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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 xji )(1 xki )(1 xli )( 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)