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.     

Explorations and Syntheses of Linear Programming And Spatial Interaction Models of Residential Location

Various “linear programming” models of residential location are explored in some detail. It is then shown that entropy maximizing “sub-optimal” versions of these can be developed, which may be more realistic at typical levels of resolution used for analysis but can still be given some of the interpretations of the programming models. Further, any programming model can be seen as a limiting case of some entropy maximizing model in which some of the parameters tend to infinity. Some empirical tests of both kinds of models are presented, and the limiting relationships are discussed.     

Estimating Spatial Models Within A Disequilibrium Framework

Modeling demand in a spatial context requires careful handling of regional interactions. In situations where there are constraints in some markets that lead to spillovers to others it is useful to build this explicitly into the model. In this paper I present a theoretical model that is related to the disequilibrium and the spatial econometric literature. Under certain conditions the model may be estimable and an appropriate estimation technique that uses the EM algorithm, is put forward. A data set from the U.K. market for secondary school places provides a test for the procedure.     

A Note on Trip Benefits in Spatial Interaction Models

We extend the well-known transport users' benefits measure (TUB) for the doubly-constrained spatial interaction model derived by Williams (1976). The original formula expresses the TUB as composed by two terms associated with the origin and the destination zones. First, the TUB is associated here with trips instead of zones, providing a natural interpretation as a rule-of-a-half measure of benefit under inelastic demand (for the short-run case). Second, a TUB formula for the long-run case is derived, that is, when the total number of trips, trip origins, and trip destinations change. We then propose updated measures of accessibility for location behavior.     

Using Simple Genetic Algorithms to Calibrate Spatial Interaction Models

The paper investigates the use of two genetic algorithms in an attempt to obtain globally optimal parameter estimates for a mix of simple and complex spatial interaction models. The genetic algorithms work well and are strongly advocated as a more robust approach particularly for use with the more complex multiparameter models where the differences in both performance and parameter values are judged to be significant.     

Building an Automated Modeling System to Explore a Universe of Spatial Interaction Models

A methodology is described for harnessing the power of supercomputer hardware to build an automated modeling system. The problems of applying this new approach to mathematical modeling in geography are discussed by reference to the design of better performing spatial interaction models. It is also possible that the results may provide clues about new theories and knowledge.     

Spatial Characteristics and Comparisons of Interaction and Median Clustering Models

Cluster analysis has been pursued from a number of directions for identifying interesting relationships and patterns in spatial information. A major emphasis is currently on the development and refinement of optimization‐based clustering models for the purpose of exploring spatially referenced data. Within this context, two basic methods exist for identifying clusters that are most similar. An interesting feature of these two approaches is that one method approximates the relationships inherent in the other method. This is significant given that the approximation approach is invariably utilized for cluster detection in spatial and aspatial analysis. A number of spatial applications are investigated which highlight the differences in clusters produced by each model. This is an important contribution because the differences are in fact quite significant, yet these contrasts are not widely known or acknowledged.     

Learning in Single Hidden-Layer Feedforward Network Models: Backpropagation in a Spatial Interaction Modeling Context

Learning in neural networks has attracted considerable interest in recent years. Our focus is on learning in single hidden-layer feedforward networks which is posed as a search in the network parameter space for a network that minimizes an additive error function of statistically independent examples. We review first the class of single hidden-layer feedforward networks and characterize the learning process in such networks from a statistical point of view. Then we describe the backpropagation procedure, the leading case of gradient descent learning algorithms for the class of networks considered here, as well as an efficient heuristic modification. Finally, we analyze the applicability of these learning methods to the problem of predicting interregional telecommunication flows. Particular emphasis is laid on the engineering judgment, first, in choosing appropriate values for the tunable parameters, second, on the decision whether to train the network by epoch or by pattern (random approximation), and, third, on the overfitting problem. In addition, the analysis shows that the neural network model whether using either epoch-based or pattern-based stochastic approximation outperforms the classical regression approach to modeling telecommunication flows.     

Optimal Facility Location in a One-Dimensional Spatial Market

This paper analyzes properties of the optimal spatial arrangement of what may be interpreted as a class of public facilities. Optimality is defined as cost minimization. Three different optimality criteria are considered, and for each, the necessary and, sufficient conditions, market area size, and production levels, are derived. The relationship between optimal production levels and number of facilities needed is also considered. Next the results of implementing various pricing strategies are analyzed with emphasis given to marginal and uniform pricing. It is shown that, given certain conditions, all facilities incur operating deficits, given marginal pricing. Estimates on the level of the deficits are derived in terms of location rents. Finally, in the appendix, several important results from other studies are derived as special cases of the basic model.     

Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels

This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.     

Location and Pricing Decisions of a MultiStore Monopoly in a Spatial Market

Abstract.  This article presents an analysis of location and pricing decisions of a monopolist about to open several stores in a compact geographical space. The number of stores is made endogenous by the introduction of fixed costs. A novel methodology is developed, by which the firm's location and price decisions are represented as continuous functions defined over the geographical space. This modeling artifact generates a negligible error but simplifies the solution considerably and allows the derivation of several intuitive results. Although the focus is on one‐dimensional markets, it is shown that the method can easily be adapted to two‐dimensional markets.     

Modern Location Factors in Dynamic Regions

Globalization has had an enormous impact on traditional industrial structures. It almost seems that everything is everywhere the same. And yet, in reality, some regions in a single industrialized country enjoy rapid economic growth while others are downsizing or stagnating. Thus there must be some remaining regional competitive advantages—even in the “Age of Globalization”. This paper engages in a quest to discover what these modern location factors might be and how and why they are necessary in creating dynamics and regional growth. In doing so, we link the driving forces behind these modern location factors with regional performance and eventually arrive at a concept of a regional lifecycle and its key dynamics. Using data that paint a comprehensive picture of industry and regional development in Germany we try to find empirical evidence for our approach.     

Spatial Models of Spread-Backwash Processes

Spread-backwash processes are central elements in regional development thought. This article argues that the main spread-backwash processes produce developmental change that has a general spatial form. Straightforward models of the processes of government incomes and expenditure flows, private capital flows, intraregional trade, migration-commuting, and the diffusion of innovations provide the rationale for the general distance decay form of developmental impact. Each model is supported by evidence from the relevant literature. It is argued that there is not a dichotomous set of spread versus backwash processes, but rather that the same set of processes yields differential spatial impacts.