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

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

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

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

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)

beh(tn) beh(tn+1)

net(tn) net(tn+1)

persistence (?)

selection

influence

persistence (?)

Agenda for this talk:

- Brief sketch of the stochastic modelling framework

- An illustrative research question

- Data

- Software

- Analysis

- Interpretation of results

- Summary

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

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?

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 60’s/70’s

Heavy Metal House

Techno Grunge

Folk/Traditional Rap

Rave Hip Hop

Other (what?)………………………………….

Music question: 16 items

Before applying SIENA: data reduction to the 3 most informative dimensions

rap

dance

reggae

techno

househiphop

chart

grunge

rave

heavymtl

rock

classica

jazz

indie

sixty70s

folk_trd

scale CLASSICAL

scale ROCK

scale TECHNO

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 don’t drink (alcohol)

5

4

3

2

1

Alcohol question: five point scale

General: SIENA requires dichotomous networks and behavioural variables on an ordinal scale.

Some descriptives:

0

0.5

1

1.5

2

2.5

3

3.5

wave 1 wave 2 wave 3

techno rock classical alcohol

average dynamics of the four behavioural variables

0

50

100

150

200

250

wave 1 wave 2 wave 3

asymmetric mutual

global dynamics of friendship ties (dyad counts)

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.

Identification of data sourcefiles

Recoding of variables and identification of missing data

Specifying subsets of actors for analyses

Data specification: insert data into the model’s “slots”.

Model specification: select parameters to include for network evolution.

Model specification: select parameters to include for behavioural evolution.

Model specification: some additional features.

Model estimation: stochastic approximation of optimal parameter values.

Network objective function:– intercept:

outdegree

– network-endogenous:reciprocitydistance-2

– covariate-determined:gender homophilygender egogender alter

– behaviour-determined:beh. homophilybeh. egobeh. alter

Rate functions were kept as simple as possible (periodwise constant).

Analysis of the music taste data:

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.

parameter s.e. t-scoreoutdegree -1.89 0.29 -6.51reciprocity 2.34 0.12 20.08distance-2 -1.09 0.07 -14.89gender sim 0.80 0.12 6.72

alter -0.21 0.12 -1.73ego 0.24 0.11 2.17

techno sim 0.08 0.33 0.26alter 0.07 0.05 1.30ego -0.10 0.05 -1.93

rock sim 0.11 0.41 0.26alter 0.19 0.07 2.75ego -0.07 0.08 -0.92

classical sim 1.44 0.69 2.07alter 0.15 0.17 0.91ego 0.40 0.17 2.42

alcohol sim 0.83 0.27 3.08alter -0.03 0.04 -0.75ego -0.03 0.03 -0.85

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 -0.62ego girl -0.18 0.41

table gives gender-related contributions to the objective function

There is alcohol homophily:

alter low high

low 0.36 -0.59ego high -0.59 0.13

table shows contributions to the objective function for highest / lowest possible scores

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

Results: behavioural evolution

par. s.e. par. s.e. par. s.e. par. s.e.intercept -0.30 0.37 0.01 0.25 0.59 0.25 0.67 1.30assimilation 0.94 0.27 0.45 0.18 0.63 0.28 0.42 1.17gender -0.06 0.19 0.25 0.12 0.01 0.19 1.57 0.83techno 0.23 0.16 --- --- -0.25 0.09 -0.46 0.40rock 0.16 0.16 -0.34 0.10 --- --- 0.64 0.39classical -0.59 0.32 -0.13 0.23 -0.34 0.30 --- ---alcohol --- --- 0.07 0.10 -0.11 0.07 -1.03 0.34

alcohol techno rock classical

• 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.

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/