s ome r esults f rom Scottish d ata

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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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… 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


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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


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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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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


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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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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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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


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


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


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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)



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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)



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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)

http://stat.gamma.rug.nl/stocnet/

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