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Modelling Sparse Interaction Matrices: Interward Migration in Hereford and Worcester, and the Underdispersion Problem

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  • P J Boyle

    (Migration Unit, Department of Geography, University College of Swansea, Singleton Park, Swansea SA2 8PP, Wales)

  • R Flowerdew

    (Department of Geography, Lancaster University, Lancaster LA1 4YB, England)

Abstract

Recently, it has been argued that migration models in which ordinary least squares regression is used are inappropriate, because the dependent variable (number of migrants) is a count. Instead, a Poisson regression approach can be adopted. Goodness of fit can be evaluated by using a deviance (log-likelihood) or X 2 statistic, whose significance can be compared with a χ 2 distribution with appropriate degrees of freedom. In this paper, such an approach is used to model ward-level migration flows within the county of Hereford and Worcester. However, it is shown that for this exceedingly sparse data set the deviance figures attained are very low, suggesting that there may be a problem of underdispersion. This is in contrast to the overdispersion which has been identified as a common problem in Poisson models. The low deviance figures arise from the large number of zeros and small flows in the data matrix, which invalidate the usual χ 2 goodness-of-fit test. A simulation approach to the assessment of model goodness of fit is suggested, and the results from applying it to the Hereford and Worcester data set are described.

Suggested Citation

  • P J Boyle & R Flowerdew, 1993. "Modelling Sparse Interaction Matrices: Interward Migration in Hereford and Worcester, and the Underdispersion Problem," Environment and Planning A, , vol. 25(8), pages 1201-1209, August.
    • Handle: RePEc:sae:envira:v:25:y:1993:i:8:p:1201-1209
    DOI: 10.1068/a251201
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    Citations

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    Cited by:

    1. Stamatis Kalogirou, 2011. "Testing local versions of correlation coefficients," ERSA conference papers ersa10p529, European Regional Science Association.
    2. Alok K. Bohara & Randall G. Krieg, 1996. "A Zero-inflated Poisson Model of Migration Frequency," International Regional Science Review, , vol. 19(3), pages 211-222, July.
    3. P Boyle, 1993. "A Three-Dimensional Approach to Multistream Migration Modelling: Local-Level Flows in Hereford and Worcester," Environment and Planning A, , vol. 25(9), pages 1279-1293, September.
    4. R Flowerdew & P J Boyle, 1995. "Migration Models Incorporating Interdependence of Movers," Environment and Planning A, , vol. 27(9), pages 1493-1502, September.
    5. Stamatis Kalogirou, 2012. "Testing local versions of correlation coefficients," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 32(1), pages 45-61, March.
    6. Paul Boyle & Robin Flowerdew & Jianfa Shen, 1998. "Modelling Inter-ward Migration in Hereford and Worcester: The Importance of Housing Growth and Tenure," Regional Studies, Taylor & Francis Journals, vol. 32(2), pages 113-132.

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