Analysing network-behavioural co-evolution with SIENA

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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
with an application to the dynamics of music
taste, alcohol consumption and friendship
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
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• 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

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persistence (?)
beh(tn)
beh(tn1)
selection
influence
net(tn)
net(tn1)
persistence (?)

• 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)

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• Agenda for this talk
• Brief sketch of the stochastic modelling
  framework
• An illustrative research question
• Data
• Software
• Analysis
• Interpretation of results
• Summary

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• 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
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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?
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Music question 16 items
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 ? 60s/70s ? Heavy
Metal ? House ? Techno ? Grunge
? Folk/Traditional ? Rap ?
Rave ? Hip Hop ? Other
(what?).
Before applying SIENA data reduction to the 3
most informative dimensions
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scale ROCK
scale CLASSICAL
scale TECHNO
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Alcohol question five point scale
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 dont drink (alcohol) ?
5 4 3 2 1
General SIENA requires dichotomous networks
and behavioural variables on an ordinal scale.
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Some descriptives
average dynamics of the four behavioural variables
global dynamics of friendship ties (dyad counts)
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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.
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Recoding of variables and identification of
missing data
Specifying subsets of actors for analyses
Identification of data sourcefiles
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(No Transcript)
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Data specification insert data into the models
slots.
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Model specification select parameters to include
for network evolution.
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Model specification select parameters to include
for behavioural evolution.
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Model specification some additional features.
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Model estimation stochastic approximation of
optimal parameter values.
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Analysis of the music taste data

• Network objective function
• intercept
• outdegree
• network-endogenous
• reciprocity
• distance-2
• covariate-determined
• gender homophily
• gender ego
• gender alter
• behaviour-determined
• beh. homophily
• beh. ego
• beh. alter
• Rate functions were kept as simple as possible
  (periodwise constant).

• 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.

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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 -0.62 ego
girl -0.18 0.41 table gives gender-related
contributions to the objective function
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
There is alcohol homophily alter
low high low 0.36 -0.59 ego
high -0.59 0.13 table shows contributions to
the objective function for highest / lowest
possible scores
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Results behavioural evolution

• 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.

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• 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/