The theoretical background of spatial interaction models is reviewed and used as a basis for the derivation of a novel approach for directly calibrating spatial interaction models concurrently with the main solution procedure. The analysis was prompted by a link with Fisher information. The new approach is compared with a number of earlier approaches, particularly that of Sen and Smith.
Get full access to this article
View all access options for this article.
References
1.
AndersonP-A, 1981, “On the convergence of iterative methods for the distribution balancing problem”Transportation Research B15173–201
2.
BattyM, 1976Urban Modelling (Cambridge University Press, Cambridge)
3.
CesarioF, 1975, “Least squares estimation of trip distribution parameters”Transportation Research913–18
4.
CrossH, 1936Analysis of Flows in Networks of Conduits or Conductors Bulletin number 286, University of Illinois, Urbana, IL
5.
DemboR SEistenstatS CSteihaugT, 1982, “Inexact Newton methods”Siam Journal on Numerical Analysis19400–408
6.
ErlanderSStewartN F, 1990The Gravity Model in Transportation Analysis: Theory and Extensions (VSP, Utrecht)
7.
FriedenB R, 1998Physics from Fisher Information: A Unification (Cambridge University Press, Cambridge)
8.
FriedenB RSofferB H, 1995, “Lagrangians of physics and the game of Fisher-information transfer”Physical Review E522274–2286
9.
GilesD E AHamptonP, 1981, “Interval estimation in the calibration of certain trip distribution models”Transportation Research B15203–219
10.
GolubGOrtegaJ M, 1993Scientific Computation: An Introduction with Parallel Computing (Academic Press, New York)
11.
HymanG M, 1969, “The calibration of trip distribution models”Environment and Planning1105–112
12.
JaynesE T, 1968, “Prior probabilities”IEEE Transactions on Systems Science and Cybernetics4(3) 227–248
13.
JaynesE T, 1994Probability Theory: The Logic of Science republished as JaynesE T, 2003 Probability Theory: The Logic of Science Ed. BretthorstG L (Cambridge University Press, Cambridge)
14.
KruithofJ, 1937Calculation of Telephone Traffic translation number 2663, Post Office Research Department Library, London
15.
OrtegaJRheinboldtW, 1970Iterative Solution of Nonlinear Equations in Several Variables (Academic Press, New York)
16.
RaoC R, 1973Linear Statistical Inferencing and its Applications (John Wiley, New York)
17.
RobillardPStewartN F, 1974, “Iterative numerical methods for trip distribution methods”Transportation Research8575–582
18.
RobinsonG M, 1998Methods and Techniques in Human Geography (John Wiley, Chichester, Sussex)
19.
ScharfL L, 1990Statistical Signal Processing (Addison-Wesley, Reading, MA)
20.
SenA, 1986, “Maximum likelihood estimation of gravity model parameters”Journal of Regional Science26461–473
21.
SenASmithT E, 1995Gravity Models of Spatial Interaction Behaviour (Springer, New York)
22.
SenASootS, 1981, “Procedures for calibrating the generalized gravity model”Proceedings of the Regional Science Association48165–176
23.
SnickarsFWeibullJ W, 1977, “A minimum information principle”Regional Science and Urban Economics7137–168
24.
Van TreesH L, 1968Detection Estimates and Modulation Theory, Volume 1 (John Wiley, New York)
25.
WilsonA G, 1967, “A statistical theory of spatial distribution models”Transportation Research1253–269
26.
WilsonA G, 1970Entropy in Urban and Regional Modelling (Pion, London)
27.
WilsonA G, 2000Complex Spatial Systems: The Modelling Foundations of Regional and Urban Analysis (Prentice-Hall, London)
