Concerned with the doubly constrained case of spatial interaction models, this paper introduces a general functional form that subsumes the usual multiplicative (Wilson) and additive (Tobler) variants as extreme variants. Specifically, this formulation depends on a scalar Λ allowed to vary between 0 (multiplicative case) and 1 (additive case). A computational procedure is suggested and then illustrated by means of an application to interregional migration data.
Get full access to this article
View all access options for this article.
References
1.
BacharachM, 1970Biproportional Matrices and Input–Output Change (Cambridge University Press, Cambridge)
2.
BoxG E PCoxD R, 1964, “An analysis of transformations”Journal of the Royal Statistical Society26211–243
3.
DorigoGToblerW, 1983, “Push-pull migration laws”Annals of the Association of American Geographers731–17
4.
EvansA W, 1971, “The calibration of trip distribution models with exponential or similar cost functions”Transportation Research515–38
5.
GossEChangH S, 1983, “Changes in elasticities of interstate migration: Implication of alternative functional forms”Journal of Regional Science23223–232
6.
KauJ BSirmansC F, 1979, “The functional form of the gravity model”International Regional Science Review4127–136
7.
KullbackS, 1959Information Theory and Statistics (John Wiley, New York)
8.
LedentJ, 1980, “Calibrating Alonso's general theory of movement: The case of interprovincial migration flows in Canada”Sistemi Urbani2327–358
9.
Statistics Canada, 1981Estimates of Population for Canada and the Provinces Catalogue 91–201 (Information Canada, Ottawa, Ontario)
10.
TermoteMFréchetteR, 1979Les Variations du Courant Migratoire Interprovincial (Institut National de la Recherche Scientifique-Urbanisation, Montréal, Québec)
11.
ToblerW, 1983, “An alternative formulation for spatial-interaction modeling”Environment and Planning A15693–703
12.
WilsonA G, 1967, “A statistical theory of spatial distribution models”Transportation Research1253–269
13.
WilsonA G, 1983, “Tobler's ‘An alternative formulation for spatial-interaction modeling’: An observation”Environment and Planning A15705–706
14.
ZarembkaP, 1974, “Transformation of variables in econometrics” in Frontiers in Econometrics Ed. ZarembkaP, (Academic Press, New York) chapter 3
