Exploring social mobility with latent trajectory group analysis

1. Exploring social mobility with latent trajectory group analysis Patrick Sturgis, University of Southampton and National Centre for Research Methods From work co-authored with Louise Sullivan

2. Motivation • Conventional focus on correspondence between ‘origin’ and ‘destination’ points • Does this overlook potentially interesting information about what goes on in-between? • Our approach aims to uncover latent mobility trajectories • And to model the antecedents of membership of different trajectory groups

3. Latent curves

4. Conceptual example • we have one child, size of vocabulary measured each year from age 1 to 5 • Plot vocabulary size against time

5. Vocabulary size child 1, t=5

6. Add line of best fit Can be expressed as regression equation: y = 0.79x + 1.39

7. Vocabulary size child 2, t=5 Less rapid growth y = 0.24x + 1.94

8. Case-by-Case approach • So each individual’s growth trajectory can be expressed as a linear equation: • If we have lots of individual growth equations… • We can find the average of the intercepts… • …and the average of the slopes • And the variances of intercepts and slopes • The averages tell us about initial status and rate of growth for sample as a whole • Variances tell us about individual variability around these averages

9. Latent curves Extend model to examine variability between individuals in initial position and rate of change

10. Latent Class Growth Analysis (LCGA) • Latent curve approach yields parameters for whole sample/population • But what if there are qualitatively different growth trajectories? • Use latent class analysis to find distinct groupings which possess similar trajectory parameters • Multinomial logistic regression of group membership on fixed covariates

11. Data • 1970 British Cohort Study • Every child born in week in 1970 • n = • Direct Maximum Likelihood

12. Registrar General’s Social Class I Professional etc occupations II Managerial and technical occupations IIIN Skilled non-manual occupations IIIM Skilled manual occupations IV Partly-skilled occupations V Unskilled occupations

13. BCS70 latent curve model

14. How many latent trajectory groups?

15. BICs for conditional LCGA Models

16. Posterior probability plot for 5 group LCGA

17. Estimated parameters for the 5 latent groups

18. Lower middle class stable (21%)

19. Working class rising

20. Covariate coefficient contrasts for trajectory group membership

21. Predicted probability of trajectory group membership

22. Predicted probability of trajectory group membership

23. Mother interested in child’s education

24. Father post-compulsory education

25. Conclusions • Potentially useful approach • But this exercise hasn’t told us much new in substantive terms • Problem = endogeneity of predictors • Extension = modelling different cohorts simultaneously