SLIDE 1 An Interval Graph Method for Cross-Cultural Comparison of Life Histories*
Sean Fitzhugh1, Carter Butts1,2, Joy Pixley1
MURI AHM 6.03.2011
1 Department of Sociology: University of California, Irvine 2 Institute of Mathematical Behavioral Sciences: University of California, Irvine
*This material is based on research supported by the Office of Naval Research under award N00014-08-1-1015
SLIDE 2
Outline
Introduction to interval graphs Exploratory results Future directions
SLIDE 3
MURI
Several MURI projects advance methods in analysis of a
single, large graph
Focus here is analysis and comparison of large numbers
(i.e. thousands) of graphs
SLIDE 4 Introduction: Life History Concepts
Lives are composed of a series of subintervals (spells)
and life history is the collection of these spells
Start and end dates of spells (school, work, marriages,
etc) allow for surprisingly deep insight into one’s life
Timing of spells has lasting impact on timing (or even
existence) of subsequent spells (Elder 1998)
SLIDE 5 Introduction: Why Networks?
We need a method for analyzing life history which
preserves maximal information on context and timing of spells
Butts and Pixley (2004): Structural approach to
representing life history data
Understand life history as a series of intervals and their
temporal overlap
SLIDE 6 Introduction: Why Networks?
Interval graph: takes a set of spells as the vertex set and
coterminousness as the edge set (Butts and Pixley 2004)
Why are we interested in spell simultaneity?
When activities are coterminous, they are linked together
in a meaningful way
SLIDE 7
Introduction: Why Networks?
Example: Four lives
SLIDE 8 Introduction: Why Networks?
Example: Four lives
School
SLIDE 9 Introduction: Why Networks?
Example: Four lives
School School + Work
SLIDE 10 Introduction: Why Networks?
Example: Four lives
School School + Work School + Work + Marriage
SLIDE 11 Introduction: Why Networks?
Example: Four lives
School School + Work School + Work + Marriage School + Work + Marriage + Children
SLIDE 12 Introduction: Why Networks?
Example: Four lives
School School + Work School + Work + Marriage School + Work + Marriage + Children
Context is important!
SLIDE 13 Methods: Interval Graphs
How do we construct an interval graph?
School School School Work Work Marriage Children Children
Time:
SLIDE 14 Methods: Interval Graphs
How do we construct an interval graph?
School School School Work Work Marriage Children Children
Time:
SLIDE 15 Methods: Interval Graphs
School 1 School 2 School 3 Work 1 Work 2 Marriage Child 1 Child 2 School 1 1 School 2 1 School 3 1 1 Work 1 1 1 1 Work 2 1 1 1 1 Marriage 1 1 1 1 1 1 Child 1 1 1 1 1 1 Child 2 1 1 1 1
- Interval graph: tie indicates coterminousness
SLIDE 16
Methods: Interval Graph Comparison
Comparison across multiple lives:
Construct an interval graph for each actor Find the graph distances between all actors
Direct comparison is inappropriate here: spells are
not comparable across domains
We must use a partial labeling function to identify
which sets of vertices (spells) are equivalent in our comparison (Butts and Carley, 2005)
SLIDE 17 Methods: Interval Graphs
School 1 School 2 School 3 Work 1 Work 2 Marriage Child 1 Child 2 School 1 1 School 2 1 School 3 1 1 Work 1 1 1 1 Work 2 1 1 1 1 Marriage 1 1 1 1 1 1 Child 1 1 1 1 1 1 Child 2 1 1 1 1
- Exchangeability list: we treat spells within domains as
comparable and allow permutation within domains
SLIDE 18
Methods: Interval Graph Comparison
Distance matrix: n x n matrix where the (i,j) cell is
the distance between i and j
In this context, graph distance corresponds to
differences in life histories
Use multidimensional scaling (MDS) to visualize the
distances
MDS represents similarities and differences among a
set of items as Euclidean distances in k-dimensional space (Kruskal and Wish 1978)
Actors grouped together in MDS space have similar
life histories
SLIDE 19
Data
Retrospective life history data: individuals provide start
and end dates for a variety of spells
Vietnam Life History Survey (Hirschman et al., 1991) Wisconsin Longitudinal Study (Hauser and Sewell,
2010)
Life Histories and Social Change in Contemporary China
(Treiman and Walder, 1998)
Domains of interest: education, work, marriage,
children, military participation
SLIDE 20
Results: Vietnam
MDS: Banding is explained by number of children
SLIDE 21
Results: Vietnam
MDS: Within bands, actors are primarily differentiated
by military participation
SLIDE 22
Results: Vietnam
Which covariates explain patterning?
SLIDE 23 Results: Vietnam
What is associated with differences in lives?
Family size Military
Might we see differences in China?
SLIDE 24 Results: China
Number of children and CCP membership explain much
- f the differences among lives
SLIDE 25
Results: China
Gender and farming are associated with differences
SLIDE 26
Results: China
3D plots allow us to explore further
SLIDE 27
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 28
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 29
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 30
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 31
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 32
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 33
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 34
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 35
Results: China
No schooling/illiterate Primary school Middle school
University
SLIDE 36
Results: China
We can see a spectrum of education levels here
No schooling/illiterate Primary school Middle school
University
SLIDE 37 Results: China
What is associated with differences in lives?
Family size Education Party membership Gender Involvement in agriculture
What patterns might we see in the United States?
SLIDE 38
Results: United States
Jobs instead of children!
SLIDE 39
Results: United States
Some differences between those with 0/1 and 2+
marriages…
SLIDE 40
Results: United States
Back to the 3D plots
SLIDE 41
Results: United States
Attended college Did not attend college
SLIDE 42
Results: United States
Attended college Did not attend college
SLIDE 43
Results: United States
Attended college Did not attend college
SLIDE 44
Results: United States
Attended college Did not attend college
SLIDE 45
Results: United States
Attended college Did not attend college
SLIDE 46
Results: United States
Attended college Did not attend college
SLIDE 47
Results: United States
Attended college Did not attend college
SLIDE 48
Results: United States
Attended college Did not attend college
SLIDE 49
Results: United States
Attended college Did not attend college
SLIDE 50
Results: United States
College education plays an important role in
differentiating lives
Attended college Did not attend college
SLIDE 51
Results: United States
More 3D plots
SLIDE 52
Results: United States
Military participation No military participation
SLIDE 53
Results: United States
Military participation No military participation
SLIDE 54
Results: United States
Military participation No military participation
SLIDE 55
Results: United States
Military participation No military participation
SLIDE 56
Results: United States
Military participation No military participation
SLIDE 57
Results: United States
Military participation No military participation
SLIDE 58
Results: United States
Military participation No military participation
SLIDE 59
Results: United States
Military participation No military participation
SLIDE 60
Results: United States
Military participation No military participation
SLIDE 61
Results: United States
Military participation also differentiates American lives
Military participation No military participation
SLIDE 62
Results: United States
One more plot
SLIDE 63
Results: United States
Male Female
SLIDE 64
Results: United States
Male Female
SLIDE 65
Results: United States
Male Female
SLIDE 66
Results: United States
Male Female
SLIDE 67
Results: United States
Male Female
SLIDE 68
Results: United States
Male Female
SLIDE 69
Results: United States
Male Female
SLIDE 70
Results: United States
Male Female
SLIDE 71
Results: United States
Male Female
SLIDE 72 Results: United States
Distinct clustering according to gender
Male Female
SLIDE 73 Results: United States
What is associated with differences in American lives?
Employment Education Military Marriages Gender
Any common themes?
Where and why might family life play a bigger role in
differentiating people’s lives? Why would we expect education/work to play a role in other cases? In which cases would military participation matter?
SLIDE 74
Future Directions
More data! Eastern European cases: Russia, Poland,
several other former Soviet States
Model-based scaling to overcome sampling issues
(missingness, censoring)
Application of latent variable models
SLIDE 75 Thank you!
An Interval Graph Method for Cross-Cultural Comparison
Sean Fitzhugh, Carter Butts, Joy Pixley sean.fitzhugh@uci.edu
