The Log Normal and the Poisson Gravity Models in the Analysis of Interactions Phenomena
American Journal of Theoretical and Applied Statistics
Volume 4, Issue 4, July 2015, Pages: 291-299
Received: May 28, 2015;
Accepted: Jun. 9, 2015;
Published: Jul. 4, 2015
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Giuseppe Ricciardo Lamonica, Department of Economics and Social Sciences, Polytechnic University of Marche, Ancona, Italy
Three problems often encountered when bilateral interaction data are analyzed by means of the log-normal gravity model: the bias created by the logarithmic transformation, the failure of the homoscedasticity assumption and the treatment of zero valued flows. When the interaction are count data type that takes non-negative integer values, to overcome these problems the literature suggests to use a Poisson gravity model instead of log-normal model. In this paper, using a real interaction phenomenon a comparative analysis of the two models is carried out. The most important results obtained highlights that if the phenomenon is correctly specified, the two specification of the gravity model have a very similar behaviour.
Giuseppe Ricciardo Lamonica,
The Log Normal and the Poisson Gravity Models in the Analysis of Interactions Phenomena, American Journal of Theoretical and Applied Statistics.
Vol. 4, No. 4,
2015, pp. 291-299.
R.J. Cook, J.D. Kalbfleisch and G.Yi, “A generalized mover-stayer model for panel data,” Biostatistics, 3(3), pp. 407-420, 2002.
E.J.Anderson,“A Theoretical Foundation for the Gravity Equation,”The American Economic Review, 63, pp.106-116, 1979.
Y. Chun and D.A. Griffith, “Modeling network autocorrelation in space-timemigration flow data: An eigenvector spatial filtering approach,”Annals of the American Geographer,101, 3, pp. 523-536, 2011.
S.J. Evenett, and W. Keller, “On the theories explaining the success of the gravity equation,” Journal of Political Economy, 110, pp. 281-316, 2002.
W. Isard, “Gravity and spatial interaction models” In: W. Isard, I. J. Azis, M. P. Drennan, R. E. Miller, S. Saltzman and E. Thorbecke, “Methods of Interregional and Regional Analysis”, Ashgate, U.K 1998.
D. Karemera, O. V. Iwuagwu, and B. Davis, “A gravity model analysis of international migration to North America,” Applied Economics, 32, 2000, pp. 1745-1755.
J.P. LeSage, “Spatial regression models”. In: Altman, M., Gill, J., and McDonald, M. (eds). “Numerical Issues in Statistical Computing for the Social Scientist” John Wiley & Sons, New York, 2004, pp. 199-218, 2004.
L. Mathyas, “The Gravity Model: Some Econometric Consideration,” The World Economy, 21, pp. 397-401, 1998.
J.P. LeSage, and R. Pace, “Spatial econometric modeling of the origin destination flows,” Journal of Regional Science 48, pp. 941-967, 2007.
A. Porojan, (2001) "Trade flows and spatial effects: the gravity model revisited", Open Economies Review, 12, 3, pp. 265-280, 2001.
A. Sen and T. E. Smith “Gravity model of spatial Interaction behaviour” Springer Verlag, Berlin, 1995.
R. Flowerdew and M. Aitkin, “A method of fitting the gravity model based on the Poisson distribution,” Journal of Regional Science, 22, pp. 191-202, 1982.
M.J. Burger, F.G. Van Oort and G.J.M. Linders, “On the specification of gravity model of trade: zeros, excess zeros and zero-inflated estimation,” Spatial Economic Analysis, 2, pp. 167-190, 2009.
W. B. Stronge and R.R. Schultz, “Heteroscedasticity and the gravity model,” Geographical Analysis, vol. X, 3, pp. 279-286, 1978.
A. Lovett and R. Flowerdew, “Analysis of count data using Poisson regression,” Professional Geographer, 41, pp. 190-198, 1989.
A. Anjomani,“Regional growth and interstate migration,”Socio Economic Planning Sciences, 36, pp. 239-65, 2002.
G.F. De Jong, D.R. Graefeand S.T. Pierre, “Welfare reform and interstate migration of poor families,” Demography, 423, pp. 469-496, 2005.
R. Forrest andA. Murie, “Moving strategies among home owners,” In Labour Migration: the internal geographical mobility of labour in the developed world. J.H. Johnson and J. Salt (eds), London, David Fulton Publisher, pp. 191-209, 1990.
M. J. Greenwood, “Human Migration: Theory, models and empirical studies,” Journal of Regional Studies, 25, 4, pp. 521-544, 1985.
A. Rogers andL.J. Castro,“Migration,” In: Migration and settlement: a multiregional comparative study. A. Rogers and F. Willekens (eds), Dordrecht, Netherland, Kluvert Academic Publishers, 1986.
P.A.G. Van Bergeijk, and B. Steven, “The gravity model in international trade: Advanced and application” Cambridge, Cambridge University Press, 2010.