Models of migration between regions are often based on the assumption that individual moves can be modelled by a Poisson distribution whose parameter is a function of origin and destination characteristics, and generalized cost; this is true of Poisson regression models and spatial interaction models. The Poisson assumption is that each individual acts independently from others making the same move. In fact, migration is usually engaged in by household groups, not independent individuals, making the Poisson assumption invalid. It is possible instead to construct a model in which the probability of a household moving is given by a Poisson model and the number of individuals in a moving household is given by an observed household-size distribution. This generalized Poisson model is explained and fitted to a set of data on local-level migration within the English county of Hereford and Worcester. However, the sparse nature of the data set raises problems in assessing goodness of fit because the deviance value is unusually low. This is tackled here with a simulation methodology.
Goodness-of-Fit Tests for Bivariate Time Series of Counts
