Transcript presentation

some
results
The Statistical Analysis of the
Dynamics of Networks and
Behaviour: An Application to
Smoking and Drinking Behaviour
among School Friends.
Christian Steglich
from
Scottish
Tom Snijders
ICS / Department of Sociology
University of Groningen
Mike Pearson
data
Centre for Mathematics and Statistics
Napier University, Edinburgh
some
results
from
Scottish
data
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
some
results
from
Scottish
data
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.
some
Problem
Empirical “network autocorrelation”:
results
Friends of smokers are smokers,
friends of non-smokers are non-smokers.
from
Scottish
Why that?
Various theoretical accounts
influence
data
selection
some
Problem refined
influence
selection
results
What is the role of cohesion ?
from
Influence is expected to be strongest in
cohesive subsets of the network.
Scottish
Selection mechanisms can generate such
cohesive subsets.
selection
data
cohesion
influence
autocorrelation
some
results
Modelling
Actor-driven, dynamic model: actors are
assumed to take two types of decisions:
• network decisions (whom to call a friend)
from
Scottish
data
• 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.
some
results
Modelling
It is assumed that the network and behaviour
evolves in continuous time between the
observation moments.
from
Network & behaviour evolve in mini steps,
in which one of the actors is permitted
(but not required)…
Scottish
 to make a change in one friendship tie:
network mini step, or
 to make a change in his/her behaviour:
data
behaviour mini step.
some
results
from
Scottish
data
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:
finet (net , x, z, t, j )  inet ( 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.)
some
results
from
Scottish
data
Modelling
The
•
•
•
network objective function includes:
The
•
•
•
behavioural objective function includes:

Interdependence between network
and behaviour is accounted for !!
network structure,
own behaviour, others’ behaviour,
and interactions.
network structure,
own behaviour, others’ behaviour,
and interactions.
some
Modelling
Model specification:
results
• Spell out the two objective functions as weighted
sums of network and behaviour effects.
• Weights  are parameters estimated from data.
from
Scottish
• Here (smoking of adolescents): model actors’
preferences…
 for cohesion,
 for adapting to their friends’ behaviour,
 for choosing friends that behave the same,
 etc.,
data
…in both types of decisions / objective functions.
some
results
Modelling
In SIENA, include measures of cohesion as
well as measures
of selection and influence,
cohesion
plus interaction terms.
+
fromreciprocity
+
+
+
+
local density
+
Scottish
#
reciprocal # peripheral to
pairs
dense triads
+
+
+
# dense
triads
+
+
–
# transitive
triplets
+
data
transitivity
+
# actors at
distance 2
–
some
Modelling
Influence and selection are based on a measure of
behavioural
similarity :
results
simij :
from
  zi  zj

Friendship similarity of actor i :
 x sim
j
ij
ij
Scottish
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.
data
some
Stepwise increase of model complexity
Start with simple cohesion measures…
results
from
xx
reciprocity effect
i
j
j
i
ij
ji
j
measures the preference difference of actor i
between right and left configuration
Scottish

transitivity effect
j
data
i
k
jk
x ij x jk x ik
j
i
k
some
results
Stepwise increase of model complexity
… and with simple measures of influence
and selection.
friendship similarity effect
 x sim
j
ij
from
“classical”
selection
Scottish
data
“classical”
influence
ij
some
Results
SIENA parameter estimates: basis model
results
from
Scottish
network evolution (1)
outdegree
-2.49 (0.30)
reciprocity
2.07 (0.18)
transitivity
0.15 (0.08)
distance-two
sameclass
data
-0.85 (0.07)
0.04 (0.03)
some
Results
SIENA parameter estimates: basis model
results
network evolution (2)
gender similarity
from
Scottish
data
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)
some
Results
SIENA parameter estimates: basis model
results
behavioural evolution
tendency
from
Scottish
data
-0.02 (0.29)
gender
0.55 (0.36)
sibling-smokes
0.95 (0.45)
similarity
0.59 (0.40)
some
Stepwise increase of model complexity
Add simple interaction.
results
reciprocity × similarity effect
 x x sim
j
from
ij
ji
selection
×
reciprocity
Scottish
data
influence
×
reciprocity
ij
some
Results
SIENA estimates extended models:
results
similarity × reciprocity in network model
network evolution
from
Scottish
data
outdegree
-2.10 (0.23)
reciprocity
2.98 (0.27)
smoke similarity
0.46 (0.12)
sim × rec
-0.81 (0.29)
(all other parameters barely change)
some
Results
SIENA estimates extended models:
results
from
Scottish
data
similarity × reciprocity in behavioural model:
Standard errors of all behavioural
parameters become high –
no meaningful estimates !
some
Results: frequency of decision types
SIENA parameter estimates: basis model
results
speed of evolution processes
network
from
Scottish
data
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)
some
results
Stepwise increase of model complexity
Add cohesion measures based on group
positions (approximated as specific
configurations of the neighbourhood).
from
group member
belongs to
“dense triad”
Scottish
peripheral
is unilaterally
data
attached to group
isolate
has no
incoming
ties
some
Stepwise increase of model complexity
For example:
results
peripheral × similarity effect

from
jkl
xij (1  x ji )(1  x ki )(1  x li )( simij  simik  simil )dense( jkl )
selection
×
peripheral
Scottish
data
influence
×
peripheral
some
Results
SIENA parameter estimates: a complex model
results
from
Scottish
data
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)
some
Results
SIENA parameter estimates: a complex model
results
network part of the model (2):
smoke similarity
from
Scottish
data
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)
some
Results
SIENA parameter estimates: a complex model
results
behavioural part of the model:
tendency
from
Scottish
data
-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)
some
Results
Selection effects are strong.
results
from
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:
Scottish
data
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 !
some
Second analysis – drinking
SIENA parameter estimates: basis model
results
from
Scottish
network evolution (1)
outdegree
-2.71 (0.33)
reciprocity
2.06 (0.18)
transitivity
0.16 (0.06)
distance-two
sameclass
data
-0.83 (0.05)
0.04 (0.03)
some
Second analysis – drinking
SIENA parameter estimates: basis model
results
network evolution (2)
gender similarity
from
Scottish
data
drink
0.77 (0.10)
alter
-0.23 (0.09)
ego
0.17 (0.08)
similarity
0.51 (0.12)
alter
-0.05 (0.03)
ego
0.01 (0.12)
some
Second analysis – drinking
SIENA parameter estimates: basis model
results
from
behavioural evolution
tendency
-0.42 (0.09)
gender
-0.04 (0.20)
similarity
Scottish
data
1.34 (0.41)
much higher t-score
than 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…
some
results
from
Scottish
data
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)