.- 4 Gravity Models: Formal Development.- 4.1 Introduction.- 4.2 Definition of Gravity Model Classes.- 4.2.1 General Gravity Models.- 4.2.2 Exponential Gravity Models.- 4.2.3 Relationships Among Model Types.- 4.3 Examples of Gravity Model Classes.- 4.3.1 Carroll-Bevis Processes.- 4.3.2 Threshold Interaction Processes.- 4.3.3 Kullback-Leibler Processes.- 4.3.4 Simple Search Processes.- 4.4 Axioms for Interaction Processes.- 4.4.1 Positive Interaction Processes.- 4.4.2 Behavioral Axioms.- 4.4.3 Relations among Axioms.- 4.5 Characterizations of Gravity Models.- 4.5.1 Analytical Preliminaries.- 4.5.2 Characterizations of General Gravity Models.- 4.5.3 Characterizations of Exponential Gravity Models.- 4.6 Generalizations of Gravity Models.- 4.6.1 Interaction Processes with Hierarchical Destinations.- 4.6.2 Interaction Processes with Random Destination Sets.- 4.6.3 Interaction Processes with Prominence Effects.- 4.7 Notes and References.- II Methods.- 5 Maximum Likelihood.- 5.1 Introduction.- 5.1.1 Preliminaries.- 5.1.2 Maximum Likelihood Estimation.- 5.1.3 A Preview of this Chapter.- 5.2 Existence and Uniqueness of ML Estimates.- 5.2.1 Condition ML1.- 5.2.2 Condition ML2.- 5.2.3 Proof of Theorem 5.1.- 5.2.4 ML Estimation for Multinomial Gravity Models.- 5.3 ML Estimation Algorithms: Special Cases.- 5.3.1 The DSF Procedure.- 5.3.2 The Evans-Kirby Procedure.- 5.3.3 The Hyman Procedure.- 5.4 The LDSF Procedure.- 5.4.1 The Procedure.- 5.4.2 An Approximation Useful for ML Estimation Algorithms.- 5.4.3 Application to Short-term Forecasting.- 5.5 General Algorithms for ML Estimates.- 5.5.1 Scoring Methods.- 5.5.2 The Modified Scoring Procedure.- 5.5.3 Gradient Search Procedures.- 5.5.4 Modified Gradient Search Procedures.- 5.5.5 GLIM.- 5.6 Performance of General Algorithms.- 5.6.1 The Data.- 5.6.2 Convergence.- 5.6.3 Speeds of Procedures.- 5.7 Covariance of Estimates.- 5.7.1 Covariance of $${\hat \theta _k}$$'s.- 5.7.2 Covariance of $$ {\hat{T}_{{ij}}} $$.- 5.7.3 Other Forecasts.- 5.8 Goodness of Fit.- 5.8.1 Global Measures.- 5.8.2 Residuals.- 5.9 Other Properties of ML Estimates.- 5.9.1 Asymptotic Properties.- 5.9.2 Small Sample Properties.- 5.9.3 ML Estimates from Factored Data.- 5.10 Notes and Concluding Remarks.- 5.10.1 Conclusion.- 6 Least Squares.- 6.1 Introduction.- 6.1.1 A Preview of this Chapter.- 6.2 LS Procedures.- 6.2.1 Reduction of Parameters.- 6.2.2 Gauss-Markov Conditions.- 6.2.3 Bias.- 6.2.4 Weighting.- 6.2.5 Procedures.- 6.3 Large Sample Theory.- 6.3.1 Preliminaries.- 6.3.2 The Main Theorem.- 6.3.3 A Projection Matrix.- 6.3.4 Proof of Theorem 6.1.- 6.3.5 Some Practical Details.- 6.4 Alternative Methods.- 6.4.1 Use of Iterative Reweighting in Procedure 1.- 6.4.2 Not Reducing Parameters.- 6.4.3 Use of OLS.- 6.4.4 Use of Generalized Inverses.- 6.5 Small Sample Properties.- 6.5.1 The Procedures.- 6.5.2 The Simulations.- 6.5.3 Results from Simulations.- 6.5.4 Conclusions.- 6.6 Non-linear Least Squares.- 6.7 Notes and Concluding Remarks.- 6.7.1 Conclusions.- Appendix: Skokie Data.- References.- List of Principal Definitions and Results.- Author Index.

Gravity Models of Spatial Interaction Behavior

The International Regional Science Review (IRSR) is an appropriate journal for a memorial to Walter Isard. Walter founded the journal in 1975, and was its first editor, though only for a brief period. Walter had several motivations for founding the IRSR. First, the field of Regional Science had grown considerably since he formally founded it over twenty years earlier, and there was a need for more journals to disseminate the research in this field. Second, Walter saw the need for a journal with greater flexibility in approaches and topics than the Journal of Regional Science, for which he was the founding editor in 1958, and the Papers and Proceedings of the Regional Science Association (now Papers in Regional Science) which he founded in 1954. Together with Åke Andersson, he also reorganized Regional Science and Urban Economics in 1975. His imprint is evident in the environmental theme of the inaugural issue of the IRSR and in the approaches and topics published in the journal over the years under leadership of its very able subsequent editors Andrew Isserman, Shelby Gerking, Luc Anselin, and Serge Rey. Walter Isard was honored in numerous ways over the course of his outstanding career, not only by the field of Regional Science but also by the fields of Economics, Geography, Planning, and Peace Science (which he also founded). His contributions are well known, and in fact Walter went so far as to discourage efforts to honor him

https://journals.sagepub.com/doi/pdf/10.1177/0160017613478576

International Regional Science Review: Special Issue in Memory of Walter Isard

A Bayesian probit model with individual effects that exhibit spatial dependencies is set forth. Since probit models are often used to explain variation in individual choices, these models may well exhibit spatial interaction effects due to the varying spatial location of the decision makers. That is, individuals located at similar points in space may tend to exhibit similar choice behavior. The model proposed here allows for a parameter vector of spatial interaction effects that takes the form of a spatial autoregression. This model extends the class of Bayesian spatial logit/probit models presented in LeSage (2000) and relies on a hierachical construct that we estimate via Markov Chain Monte Carlo methods. We illustrate the model by applying it to the 1996 presidential election results for 3,110 U.S. counties.

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A bayesian probit model with spatial dependencies

The downsizing and closing of state mental health institutions in Philadelphia in the 1990’s led to the development of a continuum care network of residential-based services. Although the diversity of care settings increased, congestion in facilities caused many patients to unnecessarily spend extra days in intensive facilities. This study applies a queuing network system with blocking to analyze such congestion processes. “Blocking” denotes situations where patients are turned away from accommodations to which they are referred, and are thus forced to remain in their present facilities until space becomes available. Both mathematical and simulation results are presented and compared. Although queuing models have been used in numerous healthcare studies, the inclusion of blocking is still rare. We found that, in Philadelphia, the shortage of a particular type of facilities may have created “upstream blocking”. Thus removal of such facility-specific bottlenecks may be the most efficient way to reduce congestion in the system as a whole.

Modeling patient flows using a queuing network with blocking.

We propose a statistical index of industrial localization based on the Kullback-Leibler divergence. This index is particularly well suited to cases where industrial data are available only at the regional level. Unlike existing regional-level indices, our index can be employed to test the significance of industrial localization relative to a hypothesized reference distribution of probable locations across regions. In addition, one can test relative degrees of localization among industries. Finally, as with all Kullback-Leibler divergence indices, our index can be decomposed into components representing localization at various levels of spatial aggregation.

/pdf/a-divergence-statistic-for-industrial-localization-3tktzbm9nq.pdf

Tony E. Smith

Papers

Gravity Models of Spatial Interaction Behavior

International Regional Science Review: Special Issue in Memory of Walter Isard

A bayesian probit model with spatial dependencies

Modeling patient flows using a queuing network with blocking.

A Divergence Statistic for Industrial Localization