Assessing influence and selection in

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Assessing influence and selection
in network-behavioural co-evolution with an
application to smoking and alcohol consumption
among adolescents. Christian Steglich, Tom
Snijders University of Groningen Mike
Pearson Napier University Edinburgh Supported by
the Netherlands Organisation for Scientific
Research (NWO) under grant 401-01-550.
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Empirical starting point Network
autocorrelation in cross-sectional
data Friends of smokers are smokers, friends of
non-smokers are non-smokers. Small companies
trade with small companies, large companies trade
with large companies. Why that? Range of
theoretical accounts influence sele
ction
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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Influence / contagion paradigm Properties of
network neighbours are assimilated. Friends of
smokers turn into smokers. Trade with big
companies makes a company big. Selection
paradigm Network neighbourhood is chosen to
match. Smokers choose other smokers as
friends. Big companies do not trade with small
companies.
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• How can selection and influence
• be assessed and separated?
• Longitudinal data are a prerequisite,
• panel density sufficiently high

Lower actor reciprocates friendship
Upper actor adapts to (re- ciprocal) friend
Upper actor adapts to (per- ceived) friend
Lower actor reciprocates friendship
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Modelling of network-behavioural co-evolution
• Continuous time model
• invisibility of to-and-fro changes in panel data
  poses no problem
• evolution can be modelled in micro steps
• Observed changes are quite complex they are
  interpreted as resulting from a sequence of micro
  steps.
• Actor-driven model
• selection and influence conceptually belong to
  the actor level

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Formalization as stochastic process (1)
• State space
• Pair (x,z)(t) contains adjacency matrix x
  andvector(s) of behaviourals z at time point t.
• Transition probabilities
• Co-evolution is modelled by specifying
  probabilities for simple transitions between
  states (x,z)(t1) and (x,z)(t2)
• network micro step
• (x,z)(t1) and (x,z)(t2) differ in one tie xij
  only.
• behavioural micro step
• (x,z)(t1) and (x,z)(t2) differ in one behavioural
• score zi only.

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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Formalization as stochastic process (2) Timing
of decisions / transitions Waiting times l
between decisions are assumed to be exponentially
distributed (Markov process) they can depend on
state, actor and time. Actor-driven
modelling Micro steps are modelled as outcomes of
an actors decisions conditionally independent,
given the current state. Schematic overview of
model components
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Modelling of the actors decisions (1)
• Network micro step by actor i
• Choice options
• change tie variable to one other actor j
• change nothing
• Maximize objective function random disturbance

Random part, i.i.d. over x, z, t, i, j, according
to extreme value type I
Deterministic part, depends on network-behavioural
neighbourhood of actor i
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Choice probabilities resulting from distribution
  of e are of multinomial logit shape

x(i,j) is the network obtained from x by changing
tie to actor j x(i,i) formally stands for
keeping the network as is
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Objective function f is linear combination of
  effects, with parameters as effect weights.
• Examples
• reciprocity effect
• measures the preference difference of actor i
  between right and left configuration
• transitivity effect

i
i
j
j
j
j
i
i
k
k
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Modelling of the actors decisions (2)
• Behavioural micro step by actor i
• Choice options
• increase, decrease, or keep score on behavioural
• Maximize objective function random disturbance
• Choice probabilities analogous to network part

Assume independence also of the network random
part
Objective function different from the network
objective function
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Modelling selection and influence (1)
• Influence and selection are based on a measure of
  behavioural similarity
• Friendship similarity of actor i
• Actor i has two ways of increasing friendship
  similarity
• by adapting own behaviour to that of friends j,
  or
• by choosing friends j who behave the same.

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Modelling selection and influence (2)
• Inclusion of friendship similarity
• in network objective function
• models transitions as these
• Inclusion of friendship similarity in behavioural
  objective function models transitions as these

classical selection
classical influence
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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Total process model Transition intensities of
Markov process are Here l waiting
times, d change in behavioural, G set of
allowed changes in behavioural change, z(i,d)
behavioural vector after change. Together with
starting value, process model is fully defined.
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Remarks on model estimation
• The likelihood of an observed data set cannot be
  calculated in closed form, but can at least be
  simulated.
• ? third generation problem of statistical
  analysis,
• ? simulation-based inference is necessary.
• Currently available
• Method of Moments estimation (Snijders 2001,
  1998)
• Maximum likelihood approach (Snijders Koskinen
  2003)
• Implementation program SIENA, part of the
  StOCNet
• software package (see link in the end).

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Application to alcohol consumption and
• smoking behaviour among adolescents
• Data three wave panel 959697,
• school year group, age 13-16
• alcohol consumption variable ranges
• from 1 (more than once a week) to 5 (not at all)
• smoking variable ranges
• from 3 (non-smokers) to 5 (regular smokers)
• Method actor-driven modelling, using SIENA
• first run separate analyses per behavioural,
• then analyse them jointly.

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Question
• Do influence and selection processes based on
• smoking behaviour and
• drinking behaviour
• differ qualitatively?
• More precisely
• Is alcohol consumption more social and smoking
  more individual?
• Is influence stronger on the alcohol dimension?
• Is alcohol consumption more accepted than
  smoking?
• What are the details of the selection mechanisms?

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Model components
• covariate effects on both evolution processes
• classmate relation (dyadic)
• parent smoking, sibling smoking
• gender (several effects)
• endogenous effects of network on network
  evolution
• reciprocity
• transitivity (two effects)
• endogenous effects of behaviour on network
  evolution
• selection based on alcohol consumption
• selection based on smoking (three effects each)
• endogenous effects of network on behavioural
  evolution
• influence from friends

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Estimation results (excerpts, 1)
• gender-based selection utilities
• Based on these estimates,
• in an artificial choice situation
• between a boy and a girl, egos
• choice probabilities are
• This result is consistent across model
  specifications.

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Estimation results (excerpts, 2)
• alcohol-based selection utilities
• Based on these estimates,
• in an artificial choice situation
• between a regular drinker and
• a non-drinker, egos choice
• probabilities are
• This result also is consistent across model
  specifications.
• Note that there is a net preference for drinkers
  as friends!

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• Estimation results (excerpts, 3)
• smoking-based selection utilities
• Based on these estimates,
• in an artificial choice situation
• between a regular smoker and
• a non-smoker, egos choice
• probabilities are
• This result also is consistent across model
  specifications.
• Note that there is a net preference against
  smokers as friends!

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• Estimation results (excerpts, 4)
• smoking-based influence effect
• model without alcohol controlling for
  alcohol
• parameter positive, p0.08 parameter positive,
  pgt0.2
• Probabilities shown are for an occasional smoker
  with 4 friends, depending on the number of
  regular smokers in his neighbourhood (other
  friends assumed to be non-smokers)

Weak pos. effect of alcohol consumption on
smoking, p0.08
increase
stay
decrease
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
23

• Estimation results (excerpts, 5)
• alcohol-based influence effect
• model without smoking controlling for
  smoking
• parameter positive, plt0.01 parameter positive,
  plt0.01
• Probabilities shown are for an occasional drinker
  with 4 friends, depending on the number of
  regular drinkers in his neighbourhood (other
  friends assumed to be non-drinkers)

No significant effect of smoking on alcohol
consumption, pgt0.4
increase
stay
decrease
RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Summary of investigation
• Selection effects occur for both alcohol and
  smoking.
• Alcohol consumption of a potential friend renders
  
• him/her more attractive as friend, while smoking
  renders him/her less attractive.
• Influence occurs only on the alcohol dimension.
• The weak appearance of an influence effect for
  smoking seems to be due to an effect of alcohol
  consumption on smoking.

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam
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• Discussion
• simultaneous statistical modelling of network
  behavioural dynamics for longitudinal panel data
• selection and influence effects are disentangled
• many other effects and applications possible
• software SIENA 2.0 beta version available from
• http//stat.gamma.rug.nl/stocnet/ (stable URL)
• and via
• http//ppswmm.ppsw.rug.nl/steglich/ (current
  updates)
• final version comes soon

RC33 Sixth International Conference on Social
Science Methodology, 17-20 August 2004, Amsterdam