s ome r esults f rom Scottish d ata
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Transcript of s ome r esults f rom Scottish d ata
some
results
from
Scottish
data
The Statistical Analysis of the Dynamics of Networks and Behaviour: An Application to Smoking and Drinking Behaviour among School Friends.
Christian SteglichTom Snijders
ICS / Department of SociologyUniversity of Groningen
Mike Pearson
Centre for Mathematics and StatisticsNapier University, Edinburgh
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Topic smoking behaviour and friendship
Problem influence and/or selection
Theory drifting smoke rings (Pearson, West, Michell)
Data three wave panel ’95’96’97,school year group, age 13-16
Method actor-driven modelling
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Literature
S. Ennett & K. Bauman (1993). Peer Group Structure and Adolescent Cigarette Smoking: A Social Network Analysis. Journal of Health and Social Behavior 34(3): 226-36.
E. Oetting and J. Donnermeyer (1998). Primary Socialization Theory: the Etiology of Drug Use and Deviance. Substance Use and Misuse 33(4): 995-1026.
M. Pearson & L. Michell (2000). Smoke Rings: Social Network Analysis of Friendship Groups, Smoking, and Drug-Taking. Drugs: Education, Prevention and Policy 7(1): 21-37.
M. Pearson & P. West (2003). Drifting Smoke Rings: Social Network Analysis and Markov Processes in a Longitudinal Study of Friendship Groups and Risk-Taking. Connections 25(2):59-76.
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Problem
Empirical “network autocorrelation”:
Friends of smokers are smokers,
friends of non-smokers are non-smokers.
Why that?
Various theoretical accounts
influenceselection
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Problem refined
influenceselection
What is the role of cohesion ?
Influence is expected to be strongest in cohesive subsets of the network.
Selection mechanisms can generate such cohesive subsets.
selection influence cohesion autocorrelation
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Modelling
Actor-driven, dynamic model: actors are assumed to take two types of decisions:
• network decisions (whom to call a friend)
• behavioural decisions (own smoking).
The interplay of both generates the evolution process of network and behaviour.
What is modelled are structural and other determinants of the actors’ preferences.
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Modelling
It is assumed that the network and behaviourevolves in continuous time between the observation moments.
Network & behaviour evolve in mini steps,in which one of the actors is permitted(but not required)… to make a change in one friendship tie:
network mini step, or to make a change in his/her behaviour:
behaviour mini step.
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Modelling
When actor i is allowed to make a network mini step, (s)he can change one tie variable, maximizing an objective function + random disturbance:
net net net( , , , , ) ( , , , )i if x z t j x z t j
The objective function expresses the actor’s preferences as a function of network position and own & others’ behaviour.
i = ego, j = alter, x= network, z = behaviour, t = time, = parameter, = random influence.
(Behavioural mini steps are modelled analogously.)
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Modelling
The network objective function includes:• network structure,• own behaviour, others’ behaviour,• and interactions.
The behavioural objective function includes: • network structure,• own behaviour, others’ behaviour,• and interactions.
Interdependence between networkand behaviour is accounted for !!
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Modelling
Model specification:
•Spell out the two objective functions as weighted sums of network and behaviour effects.
•Weights are parameters estimated from data.
•Here (smoking of adolescents): model actors’ preferences…
for cohesion, for adapting to their friends’ behaviour, for choosing friends that behave the same, etc.,
…in both types of decisions / objective functions.
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Modelling
In SIENA, include measures of cohesion as well as measures of selection and influence, plus interaction terms.
cohesion
reciprocity transitivity
# reciprocalpairs
# peripheral todense triads
# transitivetriplets
# actors atdistance 2
# densetriads
+
++
+ ++
+ –+ + ++ +
–
+
local density
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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.
Modelling
: i j
ijz z
sim
ij ijjx sim
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Stepwise increase of model complexity
Start with simple cohesion measures…
reciprocity effect
measures the preference difference of actor i between right and left configuration
transitivity effect
i i
i i j j
j j
k k
ij jijx x
ij jk ikjkx x x
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Stepwise increase of model complexity
… and with simple measures of influence and selection.
friendship similarity effect
ij ijjx sim
“classical”selection
“classical”influence
Results
SIENA parameter estimates: basis model
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network evolution (1)
outdegree
-2.49 (0.30)
reciprocity
2.07 (0.18)
transitivity
0.15 (0.08)
distance-two
-0.85 (0.07)
sameclass
0.04 (0.03)
Results
SIENA parameter estimates: basis model
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network evolution (2)
gender similarity 0.78 (0.10)
alter -0.18 (0.08)
ego 0.15 (0.07)
smoke similarity 0.24 (0.08)
alter -0.11 (0.01)
ego 0.07 (0.17)
Results
SIENA parameter estimates: basis model
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behavioural evolution
tendency
-0.02 (0.29)
gender
0.55 (0.36)
sibling-smokes
0.95 (0.45)
similarity
0.59 (0.40)
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Stepwise increase of model complexity
Add simple interaction.
reciprocity × similarity effect
selection×reciprocity
influence × reciprocity
ij ji ijjx x sim
Results
SIENA estimates extended models:
similarity × reciprocity in network model
(all other parameters barely change)
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network evolution
outdegree
-2.10 (0.23)
reciprocity
2.98 (0.27)
smoke similarity
0.46 (0.12)
sim × rec
-0.81 (0.29)
Results
SIENA estimates extended models:
similarity × reciprocity in behavioural model:
Standard errors of all behavioural parameters become high – no meaningful estimates !
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Results: frequency of decision types
SIENA parameter estimates: basis model
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speed of evolution processes
network period 1 11.84 (1.34)
period 2 9.61 (1.06)
behaviour period 1 0.86 (0.29)
period 2 0.81 (0.31)
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Stepwise increase of model complexity
Add cohesion measures based on group positions (approximated as specific configurations of the neighbourhood).
group member belongs to“dense triad”
peripheral is unilaterally attached to group
isolatehas no incomin
g ties
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Stepwise increase of model complexity
For example:
peripheral × similarity effect
selection×peripheral
influence × peripheral
(1 )(1 )(1 )( ) ( )ij ji ki li ij ik iljklx x x x sim sim sim densejkl
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Results
SIENA parameter estimates: a complex model
network part of the model (1):outdegree
-2.37 (0.32)
reciprocity
2.90 (0.27)
transitivity
-0.25 (0.09)
distance-2
-1.27 (0.06)
dense triads
0.50 (0.21)
peripheral
0.09 (0.06)
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Results
SIENA parameter estimates: a complex model
network part of the model (2):smoke similarity
0.45 (0.10)
alter
-0.13 (0.01)
sim × rec
-0.94 (0.29)
peripheral
0.03 (0.04)
sim× per 0.01 (0.01)
(other network effects remain as were before)
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Results
SIENA parameter estimates: a complex model
behavioural part of the model:tendency
-0.12 (0.48)
gender
0.45 (0.49)
sibling-smokes
1.21 (0.77)
similarity
1.27 (1.19)
dense triads
0.39 (0.50)
peripheral
-0.07 (0.16)
(again, standard errors are quite high)
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Results
Selection effects are strong.Cohesion effects also.Interaction with cohesion reduces selection effect: the more cohesive a group, the less important similarity to these friends.
Influence effects are weak or even spurious:controlling for cohesion, there is no influence effect.Q: Is smoking no ‘social thing’, while other
activities like drinking are ? run a parallel analysis of drinking behaviour !
Second analysis – drinking
SIENA parameter estimates: basis model
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network evolution (1)
outdegree -2.71 (0.33)
reciprocity 2.06 (0.18)
transitivity 0.16 (0.06)
distance-two -0.83 (0.05)
sameclass 0.04 (0.03)
Second analysis – drinking
SIENA parameter estimates: basis model
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network evolution (2)
gender similarity 0.77 (0.10)
alter -0.23 (0.09)
ego 0.17 (0.08)
drink similarity 0.51 (0.12)
alter -0.05 (0.03)
ego 0.01 (0.12)
Second analysis – drinking
SIENA parameter estimates: basis model
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behavioural evolution
tendency -0.42 (0.09)
gender -0.04 (0.20)
similarity 1.34 (0.41)
much higher t-scorethan in smoking analysis
A: Drinking indeed seems to be more of a ‘social thing’, than smoking (influence parameter significant).
follow up on this, increase model complexity…
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Summary
•simultaneous statistical modelling of network & behavioural dynamics for longitudinal panel data
•allows for disentangling selection and influence effects
•special positional effects can be investigated
•software SIENA 2.0 is available from http://stat.gamma.rug.nl/stocnet/ (beta version, final version comes soon)