We also control for the effects of how ego’s use of one substance was influenced by alters’ use of two other substances. In the network equation, we include endogenous network effects and homophily selection effects for each substance use behavior as well as additional covariates such as race , gender, grade, and parental education as the results from score-type tests suggest to do so. 501 students in Sunshine High and 166 students in Jefferson High were 12th-graders at t1 and t2and graduated at t3 . These 667 students were constructed as structural zeroes in the networks during the last wave. Due to a survey implementation error in Add Health, some adolescents could only nominate one female and one male friend at t2and t3 . We account for this with a limited nomination variable in the network equation. A Method of Moments estimation is used to estimate the behavior and network parameters in each model so that the target statistics in behaviors and networks can be most accurately calculated. We assess satisfactory model convergence with criteria of t statistics for deviations from targets and the overall maximum convergence ratio . The results of a post hoc time heterogeneity test for the models found no evidence that the co-evolution of substance use behaviors and friendship networks was significantly different across the two time periods, providing no indication of estimation or specification problems. We also perform goodness-of-fit testing for key network statistics in both schools, and display the results in the S1 File. Besides the main SAB model for each school sample,indoor grow shelves we estimate ancillary models that test whether the interdependent effects are symmetric in increasing and decreasing substance use. This is accomplished by differentiating the “creation” function and the “endowment” function in RSiena.
This technique has been applied to explore the asymmetric peer influence effect on adolescent smoking initiation and cessation.methodological challenge we face is that whereas the questions about smoking and drinking behavior were asked at all three waves, questions about marijuana use were only asked at t2 and t3 . One approach would discard all the information at t1 , but this strategy will reduce the efficiency of analysis, increase standard errors, and decrease statistical power. Instead, we reconstruct adolescent marijuana use at t1 based on four questions. Fig 2 provides a flow chart of the logic, and shows that we in fact have a considerable amount of information that can help us reconstruct probable values for the vast majority of the adolescents. First, if an adolescent has never tried marijuana at t2 , s/he would not have used it at t1, so we can safely code them as a zero at t1 . Next, if an adolescent has tried marijuana at t2 but the age at which he or she tried was above his or her age at t1 , s/he would not have reported using it at t1, so we can safely code them as a zero at t1 . Finally, if an adolescent has tried marijuana at t2 and the age of usage was below his or her age at t1 , we utilize information from two questions “During your life, how many times have you used marijuana?” and “During the past 30 days, how many times did you use marijuana?” at t2. In a few instances the difference between these two variables is zero, which appears to be a reporting error as they reported all their usage in the last 30 days and yet that they started at a young age. We code them as a zero at t1under the presumption that this earlier usage was very limited, and perhaps experimental. However, if the difference is non-zero, since the In-School Survey was conducted at least six months before the wave-1 In-Home Survey, we divide this difference by 5 to average over five months [i.e., /5]. Those with values less than 1 were categorized as non-users at t1 , those with values between 1 and 10 were categorized as light users and those with values above 10 were categorized as heavy users .
Light users comprised about 16% of adolescents in Sunshine High and 17% of adolescents in Jefferson High. Likewise, heavy users comprised about 5% of the adolescents in Sunshine High and 8% of the adolescents in Jefferson High. Overall, this reconstruction strategy enabled us to estimate a three-wave SAB model for each of the two samples without discarding any data. The last step of the reconstruction procedure for the heavy marijuana users is not perfectly accurate and might mistakenly categorize a few light users as heavy users, since they could have used marijuana outside of the last five months. The proportion of cases that might have been misclassified is less than 10%. Furthermore, sensitivity tests in which the level of marijuana use for these uncertain cases was randomly assigned to “light” or “heavy” use exhibited similar results over a large number of samples .Regarding missing data, for students in Sunshine High the response rates were 76% at t1 , 82% at t2 , and 75% at t3 . In Jefferson High the response rates were 79% , 81% , and 74% across the three waves. We imputed missing network data using the technique described in Wang et al. given the evidence that failing to do so can result in in biased estimates. Other actor attributes at t1 were imputed using the multiple imputation system of chained equations implemented in Stata. For the later waves, missing data is handled within the Stochastic Actor-Based models in RSiena software as suggested by Huisman and Steglich and Ripley et al.. The 501 and 166 students who graduated at t3 and were no longer in the network are treated as structural zeros in the Stochastic Actor-Based models at the last wave.Network statistics are measured at three waves. As shown in Table 1, in both school samples the number of out-going ties decreased over time due to limited nomination restrictions, graduation, moving, dropping out, and sample attrition/non-response/missing network data. The proportion of reciprocal ties over all out-going ties was 4% to 10% higher in Jefferson High than in Sunshine High at each wave. The transitivity index is the proportion of 2-paths that were transitive , which is similar in the two schools. The Jaccard index measures the network stability between consecutive waves.
There were substantial changes in friendship ties across waves, with the Jaccard index staying at .16 in Sunshine High and ranging from .21 to .22 in Jefferson High. Due to a survey implementation error in Add Health, some adolescents could only nominate one female and one male friend at t2 and t3 . Most limited nomination restrictions happened at wave 2,indoor garden table and involved less than 5% in the two schools. With respect to smoking behavior, there were between 69% and 78% non-smokers in Sunshine High over the three waves, and between 7% and 10% heavy-smokers . In Jefferson High, there were between 42% and 53% non-smokers and between 26% and 32% heavy smokers. Sunshine High also had more non-drinkers than Jefferson High , and more non-users of marijuana . The descriptive statistics of covariates are reported in the lower part of Table 1.As shown in Table 2, our estimated SAB model includes a smoking behavior equation, a drinking behavior equation, a marijuana use equation, and a network equation. Based on the smoking behavior equation, those who were one point higher on the marijuana scale are 25% [exp = 1.25] and 15% [exp = 1.15] more likely to increase their own smoking behavior at the next time point in Sunshine High and Jefferson High, respectively. Those who drank alcohol did not smoke more over time. There is no evidence of cross substance influence, as having more friends who drank or used marijuana did not impact a respondent’s own smoking over time. In ancillary models, we measured average level of drinking or marijuana use for friends and these effects were also statistically insignificant. These results are shown in S1 Table. Regarding the other measures in the smoking behavior equation, we detect a negative smoking behavior linear shape parameter in both school samples along with a positive smoking behavior quadratic shape parameter. This suggests that adolescents were inclined to adopt lower levels of smoking behavior over time, but they also tended to stay as or become non-smokers or escalate to heavy-drinkers due to a pull towards extreme values of this scale. Turning to the peer influence effect, we find that adolescents’ own smoking levels were affected by that of their best friends in both schools. There is no evidence that parental support or monitoring reduced levels of smoking over time in either sample. African Americans and Latinos smoked less than Whites in Sunshine High. Depressive symptoms were found to increase smoking behavior in Jefferson High. In the drinking behavior equation, we find that an adolescent who was one point higher on the marijuana use measure was 22% and 16% more likely to increase their own alcohol use at the next time point in Sunshine High and Jefferson High, respectively. However, respondents’ drinking was not related to their greater cigarette use. There is no evidence that friends’ smoking behavior or marijuana use affected respondents’ drinking behavior. This was the case whether measured as the number of friends who smoked or used marijuana, or as the average level of such behaviors. A negative linear shape effect and a positive quadratic shape effect are also confirmed regarding drinking behavior.
An adolescents’ drinking level was positively predicted by that of one’s best friends. Whereas there is no evidence in these two networks that high levels of parental support impacted drinking levels of adolescents, we do see that higher levels of parental monitoring were associated with lower levels of drinking behavior over time in Jefferson High. In Sunshine High, African Americans were found to drink less than Whites, and depressive symptoms were found to increase drinking levels. The marijuana use equation suggests no evidence that increasing usage of the other two substances leads to increasing marijuana use. We once again see no evidence of cross-substance influence, as the number of friends who smoked or drank or the average smoking or drinking level of friends is not related to ego’s marijuana use levels over time. A negative linear shape effect and a positive quadratic shape effect are also detected on marijuana use behavior. Across both samples there is very strong evidence of a peer influence effect from anadolescent’s best friends’ marijuana use to an individual’s own marijuana use. Higher levels of parental support or monitoring were not found to reduce levels of marijuana use over time. For all three substance use behaviors, there was no evidence that adolescents who are more “popular” were any more likely to increase their substance use over time. In the network equation the expected patterns are detected regarding the endogenous network structural effects across samples. At the dyadic level, adolescents did not randomly nominate peers as friends, since friendship ties inherently require the investment of time and energy, as indicated by the negative out-degree parameters; instead, adolescents tended to nominate peers who had already nominated them as friends previously, as indicated by the positive reciprocity parameters. At the triadic level, adolescents tended to nominate a friend’s friend as a friend but avoided ending in 3-person cyclic relationships. The negative out-degree/in-degree popularity parameters and the out-out degree assortativity parameters suggest that adolescents were less likely to befriend peers who have already made/received many friendship nominations or have similar out-degrees. Instead, they were more likely to befriend peers with similar in-degrees, as indicated by the positive in-in degree assortativity parameters. We also find that adolescents were more likely to nominate peers as friends if they were of the same gender, race , and grade. Grade is a particularly strong effect, as adolescents were 86% and 77% more likely to nominate a friend if they were in the same grade than if they were in a different grade in Sunshine High and Jefferson High, respectively. Lastly, the limited nomination parameter shows that for adolescents who encountered the administrative error of being limited to nominate only one male or one female friend, their odds of nominating friends is re-adjusted by the SAB models to be 132% larger in Sunshine High and 297% larger in Jefferson High than those with no such problem.