• Attractivity;
  • Bayesian;
  • Migration;
  • Random effects;
  • Retentivity;
  • Spatial correlation

Summary.  Several studies have proposed methods for deriving summary scores for describing the in-migrant attractivity of areas, as well as out-migrant push (or conversely migrant retentivity). Simple in-migration and out-migrant rates (migrant totals divided by populations) do not correct for spatial separation or the migration context of a particular area, namely the size and proximity of nearby urban areas with populations at risk of migrating to an area, or offering potential destinations for out-migrants from an area. An extended random-effects gravity model is proposed to represent the influences of attractivity and retentivity after controlling for urban structure. Whereas the existing literature is focused on fixed effects modelling (and classical estimation), the focus in this paper is on a Bayesian hierarchical random-effects approach that links estimates of pull-and-push scores across areas (i.e. allows scores to be spatially correlated) and also allows correlation between attractivity and retentivity within areas. As demonstrated by a case-study of English local authorities, a random-effects model may have a lower effective model dimension than a fixed effects model.