References

References (continued)

ANOMALIES Risk-taking Network Density Paradox Apparent contradictions in research findings Network density is an important moderator of peer delinquency, defined as a range of behaviour patterns (Haynie, 2001) Higher density implies higher delinquency Higher smoking among liaisons and isolates than among group members (Ennett & Bauman,1994) Higher smoking among popular pupils (Abel et al)

ANOMALIES Risk-taking Network Density Paradox Researchers use differing methodologies Network density defined as ego-centric measure (Urdry & Bearman, Haynie) when limited data available Ego-centric network density is NOT an ideal measure of peer cohesion

DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS Longitudinal Social Network Study selected from the sample frame of the West of Scotland study into teenage lifestyle, health behaviour and friendships Three time points selected from 1995 till 1997 in one average school in Glasgow We measured risk-taking (smoking and cannabis use) behaviour and also social network position We identified three main social positions : Group member, peripheral to group and relative isolate

SMOKE RINGS(P&M) METHODS Primary socialisation theory highlights the central part played by peer groups for the socialisation issues of selection and influence (O&D) Cohesive peer groups are central to the study, since a (near) complete data set is available (95% of year group) Group peripherals considered to be an important target for selection and influence surrounding risk- taking and non risk-taking behaviour The remaining pupils were categorised as relative isolates

SMOKE RINGS METHODOLOGY Three Cohesive Network Positions Peer Group Member Peripheral to Peer Group Relative Isolate Two Behavioural Characteristics Risk-Taker (smoker or cannabis) Non Risk-Taker

DEFINITION OF COHESION Peer cohesion defined as Mutuality of ties Closeness or reachability of subgroup members Frequency of ties among members Relative frequency of ties among subgroup members compared to non members (Wasserman & Faust)

CHOICE OF SOFTWARE NEGOPY defines cohesive groups as a set of at least 3 people who : Have more than 50% of their linkage with one another (closeness & frequency) Are connected by some path lying entirely within the group to each of the other members in the group (reachability) Who remain so connected when up to 10% of the group is removed (relative frequency)

Smoke Rings : Male Groups and Peripherals (time point 2) Smokes occasionally/regularly Tried/uses cannabis Tried/uses glue Tried/uses other drugs KEY

51 LF Group 5 All Girls Group 1 All Girls Group 13 All Girls Drifting Smoke Rings : Top Girls and Peripherals (time point 2)

Group 7 All Girls

DRIFTING SMOKE RINGS LONGITUDINAL METHODOLOGY Panel Data Collected Behavioural effect (risk-taking or non risk-taking) together with network effect (peer group, peripheral, isolate) give 6 states Extension to two time points gives rise to 36 Markov transitional states In Drifting Smoke Rings we studied the Markov transitional matrices for time points 1 to 2 and for time points 2 to 3.

MARKOV METHODS Singer & Spilerman determined whether observations on an empirical process arise via the evolution of a continuous time Markov model (Embeddability) Kalbfleisch & Lawless avoid complexity of embeddability by using a Maximum Likelihood estimator for the intensity matrix rather than the transitional matrix

SMOKE RINGS AND DRIFTING SMOKE RINGS KEY FINDINGS(PERIPHERALS) The Markov process is non-stationary. More peripherals than expected move to Group Risk- Taking at the transition from age 14 to 15 The expected time spent in the peripheral states (PENRT and PERT) is less than that spent in other states (unstable) At all time points of the study the risk-taking behaviour of the pupils on the periphery of peer groups significantly reflected the behaviour of the groups themselves (gullible)

EXPECTED SOJOURN TIMES Maximum Likelihood Approach (K & L) Algorithm implemented using MATLAB Search for a solution, Q, to Where P is the transitional matrix and Q is the intensity matrix

SOJOURN TIMES Once Q is identified then the expected waiting (sojourn) times spent in each state (i) during a transitional period are given by : Expected time (i) = Find an initial approximation for Q as :

SOJOURN TIMES Assign other values using : And expm(Q) = P (since t=1) Where expm( ) is the MATLAB operator for matrix exponentiation

SOJOURN TIMES Choose a basis : For the intensity matrix, Q, such that We tested models with b=12,18 and 22 and identified an improved value of using the K&L algorithm.

GPRT INFLUENCE TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS INFLUENCE WITHIN A GROUP Group Non Risk-Taker matches Group behaviour and becomes a Group Risk-Taker GPNRTGPRT Expected time for GPNRT to make transition is 12.9 months Expected time for GPRT to make transition is 16.9 months

PENRT GPRT PERT GPRT INFLUENCESELECTION TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS INFLUENCE FOLLOWED BY SELECTION (EVOLUTIONARY) Peripheral Non Risk-Taker changes behaviour to match that of the Group Peripheral Risk-Taker is selected by the Group and becomes a Group Risk-Taker GPRT Expected time for PENRT to make transition is 7 months Expected time for PERT to make transition is 6.4 months Total = 13.4 Months

PENRT GPRT SELECTIONINFLUENCE TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS SELECTION FOLLOWED BY INFLUENCE (NON-EVOLUTIONARY) Peripheral Non Risk-Taker is selected by the Group and becomes a Group Non Risk-Taker Group Non Risk-Taker matches Group behaviour and becomes a Group Risk-Taker GPNRT Expected time for PENRT to make transition is 7 months Expected time for GPNRT to make transition is 12.9 months Total = 19.9 Months GPRT

PENRT GPRT PERT GPRT ISRT INFLUENCEREJECTION TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS INFLUENCE FOLLOWED BY REJECTION EVOLUTIONARY RISK Peripheral Non Risk-Taker changes behaviour to match that of the Group Peripheral Risk-Taker is rejected by the Group and becomes an Isolate Expected time for PENRT to make transition is 7 months Expected time for PERT to make transition is 6.4 months Expected time for ISRT to make transition is 12 months

ISNRT GPRT PENRT GPRT PERT SELECTIONINFLUENCE TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS Isolate Non Risk-Taker selects friend in the Group Peripheral Non Risk-Taker changes behaviour to match that of the Group Expected time for ISNRT to make transition is 8.6 months Expected time for PENRT to make transition is 7 months Expected time for PERT to make transition is 6.4 months ASYMMETRICAL SELECTION/INFLUENCE (EVOLUTIONARY) Total = 22 Months SELECTION

ISNRT GPRT ISRT GPRT PERT INFLUENCESELECTION TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS Isolate Non Risk-Taker changes behaviour to match that of the Group Isolate Risk-Taker is selected by the Group and becomes a Peripheral Expected time for ISNRT to make transition is 8.6 months Expected time for ISRT to make transition is 12 months Expected time for PERT to make transition is 6.4 months Total = 27 Months SYMMETRICAL INFLUENCE /SELECTION (NON-EVOLUTIONARY) SELECTION

PERT GPNRT PENRT GPNRT INFLUENCESELECTION TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS INFLUENCE FOLLOWED BY SELECTION (EVOLUTIONARY) Peripheral Risk-Taker changes behaviour to match that of the Group Peripheral Non Risk-Taker is selected by the Group and becomes a Group Non Risk-Taker GPNRT Expected time for PERT to make transition is 6.4 months Expected time for PENRT to make transition is 7 months Total = 13.4 Months

PERT GPNRT SELECTIONINFLUENCE TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS SELECTION FOLLOWED BY INFLUENCE (NON-EVOLUTIONARY) Peripheral Risk-Taker is selected by the Group and becomes a Group Risk-Taker Group Risk-Taker matches Group behaviour and becomes a Group Non Risk-Taker GPRT Expected time for PERT to make transition is 6.4 months Expected time for GPRT to make transition is 16.9 months Total = 23.3 Months GPNRT

ISRT GPNRT PERT GPNRT PENRT SELECTIONINFLUENCE TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS Isolate Risk-Taker selects friend to become a peripheral Peripheral Risk-Taker changes behaviour to match that of the Group Expected time for ISRT to make transition is 12 months Expected time for PERT to make transition is 6.4 months Expected time for PENRT to make transition is 7 months ASYMMETRICAL SELECTION/INFLUENCE (EVOLUTIONARY) Total = 25.6 Months SELECTION

ISRT GPNRT ISNRT GPNRT PENRT INFLUENCESELECTION TIME DYNAMIC EFFECTS IN DRIFTING SMOKE RINGS Isolate Risk-Taker changes behaviour to match that of the Group Isolate Non Risk-Taker selects friend in the Group and becomes a Peripheral Expected time for ISRT to make transition is 12 months Expected time for ISNRT to make transition is 8.6 months Expected time for PENRT to make transition is 7 months SYMMETRICAL SELECTION/INFLUENCE (NON-EVOLUTIONARY) Total = 27.6 Months SELECTION

Evolutionary Network Paths Existing Link with Another Change behaviour to match other (influence) Selection into Group (or rejection) follows No Existing Link with Another (isolate) Establish link (selection) Match behaviour (influence) Selection into Group (or rejection) follows

Anomalies Revisited: Possible Explanations Stagnating effect of isolate risk-taking compared with isolate non risk-taking reflected in higher sojourn times Confusion between network density and popularity (measured by in-degree) The anomaly of smoking and risk-taking associated with sociometric position and popularity (in-degree) is largely explained by Socio-Economic Status (West of Scotland THiS Study)

OTHER FINDINGS Abel et al. support the findings of Pearson & Michell concerning high-status ‘top girls’, who are popular and smoke together in small groups low-status peripheral ‘try-hards’, who smoke in an effort to be included in a group