1. Assessing influence and selection in network-behavioural co-evolution with an application to smoking and alcohol consumption among adolescents. Christian Steglich, Tom Snijders University of Groningen Mike Pearson Napier University Edinburgh Supported by the Netherlands Organisation for Scientific Research (NWO) under grant # 401-01-550.

2. Empirical starting point: “Network autocorrelation” in cross-sectional data: Friends of smokers are smokers, friends of non-smokers are non-smokers. Small companies trade with small companies, large companies trade with large companies. Why that? Range of theoretical accounts: influence selection RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

3. Influence / contagion paradigm: Properties of network neighbours are assimilated. Friends of smokers turn into smokers. Trade with big companies makes a company big. Selection paradigm: Network neighbourhood is chosen to match. Smokers choose other smokers as friends. Big companies do not trade with small companies. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

4. How can selection and influence be assessed and separated?  Longitudinal data are a prerequisite,  ‘panel density’ sufficiently high: RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam Lower actor reciprocates friendship Upper actor adapts to (re- ciprocal) friend Upper actor adapts to (per- ceived) friend Lower actor reciprocates friendship

5. Modelling of network-behavioural co-evolution Continuous time model  invisibility of to-and-fro changes in panel data poses no problem  evolution can be modelled in micro steps Observed changes are quite complex – they are interpreted as resulting from a sequence of micro steps. Actor-driven model  selection and influence conceptually belong to the actor level RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

6. Formalization as stochastic process (1) State space Pair (x,z)(t) contains adjacency matrix x andvector(s) of behaviourals z at time point t. Transition probabilities Co-evolution is modelled by specifying probabilities for simple transitions between states (x,z)(t 1 ) and (x,z)(t 2 ) network micro step: (x,z)(t 1 ) and (x,z)(t 2 ) differ in one tie x ij only. behavioural micro step: (x,z)(t 1 ) and (x,z)(t 2 ) differ in one behavioural score z i only. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

7. Formalization as stochastic process (2) Timing of decisions / transitions Waiting times between decisions are assumed to be exponentially distributed (Markov process); they can depend on state, actor and time. Actor-driven modelling Micro steps are modelled as outcomes of an actor’s decisions; conditionally independent, given the current state. Schematic overview of model components Occurrence of decisionsDecision rule NetworkNetwork rate functionNetwork decision rule BehaviouralBehavioural rate functionBehavioural decision rule RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

8. Modelling of the actors’ decisions (1) Network micro step by actor i Choice options - change tie variable to one other actor j - change nothing Maximize objective function + random disturbance Random part, i.i.d. over x, z, t, i, j, according to extreme value type I Deterministic part, depends on network-behavioural neighbourhood of actor i RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

9. Choice probabilities resulting from distribution of  are of multinomial logit shape x(i,j) is the network obtained from x by changing tie to actor j; x(i,i) formally stands for keeping the network as is RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

10. Objective function f is linear combination of effects, with parameters as effect weights. Examples: reciprocity effect measures the preference difference of actor i between right and left configuration transitivity effect i i i i j j j j kk RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

11. Modelling of the actors’ decisions (2) Behavioural micro step by actor i Choice options - increase, decrease, or keep score on behavioural Maximize objective function + random disturbance Choice probabilities analogous to network part Assume independence also of the network random part Objective function different from the network objective function RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

12. Modelling selection and influence (1) 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. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

13. Modelling selection and influence (2) Inclusion of friendship similarity in network objective function models transitions as these: Inclusion of friendship similarity in behavioural objective function models transitions as these: “classical” selection “classical” influence RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

14. Total process model Transition intensities of Markov process are Here  waiting times,  = change in behavioural,  = set of allowed changes in behavioural change, z(i,  ) = behavioural vector after change. Together with starting value, process model is fully defined. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

15. Remarks on model estimation: The likelihood of an observed data set cannot be calculated in closed form, but can at least be simulated.  ‘third generation problem’ of statistical analysis,  simulation-based inference is necessary. Currently available: – Method of Moments estimation (Snijders 2001, 1998) – Maximum likelihood approach (Snijders & Koskinen 2003) Implementation: program SIENA, part of the StOCNet software package (see link in the end). RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

16. Application to alcohol consumption and smoking behaviour among adolescents Data three wave panel ’95’96’97, school year group, age 13-16 alcohol consumption variable ranges from 1 (more than once a week) to 5 (not at all) smoking variable ranges from 3 (non-smokers) to 5 (regular smokers) Method actor-driven modelling, using SIENA first run separate analyses per behavioural, then analyse them jointly. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

17. Question Do influence and selection processes based on (a) smoking behaviour and (b) drinking behaviour differ qualitatively? More precisely: Is alcohol consumption more “social” and smoking more “individual”?  Is influence stronger on the alcohol dimension? Is alcohol consumption more “accepted” than smoking?  What are the details of the selection mechanisms? RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

18. Model components covariate effects on both evolution processes -classmate relation (dyadic) -parent smoking, sibling smoking -gender (several effects) endogenous effects of network on network evolution -reciprocity -transitivity (two effects) endogenous effects of behaviour on network evolution -selection based on alcohol consumption -selection based on smoking (three effects each) endogenous effects of network on behavioural evolution -influence from friends RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

19. Estimation results (excerpts, 1) gender-based selection utilities Based on these estimates, in an artificial choice situation between a boy and a girl, ego’s choice probabilities are: This result is consistent across model specifications. alter egoboy girl boy0.78 -0.17 girl0.17 0.77 alter egoboy girl boy72% 28% girl35% 65% RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

20. Estimation results (excerpts, 2) alcohol-based selection utilities Based on these estimates, in an artificial choice situation between a regular drinker and a non-drinker, ego’s choice probabilities are: This result also is consistent across model specifications. Note that there is a net preference for drinkers as friends! alter egonon-drinkerreg.drinker non-drinker0.31-0.02 reg.drinker-0.230.47 alter egonon-drinkerreg.drinker non-drinker58%42% reg.drinker33%67%

21. Estimation results (excerpts, 3) smoking-based selection utilities Based on these estimates, in an artificial choice situation between a regular smoker and a non-smoker, ego’s choice probabilities are : This result also is consistent across model specifications. Note that there is a net preference against smokers as friends! alter egonon-smokerreg.smoker non-smoker-0.08-0.55 reg.smoker-0.18-0.27 alter egonon-smokerreg.smoker non-smoker61%39% reg.smoker48%52%

22. Estimation results (excerpts, 4) smoking-based influence effect: model without alcohol: controlling for alcohol: parameter positive, p=0.08 parameter positive, p>0.2 Probabilities shown are for an occasional smoker with 4 friends, depending on the number of regular smokers in his neighbourhood (other friends assumed to be non-smokers) RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam increase decrease stay Weak pos. effect of alcohol consumption on smoking, p=0.08

23. Estimation results (excerpts, 5) alcohol-based influence effect: model without smoking: controlling for smoking: parameter positive, p<0.01 Probabilities shown are for an occasional drinker with 4 friends, depending on the number of regular drinkers in his neighbourhood (other friends assumed to be non-drinkers) RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam increase decrease stay No significant effect of smoking on alcohol consumption, p>0.4

24. Summary of investigation Selection effects occur for both alcohol and smoking. Alcohol consumption of a potential friend renders him/her more attractive as friend, while smoking renders him/her less attractive. Influence occurs only on the alcohol dimension. The weak appearance of an influence effect for smoking seems to be due to an effect of alcohol consumption on smoking. RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam

25. Discussion simultaneous statistical modelling of network & behavioural dynamics for longitudinal panel data selection and influence effects are disentangled many other effects and applications possible software SIENA 2.0 beta version available from http://stat.gamma.rug.nl/stocnet/(“stable URL”) and via http://ppswmm.ppsw.rug.nl/steglich/ (current updates) final version comes soon RC33 Sixth International Conference on Social Science Methodology, 17-20 August 2004, Amsterdam