analysing network-behavioural co-evolution with siena christian steglichuniversity of groningen tom...
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Analysing network-behavioural co-evolution with SIENA
Christian Steglich University of Groningen
Tom Snijders University of Groningen
Mike Pearson Napier University, Edinburgh
Patrick West University of Glasgow
Prepared for XXV Sunbelt Social Network Conference – Redondo Beach, February 16-20, 2005
Funded by The Netherlands Organization for Scientific Research (NWO) under grant 401-01-550
with an application to the dynamics of music taste, alcohol consumption and friendship
Social network dynamics often depend on actors’ characteristics…
– patterns of homophily:• interaction with similar others can be more rewarding
than interaction with dissimilar others
– patterns of exchange:• selection of partners such that they complement own
abilities
…but also actors’ characteristics can depend on the social network:
– patterns of assimilation:• spread of innovations in a professional community • pupils copying ‘chic’ behaviour of friends at school• traders on a market copying (allegedly) successful
behaviour of competitors
– patterns of differentiation:• division of tasks in a work team
How to analyse this?
- structure of complete networks is complicated to model
- additional complication due to the interdependence with behavior
- and on top of that often incomplete observation (panel data)
beh(tn) beh(tn+1)
net(tn) net(tn+1)
persistence (?)
selection
influence
persistence (?)
Agenda for this talk:
- Brief sketch of the stochastic modelling framework
- An illustrative research question
- Data
- Software
- Analysis
- Interpretation of results
- Summary
Brief sketch of the stochastic modelling framework
- Stochastic process in the space of all possible network-behaviour configurations
(huge!)
- First observation as the process’ starting value.
- Change is modelled as occurring in continuous time.
- Network actors drive the process: individual decisions.
two domains of decisions*:• decisions about network neighbours (selection, deselection),• decisions about own behaviour.
per decision domain two submodels:• When can actor i make a decision? (rate function)• Which decision does actor i make? (objective function)
- Technically: Continuous time Markov process.
- Beware: model-based inference!
* assumption: conditional independence, given the current state of the process.
beh
net
A set of illustrative research questions:
To what degree is music taste acquired via friendship ties?
Does music taste (co-)determine the selection of friends?
Data: social network subsample of the West of Scotland 11-16 Study(West & Sweeting 1996)
three waves, 129 pupils (13-15 year old) at one school
pupils named up to 12 friends
Take into account previous results on same data (Steglich, Snijders & Pearson 2004):
What is the role played by alcohol consumption in both friendship formation and the dynamics of music taste?
43. Which of the following types of music do you like listening to? Tick one or more boxes.
Rock Indie Chart music Jazz
Reggae Classical
Dance 60’s/70’s
Heavy Metal House
Techno Grunge
Folk/Traditional Rap
Rave Hip Hop
Other (what?)………………………………….
Music question: 16 items
Before applying SIENA: data reduction to the 3 most informative dimensions
rap
dance
reggae
techno
househiphop
chart
grunge
rave
heavymtl
rock
classica
jazz
indie
sixty70s
folk_trd
scale CLASSICAL
scale ROCK
scale TECHNO
32. How often do you drink alcohol?Tick one box only.
More than once a week
About once a week
About once a month
Once or twice a year
I don’t drink (alcohol)
5
4
3
2
1
Alcohol question: five point scale
General: SIENA requires dichotomous networks and behavioural variables on an ordinal scale.
Some descriptives:
0
0.5
1
1.5
2
2.5
3
3.5
wave 1 wave 2 wave 3
techno rock classical alcohol
average dynamics of the four behavioural variables
0
50
100
150
200
250
wave 1 wave 2 wave 3
asymmetric mutual
global dynamics of friendship ties (dyad counts)
Software:
The models briefly sketched above are instantiated in the SIENA program. Optionally, evolution models can be estimated from given data, or evolution processes can be simulated, given a model parametrisation and starting values for the process.
SIENA is implemented in the StOCNET program package, available at http://stat.gamma.rug.nl/stocnet (release 14-feb-05).
Currently, it allows for analysing the co-evolution of one social network (directed or undirected) and multiple behavioural variables.
Identification of data sourcefiles
Recoding of variables and identification of missing data
Specifying subsets of actors for analyses
Data specification: insert data into the model’s “slots”.
Model specification: select parameters to include for network evolution.
Model specification: select parameters to include for behavioural evolution.
Model specification: some additional features.
Model estimation: stochastic approximation of optimal parameter values.
Network objective function:– intercept:
outdegree
– network-endogenous:reciprocitydistance-2
– covariate-determined:gender homophilygender egogender alter
– behaviour-determined:beh. homophilybeh. egobeh. alter
Rate functions were kept as simple as possible (periodwise constant).
Analysis of the music taste data:
Behaviour objective function(s):– intercept:
tendency
– network-determined:assimilation to neighbours
– covariate-determined:gender main effect
– behaviour-determined:behaviour main effect
“behaviour” stands shorthand for the three music taste dimensions and alcohol consumption.
parameter s.e. t-scoreoutdegree -1.89 0.29 -6.51reciprocity 2.34 0.12 20.08distance-2 -1.09 0.07 -14.89gender sim 0.80 0.12 6.72
alter -0.21 0.12 -1.73ego 0.24 0.11 2.17
techno sim 0.08 0.33 0.26alter 0.07 0.05 1.30ego -0.10 0.05 -1.93
rock sim 0.11 0.41 0.26alter 0.19 0.07 2.75ego -0.07 0.08 -0.92
classical sim 1.44 0.69 2.07alter 0.15 0.17 0.91ego 0.40 0.17 2.42
alcohol sim 0.83 0.27 3.08alter -0.03 0.04 -0.75ego -0.03 0.03 -0.85
Results: network evolution
Ties to just anyone are but costly.Reciprocated ties are valuable (overcompensating the costs).There is a tendency towards transitive closure.There is gender homophily:
alter boy girl
boy 0.38 -0.62ego girl -0.18 0.41
table gives gender-related contributions to the objective function
There is alcohol homophily:
alter low high
low 0.36 -0.59ego high -0.59 0.13
table shows contributions to the objective function for highest / lowest possible scores
There is no general homophily according to music taste:
alter techno rock
classical
techno -0.06 0.25 -1.39
ego rock -0.15 0.54 -1.31
classical 0.02 0.50 1.73
table renders contributions to the objective function for highest possible scores & mutually exclusive music tastes
Results: behavioural evolution
par. s.e. par. s.e. par. s.e. par. s.e.intercept -0.30 0.37 0.01 0.25 0.59 0.25 0.67 1.30assimilation 0.94 0.27 0.45 0.18 0.63 0.28 0.42 1.17gender -0.06 0.19 0.25 0.12 0.01 0.19 1.57 0.83techno 0.23 0.16 --- --- -0.25 0.09 -0.46 0.40rock 0.16 0.16 -0.34 0.10 --- --- 0.64 0.39classical -0.59 0.32 -0.13 0.23 -0.34 0.30 --- ---alcohol --- --- 0.07 0.10 -0.11 0.07 -1.03 0.34
alcohol techno rock classical
• Assimilation to friends occurs:
– on the alcohol dimension,
– on the techno dimension,
– on the rock dimension.
• There is evidence for mutual exclusiveness of:
– listening to techno and listening to rock,
– listening to classical and drinking alcohol.
• The classical listeners tend to be girls.
Summary:
Does music taste (co-)determine the selection of friends?
Somewhat. • There is no music taste homophily
(possible exception: classical music). • Listening to rock music seems to coincide with popularity, • listening to classical music with unpopularity.
To what degree is music taste acquired via friendship ties?
It depends on the specific music taste:• Listening to techno or rock music is ‘learnt’ from peers, • listening to classical music is not – maybe a ‘parent thing’?
Check out the software at http://stat.gamma.rug.nl/stocnet/
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