Modelling Sparse Interaction Matrices

Interward Migration in Hereford and Worcester, and the Underdispersion Problem

Bibliographic Data

ID4849656
AuthorsP J Boyle (Migration Unit, Department of Geography, University College of Swansea, Singleton Park, Swansea SA2 8PP, Wales), Robin Flowerdew (Lancaster University)
Year1993
Volume25
Issue8
Pages1201-1209
Publication date1993-08-01
Peer ReviewedYes
Open AccessYes
TypeARTICLE
VenueEnvironment and Planning A Economy and Space (JOURNAL)
Journal identifiersISSN: 0308-518X • E-ISSN: 1472-3409
PublisherSAGE Publications Inc (PUBLISHER)
DOI10.1068/a251201
PMID12318206
OpenAlexW1997367990
LanguageEN
Citations received9
References cited10

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 X2 statistic, whose significance can be compared with a χ2 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 χ2 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

Computer Science · Regional Economics and Spatial Analysis · Spatial and Panel Data Analysis · Urban, Neighborhood, and Segregation Studies

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