exploring social mobility with latent trajectory group analysis
DESCRIPTION
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 - PowerPoint PPT PresentationTRANSCRIPT
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
ittiiity
ii
ii
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
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
1 2 3 4 5
time
sco
re
Add line of best fit
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
1 2 3 4 5
time
sco
re
y = 0.79x + 1.39
Can be expressed as regression equation:
Vocabulary size child 2, t=5
1
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
1 2 3 4 5
time
sco
re y = 0.24x + 1.94
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
ttty
Latent curves
ittiiity
ii
ii
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
IIIN Skilled non-manual occupations
IIIM Skilled manual occupations
IV Partly-skilled occupations
V Unskilled occupations
BCS70 latent curve model
Growth Factors Men
Estimate s.e.
Growth factor means
0 -
0.384 0.030
Growth factor variances
2 7.308 0.465
2 2.191 0.172
Growth factor covariances
-1.787 0.183
Sample size 6355
Source: BCS70 1980, 1996, 2000.
How many latent trajectory groups?
BICs for conditional LCGA Models
31600
31800
32000
32200
32400
32600
32800
33000
33200
33400
33600
33800
1 2 3 4 5 6 7 8 Number of latent of classes
BIC
Posterior probability plot for 5 group LCGA
Mean posterior probabilities
Most likely
trajectory
group Group 1 Group 2 Group 3 Group 4 Group 5
Group 1 0.727 0.073 0.114 0.073 0.014
Group 2 0.141 0.623 0.049 0.001 0.186
Group 3 0.116 0.019 0.733 0.003 0.129
Group 4 0.202 0.003 0.014 0.780 0.000
Group 5 0.01 0.053 0.129 0.000 0.807
Source: BCS70, 1980, 1996, 2000 waves
Estimated parameters for the 5 latent groups
Growth parameters Trajectory
Group s.e. s.e. Estimated posterior %
1. lower middle stable 4.846 0.398 -0.253 0.152 21%
2. middle declining 4.108 0.248 -2.103 0.183 9%
3. working rising 0.743 0.209 1.855 0.162 27%
4. upper middle stable 6.290 0.274 0.460 0.750 4%
5. working stable 0 - -0.024 0.042 40%
Source: BCS70, 1980, 1996, 2000 waves; n=6355; coefficients in logit scale.
Lower middle class stable (21%)
0
0.10.2
0.3
0.4
0.50.6
0.7
10 26 30
age
p
0
0.1
0.2
0.3
0.40.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
p
10 26 30
age
1. middle stable 22%
Professional
Managerial & Technical
Skilled non-manual
Skilled manual
Partly-skilled
Unskilled
Working class rising
0
0.10.2
0.3
0.4
0.50.6
0.7
10 26 30
age
p
0
0.1
0.2
0.3
0.40.5
0.6
0.7
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
p
10 26 30
age
1. middle stable 22%
Professional
Managerial & Technical
Skilled non-manual
Skilled manual
Partly-skilled
Unskilled
Covariate Trajectory Group contrast 1v3 1v4 1v2 3v5 2v4 5v1 3v2 Merit variables General ability
0.209 (0.116)
-0.805* (0.235)
0.537* (0.146)
0.537* (0.062)
-1.341* (0.182)
-0.746* (0.113)
0.328* (0.094)
Academic motivation
0.023 (0.071)
-0.067 (0.168)
0.133 (0.121)
0.286* (0.056)
-0.20 (0.169)
-0.309* (0.064)
0.110 (0.103)
Social advantage variable Private secondary school
2.481* (0.757)
-1.129 (0.633)
0.836 (0.662)
-0.577 (0.867)
-1.965* (0.589)
-1.903* (0.454)
-1.644* (0.802)
Cultural capital variables Father had post-compulsory education
1.474* (0.249)
-0.878 (0.562)
0.273 (0.309)
-0.136 (0.210)
-1.151* (0.405)
-1.338* (0.242)
-1.201* (0.232)
Mother had post-compulsory education
0.608* (0.261)
-0.946* (0.460)
-0.033 (0.313)
0.516* (0.204)
-0.913* (0.340)
-1.124* (0.239)
-0.641* (0.220)
Post-compulsory education anticipated for child
1.242* (0.197)
-2.181 (2.650)
0.929* (0.276)
0.494* (0.131)
-3.11 (2.60)
-1.736* (0.218)
-0.313 (0.193)
Father very interested in child’s education
0.389* (0.158)
-0.450 (0.354)
0.258 (0.222)
0.095 (0.136)
-0.708 (0.361)
-0.485* (0.146)
-0.131 (0.200)
Mother very interested in child’s education
0.211 (0.159)
0.006 (0.377)
0.117 (0.229)
0.250* (0.127)
-0.111 (0.367)
-0.461* (0.137)
-0.094 (0.199)
Trajectory group key: 1 – lower middle stable; 2 – middle declining; 3 – working rising; 4 – upper middle stable; 5 – working stable; *=significantly different from zero with p0.05; Source: BCS70, 1980, 1996, 2000 waves; n=6355.
Covariate coefficient contrasts for trajectory group membership
Predicted probability of trajectory group membership
general ability
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-4.393 -3.393 -2.393 -1.393 -0.393 0.607 1.607 2.607 3.607
z score
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-4.393 -3.393 -2.393 -1.393 -0.393 0.607 1.607 2.607 3.607
lower middle stable
middle declining
working rising
jpper middle stable
working stable
Predicted probability of trajectory group membership
academic motivatoin
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
-3.199 -2.199 -1.199 -0.199 0.801 1.801 2.801
z score
p
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
-4.393 -3.393 -2.393 -1.393 -0.393 0.607 1.607 2.607 3.607
lower middle stable
middle declining
working rising
jpper middle stable
working stable
Mother interested in child’s education
mother interested in child's education?
0
0.1
0.2
0.3
0.4
0.5
0.6
no yes
0
0.1
0.2
0.3
0.4
0.5
0.6
no yes
lower middle stable
middle declining
working rising
upper middle stable
working stable
Father post-compulsory education
0
0.1
0.2
0.3
0.4
0.5
0.6
no yes
lower middle stable
middle declining
working rising
upper middle stable
working stable
0
0.1
0.2
0.3
0.4
0.5
0.6
no yes
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