1. 1 Analysing Structures of Interregional Migration in England James Raymer and Corrado Giulietti Southampton Statistical Sciences Research Insitute (S3RI) Session 40: Handling Migration and Commuting Flow Data, ESRC Research Methods Festival, Oxford, 2 July 2008

2. 2 Context and significance Context –First part of an ESRC-funded project on combining census and registration migration data in England and Wales Significance –Helps us to better understand aggregate population change and migration behaviour –Provides a basis for the estimation of migration patterns, including projection

3. 3 Outline Introduction Analysing migration structures –Multiplicative component framework –Log-linear models Interregional migration in England –Analysis of multiplicative components –Log-linear analyses of migration flow tables Summary and next steps

4. 4 Data 1991 and 2001 censuses Interregional migration flows in England –Origin (9) by destination (9) by age (16) –Origin (9) by destination (9) by ethnicity (4) Inconsistencies in measurement over time –Student population –Mixed ethnicity group

5. Migration flow table Multiplicative components n ij = (T)(O i )(D j )(OD ij ),where T = n ++ O i =n i+ / T D j = n +j / T OD ij = n ij / (T)(O i )(D j ) Multiplicative component model for a 2-way table: Origin by destination

6. Multiplicative Models for Three-Way Tables Interregional migration by age Interregional migration by ethnicity Overall Level Main Effects (proportions) Two-way Inteactions (odds) Three-way Interaction (odds ratios)

7. Log-linear models for analysing structures in three-way migration flow tables Saturated model: ODE Unsaturated model (mutual independence): O, D, E Unsaturated model: OD, E Note, we use the likelihood ratio statistic (G 2 ) and the Akaike Information Criteria (AIC) to compare the overall fits of unsaturated models

8. The proportions of all migration from and to each region in England, 1991 and 2001 Overall levels 1991: 630 thousand 2001: 920 thousand

9. The observed to expected ratios of interregional migration (OD ij ) in England, 1991 2.783 = 5,159 / (628,610 * 0.082 * 0.036) = 5,159 / 1,854 0.539 = 6,046 / (628,610 * 0.220 * 0.081) = 6,046 / 11,225

10. The observed to expected ratios of interregional migration (OD ij ) from Yorkshire and the Humber and London, 1991 and 2001

11. Proportions of all interregional migration in England by age, 1991 and 2001

12. Origin-age and destination-age interaction effects of interregional migration in England, 1991 and 2001: London OA ix DA jx

13. Proportions of all interregional migration in England by ethnicity, 1991 and 2001

14. Origin-ethnicity and destination-ethnicity interaction effects of interregional migration in England, 1991 and 2001: White OE ig DE jg

15. Origin-ethnicity and destination-ethnicity interaction effects of interregional migration in England, 1991 and 2001: South Asian OE ig DE jg

16. Origin-ethnicity and destination-ethnicity interaction effects of interregional migration in England, 1991 and 2001: Black OE ig DE jg

17. A comparison of unsaturated log-linear model fits: England migration tables cross-classified by origin (O), destination (D), age (A) and time (T) Note, df = residual degrees of freedom

18. Estimated age patterns of migration between North East and London and South West, 2001 A comparison of two unsaturated log-linear models North East to LondonLondon to North East South West to LondonLondon to South West

19. A comparison of unsaturated log-linear model fits: England migration tables cross-classified by origin (O), destination (D), ethnicity (E) and time (T) Note, df = residual degrees of freedom

20. Estimated South Asian interregional migration from North East and London, 1991 and 2001: A comparison of two unsaturated log-linear models

21. 21 Main points –Despite a large increase in the level of interregional migration, the underlying structures have remained remarkably stable over time (except with some of the ethnic structures) –Large differences in the patterns occur by age (not much change over time) and ethnicity (lots of change over time) –The three-way interaction terms of the multiplicative model do not contribute much to the overall fit Future work –Extend analysis to county level and other variables (e.g., education and employment) –Build model for combining census and registration migration data to estimate detailed patterns annually over time