In this paper the modelling of overdispersion in generalised Poisson and multinomial models of migration flows and rates is considered, and its importance within the wider question of substantive model specification is shown. It is argued that substantive specification and the modelling of overdispersion are closely interrelated. Simplified ways of estimating the form of overdispersion—moments methods and pseudo-likelihood—are considered wherever possible. Overdispersion is set within the broader context of correlation effects which relate to migration—correlation across different destinations, between spatially adjacent origins and destinations, and between different time periods. The data used to illustrate the modelling development are drawn from the Office of Population Censuses and Surveys Longitudinal Study, the decennial Census, and the National Health Service Central Register.
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