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Effects of scale in spatial interaction models

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  • Giuseppe Arbia
  • Francesca Petrarca

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. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Giuseppe Arbia & Francesca Petrarca, 2013. "Effects of scale in spatial interaction models," Journal of Geographical Systems, Springer, vol. 15(3), pages 249-264, July.
    • Handle: RePEc:kap:jgeosy:v:15:y:2013:i:3:p:249-264
    DOI: 10.1007/s10109-013-0180-9
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    1. Manfred M. Fischer & Arthur Getis (ed.), 2010. "Handbook of Applied Spatial Analysis," Springer Books, Springer, number 978-3-642-03647-7, November.
    2. Pesaran, M Hashem & Pierse, Richard G & Kumar, Mohan S, 1989. "Econometric Analysis of Aggregation in the Context of Linear Prediction Models," Econometrica, Econometric Society, vol. 57(4), pages 861-888, July.
    3. Daniel Griffith, 2009. "Modeling spatial autocorrelation in spatial interaction data: empirical evidence from 2002 Germany journey-to-work flows," Journal of Geographical Systems, Springer, vol. 11(2), pages 117-140, June.
    4. Daniel A. Griffith, 2009. "Spatial Autocorrelation in Spatial Interaction," Advances in Spatial Science, in: Aura Reggiani & Peter Nijkamp (ed.), Complexity and Spatial Networks, chapter 0, pages 221-237, Springer.
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    Cited by:

    1. Nan Dong & Xiaohuan Yang & Hongyan Cai & Liming Wang, 2015. "A Novel Method for Simulating Urban Population Potential Based on Urban Patches: A Case Study in Jiangsu Province, China," Sustainability, MDPI, vol. 7(4), pages 1-20, April.
    2. Zhijiao Qin & Yan Yu & Dianfeng Liu, 2019. "The Effect of HOPSCA on Residential Property Values: Exploratory Findings from Wuhan, China," Sustainability, MDPI, vol. 11(2), pages 1-18, January.
    3. Olga Demidova & Tatiana Bukina & Natalia Sverchkova, 2015. "Dependence of spatial effects on the level of regional aggregation, weights matrix, and estimation method," ERSA conference papers ersa15p322, European Regional Science Association.
    4. Juan C Duque & Henry Laniado & Adriano Polo, 2018. "S-maup: Statistical test to measure the sensitivity to the modifiable areal unit problem," PLOS ONE, Public Library of Science, vol. 13(11), pages 1-25, November.

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    More about this item

    Keywords

    Spatial interaction models; Gravity models; Spatial autoregressive random fields; Modifiable areal unit problem; C21; R19;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • R19 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Other

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