s ome r esults f rom Scottish d ata

1. The Statistical Analysis of the Dynamics of Networks and Behaviour: An Application to Smoking and Drinking Behaviour among School Friends. Christian Steglich Tom Snijders ICS / Department of Sociology University of Groningen Mike Pearson Centre for Mathematics and Statistics Napier University, Edinburgh some results from Scottish data

2. some results from Scottish data Topicsmoking behaviour and friendship Probleminfluence and/or selection Theorydrifting smoke rings (Pearson, West, Michell) Datathree wave panel ’95’96’97, school year group, age 13-16 Method actor-driven modelling

3. 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.

4. some results from Scottish data • Problem • Empirical “network autocorrelation”: • Friends of smokers are smokers, • friends of non-smokers are non-smokers. • Why that? • Various theoretical accounts • influence selection

5. some results from Scottish data Problem refined influence selection 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

6. some results from Scottish data • 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.

7. some results from Scottish data • Modelling • It is assumed that the network and behaviour • evolves 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.

8. 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: 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.)

9. some results from Scottish data • 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 network • and behaviour is accounted for !! 

10. 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. some results from Scottish data

11. some results from Scottish data Modelling In SIENA, include measures of cohesion as well as measures of selection and influence, plus interaction terms. cohesion + + + reciprocity local density transitivity + + + + + + + – # reciprocal pairs # peripheral to dense triads # dense triads # transitive triplets # actors at distance 2 + – + +

12. some results from Scottish data Modelling • Influence and selection are based on a measure of behavioural similarity : • Friendship similarity of actor i: • Actor ihastwo ways of increasing friendship similarity: • by adapting own behaviour to that of friends j, or • by choosing friends j who behave the same.

13. some results from Scottish data • Stepwise increase of model complexity • Start with simple cohesion measures… • reciprocity effect • measures the preference difference of actor ibetween right and left configuration • transitivity effect i j i j j j i i k k

14. some results from Scottish data • Stepwise increase of model complexity • … and with simple measures of influence • and selection. • friendship similarity effect “classical” selection “classical” influence

15. some results from Scottish data • Results • SIENA parameter estimates: basis model

16. some results from Scottish data • Results • SIENA parameter estimates: basis model

17. some results from Scottish data • Results • SIENA parameter estimates: basis model

18. some results from Scottish data • Stepwise increase of model complexity • Add simple interaction. • reciprocity × similarity effect selection × reciprocity influence × reciprocity

19. some results from Scottish data • Results • SIENA estimatesextended models: • similarity × reciprocity in network model • (all other parameters barely change)

20. some results from Scottish data • Results • SIENA estimatesextended models: • similarity × reciprocity in behavioural model: • Standard errors of all behavioural parameters become high – • no meaningful estimates !

21. some results from Scottish data • Results: frequency of decision types • SIENA parameter estimates: basis model

22. some results from Scottish data 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” isolate has no incoming ties peripheral is unilaterally attached to group

23. some results from Scottish data • Stepwise increase of model complexity • For example: • peripheral × similarity effect selection × peripheral influence × peripheral

24. some results from Scottish data • Results • SIENA parameter estimates: a complex model • network part of the model (1):

25. some results from Scottish data • Results • SIENA parameter estimates: a complex model • network part of the model (2): (other network effects remain as were before)

26. some results from Scottish data • Results • SIENA parameter estimates: a complex model • behavioural part of the model: (again, standard errors are quite high)

27. some results from Scottish data 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 !

28. some results from Scottish data • Second analysis – drinking • SIENA parameter estimates: basis model

29. some results from Scottish data • Second analysis – drinking • SIENA parameter estimates: basis model

30. some results from Scottish data • Second analysis – drinking • SIENA parameter estimates: basis model 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…

31. some results from Scottish data • Summary • simultaneous statistical modelling of network & behavioural dynamics for longitudinal panel data • allows for disentanglingselection 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)