Approaches to Modelling Overdispersion in the Analysis of Migration

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.

[1]  D. Brillinger,et al.  The natural variability of vital rates and associated statistics. , 1986, Biometrics.

[2]  H W Richardson,et al.  The Distribution of Population and Employment in a Polycentric City: The Case of Los Angeles , 1986, Environment & planning A.

[3]  H. Andreß,et al.  Recurrent unemployment—The West German experience: An exploratory analysis using count data models with panel data , 1989 .

[4]  David R. Cox,et al.  Some remarks on overdispersion , 1983 .

[5]  Marie Davidian,et al.  A Note on Extended Quasi-Likelihood , 1988 .

[6]  Peter Congdon.  Spatiotemporal models for small-area social indicators , 1991 .

[7]  P Congdon,et al.  Aspects of general linear modelling of migration. , 1992, The Statistician : journal of the Institute of Statisticians.

[8]  J. Mosimann.  On the compound multinomial distribution, the multivariate β-distribution, and correlations among proportions , 1962 .

[9]  P. Thall,et al.  Some covariance models for longitudinal count data with overdispersion. , 1990, Biometrics.

[10]  A. Cameron,et al.  Econometric models based on count data. Comparisons and applications of some estimators and tests , 1986 .

[11]  Martin Crowder,et al.  Gaussian Estimation for Correlated Binomial Data , 1985 .

[12]  A. Forcina,et al.  Modelling Transition Probabilities in the Analysis of Aggregated Data , 1989 .

[13]  S J Pocock,et al.  Regression of area mortality rates on explanatory variables: what weighting is appropriate? , 1981, Journal of the Royal Statistical Society. Series C, Applied statistics.

[14]  Dirk F. Moore,et al.  Asymptotic properties of moment estimators for overdispersed counts and proportions , 1986 .

[15]  Kao-Lee Liaw,et al.  Nested logit model and maximum quasi-likelihood method: a flexible methodology for analyzing interregional migration patterns. , 1987, Regional science and urban economics.

[16]  Tony Lancaster,et al.  The Analysis of Re‐Employment Probabilities for the Unemployed , 1980 .

[17]  J. Nelder,et al.  An extended quasi-likelihood function , 1987 .

[18]  Neil Wrigley,et al.  Categorical Data Analysis for Geographers and Environmental Scientists , 1985 .

[19]  B. Cushing.  Use and misuse of the allocation rate in models of population migration , 1989, The Annals of regional science.

[20]  P. Doreian.  Linear Models with Spatially Distributed Data , 1980 .

[21]  D. J. Bartholomew,et al.  Errors of Prediction for Markov Chain Models , 1975 .

[22]  J. Lawless.  Negative binomial and mixed Poisson regression , 1987 .

[23]  K. Ord.  Estimation Methods for Models of Spatial Interaction , 1975 .

[24]  C. Gourieroux,et al.  Pseudo Maximum Likelihood Methods: Applications to Poisson Models , 1984 .

[25]  Z. Griliches,et al.  Econometric Models for Count Data with an Application to the Patents-R&D Relationship , 1984 .

[26]  Martyn Cordey-Hayes,et al.  Migration Dynamics And Labour Market Turnover , 1977 .

[27]  R. Hart.  Economic expectations and the decision to migrate: An analysis by socio-economic group , 1973 .

[28]  F. J. Willekens,et al.  Forecasting place-to-place migration with generalized linear models. , 1983 .

[29]  P Congdon,et al.  Modelling migration flows between areas: an analysis for London using the census and OPCS Longitudinal Study. , 1989, Regional studies.

[30]  Ian Masser,et al.  Hierarchical Aggregation Procedures for Interaction Data , 1975 .

[31]  Richard Morton,et al.  A generalized linear model with nested strata of extra-Poisson variation , 1987 .

[32]  N. Breslow.  Extra‐Poisson Variation in Log‐Linear Models , 1984 .

[33]  R. Jackman,et al.  Regional Migration in Britain: An Analysis of Gross Flows Using NHS Central Register Data , 1992 .

[34]  D. A. Williams,et al.  Extra‐Binomial Variation in Logistic Linear Models , 1982 .

[35]  J. A. Nelder,et al.  Quasi-Likelihood and GLIM , 1985 .

[36]  Mike Baxter.  Misspecification in Spatial Interaction Models: Further Results , 1985 .