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

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

Latent curves

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

Vocabulary size child 1, t=5

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

Vocabulary size child 2, t=5 y = 0.24x Less rapid growth

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

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

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

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

Registrar General’s Social Class I Professional etc occupations II Managerial and technical occupations IIINSkilled non-manual occupations IIIMSkilled manual occupations IVPartly-skilled occupations VUnskilled occupations

BCS70 latent curve model

How many latent trajectory groups?

BICs for conditional LCGA Models

Posterior probability plot for 5 group LCGA

Estimated parameters for the 5 latent groups

Lower middle class stable (21%)

Working class rising

Covariate coefficient contrasts for trajectory group membership

Predicted probability of trajectory group membership

Mother interested in child’s education

Father post-compulsory education

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