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Interaction (I) between i and j is a function of repulsive forces (R) at i and attractive forces (A) at j, and an inverse function of the friction/distance (D) between i and j
|Iij||The interaction volume from i to j|
|Ri||a parameter representing (repulsive) factors which are associated with "leaving" i (such as outmigration)|
|Aj||a parameter representing (attractive) factors related to going to j (such as inmigration)|
|Dij||the distance between i and j|
|P||Population of i & j|
|k & b||constants|
The most basic formulation of the gravity model simply substitutes the populations at i and j for the R and A factors. George Zipf's Pi Pj/Dij hypothesis is probably the most widely accepted form of the gravity model. [Migration between two cities i and j is proportional to the product of the two cities' populations and inversely proportional to the intervening distance.]
|eL||=||proportion of total non-housing expenditures that an individual is likely to make in her local environment|
|RSL||=||total period retail sales in the local environment|
|DL||=||average distance or travel time for a local individual to make a purchase within her local environment|
|RSNn||=||total period retail sales in the nth competing neighboring community|
|DNn||=||average distance or travel time for the local individual to make a purchase in the nth competing neighboring community|
M = number of migrants
Source: Ira Lowry, Migration and Metropolitan Growth: Two Analytical
L = persons in labor force
U = unemployment in %
W = hourly wage in manufacturing
D = airline distance
k = gravitational constant
e = error term
Source: Ira Lowry, Migration and Metropolitan Growth: Two Analytical Models (1966)
Travel Demand Models for the San Francisco Bay Area [June 1997; (BAYCAST-90) Technical Summary Charles L. Purvis, AICP]
Calibrating and Adjustment of System Planning Models - December 1990 [National Transportation Library]
Calibrating & Testing a GRAVITY MODEL for Any Size Urban Area [U.S. DEPARTMENT OF TRANSPORTATION Federal Highway Administration Reprinted August 1983]
TRANSPORTATION MODELS AND FORECASTS [The Council of Fresno County Governments (COG) is the State Regional Transportation Planning Agency and the Federal Metropolitan Planning Organization for Fresno County. As a transportation planning agency, COG is responsible for developing and maintaining a microcomputer-based traffic simulation model that represents Fresno County.]
Predictive Gravity Modeling for Marketing
Anderson, James E., "A Theoretical Foundation for the Gravity Equation," American Economic Review 69(1979), 106-16.
Caffrey, John and Herbert H. Isaacs, Estimating the Impact of College or University on the Local Economy. American Council on Education: Washington D.C. 1971. [Appendix C: The Gravity Model, pp.46ff.]
Erlander, S. and N.F. Stewart, The Gravity Model in Transportation Analysis -- Theory and Extensions: Topics in Transportation 1990; x+226 pages ISBN 90-6764-089-1 [book series Topics in Transportation]
Gossman, Charles S., Calvin F. Schmid et al., Migration of College and University Students in the United States. Seattle: University of Washington Press, 1968. [Ch.11 (pp.145ff.) "The Distance Factor in Student Migration"; Ch.12 (pp.153ff. "A Gravity Model of Student Migration"]]
Haynes, Kingsley E. and A.S. Fotheringham, Gravity and Spatial Interaction Models, Sage-Publications 1984.
Isard, Walter et al., Methods of Interregional and Regional Analysis, Ashgate 1998, ch.6 ("Gravity and Spatial Interaction Models"), pp. 243ff.
Isard, W., "A simple Rationale for Gravity Model Type Behavior," Papers of the Regional Science Association. 35 (1975), 25-30.
Long, W.H., The Economics of Air Travel Gravity Models, Journ. of Regional Science 10(3), 1970, 353ff.
Lowe, J.M. and A.Sen, Gravity Model Applications in Health Planning: Analyses of an Urban Hospital Market," Journal of Regional Science, 36 (1996), 437-62.
Mathur, V.K., "An Economic Derivation of the 'Gravity Law' of Spatial Interaction: A Comment," Journ. of Regional Science 10(3), 1970, 403ff.
Mikkonen-K.; Luoma-M. The parameters of the gravity model are changing - how and why? Journal-of-Transport-Geography. 1999; 7(4): 277-283
Melling-J.; Turner-R. The road to the asylum: Institutions, distance and the administration of pauper lunacy in Devon, 1845-1914, Journal-of-Historical-Geography. 1999; 25(3): 298-332
O'Kelly, M.E., Trade-area models and choice-based samples: Methods. Environment and Planning A. 1999; 31(4): 613-627
Olsson, Gunnar, Distance and Human Interaction: A Review and Bibliography. Regional Scienc e Research Institute, 1965.
Reilly, W.J., The Law of Retail Gravitation. New York: The Knickerbocker Press, 1931
Sen, A. and T.E. Smith, Gravity Models of Spatial Interaction Behavior. NY: Springer, 1995. [Sen & Smith, Gravity Models of Spatial Interaction Behavior Ashish Sen, University of Illinois at Chicago, Chicago and Tony E. Smith, University of Pennsylvania, Philadelphia, Advances in Spatial and Network Economics Series, Springer-Verlag, Berlin Heidelberg, 1995 [ISBN 3-540-60026-4]. Hardcover US $139.00.]
Stewart, John Q., "The Development of Social Physics," American Journal of
Physics, 18, 1950, 239-53.
Thorsen, Inge & Jens Petter Gitlesen,
Evaluation of Alternative Model Specifications to Predict
Journal of Regional Science
Volume 38 Issue 2 Page 273 - May 1998
Zipf, George Kingsley. "The P1P2/D Hypothesis: On
the Intercity Movement
of Persons," American Sociological Review, II(December 1946), 677-686.
Zipf, George Kingsley. Human Behavior and the Principle of Least Effort.
Cambridge, Mass., : Addison-Wesley, 1949.
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Thorsen, Inge & Jens Petter Gitlesen, Empirical Evaluation of Alternative Model Specifications to Predict Commuting Flows Journal of Regional Science Volume 38 Issue 2 Page 273 - May 1998
Zipf, George Kingsley. "The P1P2/D Hypothesis: On the Intercity Movement of Persons," American Sociological Review, II(December 1946), 677-686.
Zipf, George Kingsley. Human Behavior and the Principle of Least Effort. Cambridge, Mass., : Addison-Wesley, 1949.
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