2. Stochastic Actor-Based (SAB) Model Specification

Supplementary Materials

1 1. Covariates

We include as covariates the measures of gender, grade, highest level of education attained by either parent, depressive symptoms based on the Center for Epidemiologic Studies

Depression Scale (CES-D) (Radloff 1977), parental support based on six questions, parental monitoring based on nine questions, and home drinking environment based on whether the parent drank or whether alcohol was available at home. Among covariates, parental support and parental monitoring are computed as standardized factor scores (means = 0, standard deviations

= 1) through confirmatory factor analysis (CFA). These measures rely on items from parental survey with a Root Mean Squared Error of Approximation (RMSEA) of about .05 and a

Comparative Fit Index (CFI) greater than .95 – suggesting a good fit. Items indicating parental support include whether the student had talked about a personal problem with their parents (0 = no, 1 = yes), whether the parents and the student communicated well, whether the parents were warm and loving, whether the student reported a "good relationship" with parents (same response categories for three items above: 1 = strongly disagree, 2 = disagree, 3= neither agree nor disagree, 4 = agree, 5= strongly agree), the student's closeness to their parents, and how much the student felt his or her parents cared about him or her (same response categories for two items above: 1 = not at all, 2 = very little, 3 = somewhat, 4 = quite a bit, 5 = very much). Items indicating parental monitoring include whether parents let the student make decisions about a weekend curfew, the people the student hung around with, how much television the student watched, which television program the student watched, and what the week night bedtime was

(same response categories for five items above: 0 = yes, 1 = no), and the presence of parents when the student left for/returned from school (0 = never, 1 = almost never, 2 = some of the time, 3 = most of the time, 4 = always, 5 = they took/brought the student home to/from school),

2 eating dinner (0~7 days per week), and going to bed (0 = never, 1 = almost never, 2 = some of the time, 3 = most of the time, 4 = always). A small number of participants were only able to nominate one male and one female best friend during the second wave (less than 5% of subjects).

A 3-category control variable accounts for the occurrence of limited nominations: -1 = going from full to limited nominations, 0 = no change, and +1 = going from limited to full nominations.

Table S1 Covariate statistics

School Sunshine High Jefferson High Female (%) 47.52 48.46 Grade level (%) 9th grade 0.00 28.79 10th grade 37.23 28.38 11th grade 33.43 21.82 12th grade 29.34 21.00 Parent education level (%) Less than high school 21.67 5.02 High school 30.62 38.22 Some college or trade school 28.79 37.09 College/university graduate 18.92 19.67 Depressive symptoms, mean (sd) 0.14(0.53) 0.01(0.53) Home drinking environment, mean (sd) 0.84(0.73) 1.19(0.73) Parental support, mean (sd) -0.05(0.30) -0.05(0.29) Parental monitoring, mean (sd) -0.01(0.12) -0.04(0.10)

3 2. Stochastic actor-based (SAB) model specification

Table S2 Effects for modeling network evolution

Effect Network statistic Network change Description The expected number of change opportunities for Rate parameter - each respondent during each period General tendency to Out-degree (density) choose a friend Tendency to have Reciprocity reciprocal (mutual) friendships Tendency for a friend's Transitive triplets friend to a friend Tendency for a friendship Three cycles nominator's nominator as a friend Tendency to choose a In-degree popularity popular adolescent as a friend In-in degree Tendency to choose an assortativity (square adolescent similar in in- root) degree as a friend Main effect of selecting Alter (friend) others with high drinking drinking behavior level as a friend Main effect of an Ego drinking adolescent with high behavior drinking level to have more friends Drinking similarity, Tendency to befriend grade similarity, others similar in drinking parental education level (selection effect) or similarity other covariate levels low score (negative) high score (positive) arbitrary score

4 Table S3 Effects for modeling behavioral evolution

Effect Behavior statistic Behavior change Description The expected number of Drinking rate - change opportunities for each parameter respondent in each period The basic drive toward high Linear shape values of drinking The self-reinforcing function Quadratic shape of drinking behavior Tendency for popular In-degree respondent to have high levels of drinking Main effect of drinking Peer influence similarity between adolescent and friends Covariate: gender, depressive Main effect of covariate on symptoms, drinking parental influence, low score (negative) high score (positive) arbitrary score

5 3. Goodness-of-fit (GOF) for SAB models

Goodness-of-fit (GOF) helps examine to what extent an estimated SAB model can replicate the observed data (Snijders 2014). Lospinoso (2012) introduces the Monte Carlo Mahalanobis

Distance test for SAB model specification, which is implemented in the RSiena package (Ripley et al. 2016). The empirical data are compared with m (1000 by default) simulations from the estimated SAB model on the auxiliary statistics of networks (e.g., distribution of in-degree, out- degree, geodesic distance, and triad census) and behavior (e.g., behavior distribution and behavior transition). A p-value is calculated for each auxiliary statistic to test whether the estimated model fit the empirical data well. The GOF results can be represented with violin plots (see more details in Ripley et al. 2016; Lospinoso and Snijders 2011).

The GOF of our estimated model is applied to each school individually. The violin plots in Fig. S1 and Fig. S2 show the results of simulated networks and behavior with observed values superimposed during the final time point (wave 3). The p-values of all six auxiliary statistics are greater than 0.05, suggesting the null hypothesis that the estimated SAB model can reproduce several key network and behavior statistics at the final time point is not rejected.

References

Lospinoso, J. A. (2012). Statistical Models for Social Network Dynamics. PhD thesis, University of Oxford, UK. Lospinoso, J. A., & Snijders, T. A. B. (2011). Goodness of Fit for Social Network Dynamics. Presentation at the Sunbelt XXXI, St. Pete's Beach, FL, 2011. Retrieved from http://www.stats.ox.ac.uk/~lospinos/pubs/GOFPresentation.pdf. Radloff, L. S. (1977). The CES-D scale. Applied Psychological Measurement, 1, 385–401. Ripley, R. M., Snijders, T. A. B., Boda, Z., Vörös, A., & Preciado, P., (2016). Manual for SIENA version 4.0 (version May 28, 2016). Oxford: University of Oxford, Department of Statistics, Nuffield College. Retrieved from http://www.stats.ox.ac.uk/~snijders/siena/RSiena_Manual.pdf. Snijders, T. A. B. (2014). Siena Advanced Users' Meeting 2014. Presentation at the Sunbelt XXXIV, St. Petersberg, Florida, 2014. Retrieved from https://www.stats.ox.ac.uk/~snijders/siena/Siena AdvancedUsersSunbelt2014.pdf.

8 Fig. S1 Goodness-of-fit testing of SAB model for Sunshine High Note: ND represents non-drinkers and D represent drinkers (no matter what their drinking levels were).

Fig. S2 Goodness-of-fit testing of SAB model for Jefferson High Note: ND represents non-drinkers and D represent drinkers (no matter what their drinking levels were).