Abstract
We study the effects of aggregation on four different cases of nonlinear spatial gravity models. We present some theoretical results on the relationship between the mean flows at an aggregated level and the mean flow at the disaggregated level. We then focus on the case of perfect aggregation (scale problem) showing some results based on the theoretical expressions previously derived and on some artificial data. The main aim is to test the effects on the aggregated flows of the spatial dependence observed in the origin and in the destination variables. We show that positive spatial dependence in the origin and destination variables moderate the increase of the mean flows connatural with aggregation while negative spatial dependence exacerbates it.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arbia G (1989) Spatial data configuration in the statistical analysis of regional economics and related problems. Kluwer, Dordrecht
Arbia G, Petrarca F (2011) Effects of MAUP on spatial econometric. Lett Spat Resour Sci 4(3):173–185
Cliff AD, Ord JK (1981) Spatial processes: models and applications. Pion, London
Cramer JS (1964) Efficient grouping, regression and correlation in Engel curve analysis. J Am Stat Assoc 59:233–250
Eurostat (2012) http://epp.eurostat.ec.europa.eu/portal/page/portal/nuts_nomenclature/introduction
Griffith DA (2009) Modeling spatial autocorrelation in spatial interaction data: empirical evidence from 2002 Germany journey-to-work flows. J Geogr Syst 11(2):117–140
Haitovsky J (1973) Regression estimation from grouped observations. Hafner Press, New York, Griffin, Statistical Courses and monographs, No. 33
LeSage J, Fisher M (2010) Spatial econometric methods for modeling origin-destination flows. In: Fischer MM, Getis A (eds) Handbook of applied spatial analysis. Springer, Berlin
Openshaw S, Taylor PJ (1979) A million or so of correlated coefficients: three experiments on the modifiable areal unit problem. In: Wrigley N (ed) Statistical applications in the spatial sciences. Pion, London, pp 120–438
Orcutt GH, Watts HW, Edwards JB (1968) Data aggregation and information loss. Am Econ Rev 58:773–787
Pesaran MH, Pierse RG, Kumar MS (1989) Econometric analysis of aggregation in the context of linear prediction models. Econometrica 57(4):861–888
Prais S, Aitchinson J (1954) The grouping of observations in regression analysis. Rev Int Stat Inst 1:1–22
Theil H (1954) Linear aggregation on economic relations. North-Holland Publ. Company, Amsterdam
Yule U, Kendall MS (1950) An introduction to the theory of statistics. Griffin, London
Zellner A (1962) An efficient method of estimating seemingly unrelated regression equations and tests for aggregation bias. J Am Stat Assoc 57:348–368
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Arbia, G., Petrarca, F. Effects of scale in spatial interaction models. J Geogr Syst 15, 249–264 (2013). https://doi.org/10.1007/s10109-013-0180-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10109-013-0180-9
Keywords
- Spatial interaction models
- Gravity models
- Spatial autoregressive random fields
- Modifiable areal unit problem