3.2. Negative Binomial Regression under the Homogeneity Assumption
Given the long right tail of the distribution of alcohol consumption (90.48% of youth had 0, 1, or 2 drinks in the past 30 days) and the count nature of the dependent variable (the number of drinks consumed in the past 30 days), we used a negative binomial regression model to estimate the relationship between peer drinking and youth’s consumption of alcoholic drinks controlling for youth demographic, socioeconomic, parental, and neighborhood characteristics. Results of the multivariate negative binomial regression are shown in
Table 2. Under the homogeneity assumption, the size of the relationship between peer and youth alcohol consumption was equal among all youth with a coefficient size of 2.40 regardless of their probability of contact with drinking peers. This indicates that youth’s affiliation with peer drinkers was associated with a difference of 2.40 in the log of the expected count of drinks. Alternatively, youth associated with peer drinkers, compared to having no friends who drink, was expected to have a rate 11 times greater (=
e2.40) for own alcohol consumption behavior. These findings are consistent with the claim that youth drinking patterns do not occur in isolation, but are positively associated with peer-drinking patterns [
33]. However, the size of the peer-drinking coefficient under the homogeneity assumption may potentially be confounded by selection bias and should be interpreted with caution. More specifically, it may be important to identify possible heterogeneous treatment effects, and examine whether some youth respond differently to the effects of peer drinking compared to others by adopting propensity score methods.
Control variables highlighted the important role of demographic and environmental contexts. Consistent with previous research [
34], older age was positively associated with higher frequency of drinks. There was some evidence that being male and parent’s level of alcohol consumption was associated with increased level of youth drinking behavior. Neighborhood risk was positively correlated with greater levels of alcohol consumption. Social processes such as increased exposure to opportunities for unstructured and unsupervised activities in at-risk neighborhoods may have increased the risk of youth’s engagement in problem behaviors [
35].
Table 2.
Relationship between Peer-Drinking and Youth-Drinking under Homogeneity Assumption (N = 914).
Table 2.
Relationship between Peer-Drinking and Youth-Drinking under Homogeneity Assumption (N = 914).
Variables | Coefficient | Standard Error | Significance |
---|
Peers |
Peer alcohol consumption | 2.40 | 0.35 | *** |
Youth |
Male | 0.40 | 0.23 | † |
Age | 0.57 | 0.09 | *** |
Family Context |
Monthly income (unit: 100 Chilean pesos) | −0.47 | 0.29 | |
Monthly income (squared) | 0.05 | 0.03 | |
Less than middle school a | 0.04 | 0.73 | |
Middle school to less than high school a | −0.39 | 0.60 | |
High school a | −0.39 | 0.59 | |
Married | −0.04 | 0.25 | |
Number of drinks consumed in the past 30 days | 0.01 | 0.00 | † |
Social Context |
Neighborhood danger and drugs | 1.88 | 0.66 | ** |
Neighborhood danger and drugs (squared) | −0.27 | 0.10 | ** |
Advertisement on newspapers/magazines (low exposure) b | −0.34 | 0.38 | |
Advertisement on newspapers/magazines (moderate exposure) b | −0.45 | 0.26 | |
Advertisement on television (low exposure) c | −0.47 | 0.40 | |
Advertisement on television (moderate exposure) c | 0.06 | 0.26 | |
Constant | −12.10 | 1.75 | *** |
3.3. Propensity Score Analysis under the Heterogeneity Assumption
Treatment effects estimated under the homogeneity assumption can be viewed as the weighted average of heterogeneous effects across individuals. Considering the complex nature of the relationship between peer drinking and youth drinking, in which individuals have different levels of susceptibility and responsiveness to peers, relying on a single weighted treatment effect can be misleading and unrealistic [
16]. Therefore, we derived a series of parameter estimates assuming heterogeneity in the probability of associating with deviant peers, using propensity score stratification.
First, we computed the propensity scores by estimating an individual’s predicted probability of affiliating with drinking peers based on observed information (
Table 3). Age had a positive relationship with youth’s affiliation with peer drinkers. Dangerous neighborhoods and exposure to alcohol advertisements were also associated with a greater chance of having friends who drink.
Table 3.
Propensity Score Estimation with Probit Regression Model (N = 914).
Table 3.
Propensity Score Estimation with Probit Regression Model (N = 914).
Variables | Coefficient | Standard Error | Significance |
---|
Youth |
Male | −0.11 | 0.10 | |
Age | 0.46 | 0.04 | *** |
Family Context |
Monthly income (unit: 100 Chilean pesos) | −0.05 | 0.12 | |
Monthly income (squared) | 0.01 | 0.01 | |
Less than middle school a | 0.10 | 0.33 | |
Middle school to less than high school a | −0.14 | 0.28 | |
High school a | 0.17 | 0.27 | |
Married | 0.01 | 0.10 | |
Number of drinks consumed in the past 30 days | 0.00 | 0.00 | |
Social Context |
Neighborhood danger and drugs | 0.58 | 0.24 | * |
Neighborhood danger and drugs (squared) | −0.07 | 0.04 | † |
Advertisement on newspapers/magazines (low exposure) b | −0.27 | 0.14 | † |
Advertisement on newspapers/magazines (moderate exposure) b | −0.01 | 0.12 | |
Advertisement on television (low exposure) c | −0.20 | 0.14 | |
Advertisement on television (moderate exposure) c | −0.06 | 0.12 | |
Constant | −6.79 | 0.75 | *** |
A histogram (
Figure 1) shows the relative distribution of estimated propensity scores for youths who associated with peers who drink and youths who associated with peers who do not drink. Among youth who actually had friends who drank, their predicted probability of having drinking friends was high, and
vice versa. These results were consistent with the way in which the propensity scores were initially constructed [
17].
Figure 1.
Histogram of Estimated Propensity Score by Association with Peer Drinkers (N = 914).
Figure 1.
Histogram of Estimated Propensity Score by Association with Peer Drinkers (N = 914).
We then stratified our sample into five groups based on these propensity scores and confirmed that the balancing conditions were met for each stratum. The number of observations in each stratum ranged from 108 to 330. Although the overall distributions of propensity scores were different between youth who associated and did not associate with peer drinkers (
Figure 1), within each stratum, mean values of the covariates were generally not statistically different between the two groups (
Table 4).
Table 4.
Test of Balance across Propensity Score Strata (N = 914).
Table 4.
Test of Balance across Propensity Score Strata (N = 914).
Peer Alcohol Consumption | Stratum 1 | Stratum 2 | Stratum 3 | Stratum 4 | Stratum 5 |
---|
Mean | p-Value a | Mean | p-Value a | Mean | p-Value a | Mean | p-Value a | Mean | p-Value a |
---|
Yes (n = 38) | No (n = 70) | Yes (n = 84) | No (n = 96) | Yes (n = 80) | No (n = 56) | Yes (n = 129) | No (n = 31) | Yes (n = 300) | No (n = 30) |
---|
Youth |
Male | 0.68 | 0.56 | 0.20 | 0.54 | 0.52 | 0.84 | 0.54 | 0.66 | 0.15 | 0.42 | 0.48 | 0.51 | 0.48 | 0.43 | 0.60 |
Age | 12.35 | 12.40 | 0.59 | 13.27 | 13.22 | 0.65 | 13.93 | 13.85 | 0.34 | 14.35 | 14.43 | 0.45 | 15.95 | 15.21 | 0.00 |
Family Context |
Monthly income (unit: 100 Chilean pesos) | 2.52 | 2.78 | 0.26 | 3.02 | 3.22 | 0.41 | 3.10 | 2.94 | 0.50 | 3.22 | 2.46 | 0.02 | 3.34 | 3.28 | 0.85 |
Less than middle school | 0.05 | 0.03 | 0.53 | 0.13 | 0.03 | 0.01 | 0.04 | 0.11 | 0.11 | 0.06 | 0.06 | 0.96 | 0.04 | 0.13 | 0.03 |
Middle school to less than high school | 0.53 | 0.63 | 0.30 | 0.37 | 0.40 | 0.71 | 0.40 | 0.34 | 0.47 | 0.34 | 0.48 | 0.14 | 0.31 | 0.23 | 0.38 |
High school | 0.39 | 0.31 | 0.40 | 0.48 | 0.53 | 0.46 | 0.53 | 0.50 | 0.77 | 0.56 | 0.45 | 0.29 | 0.61 | 0.60 | 0.94 |
Some college or more | 0.03 | 0.03 | 0.95 | 0.02 | 0.04 | 0.51 | 0.04 | 0.05 | 0.65 | 0.04 | 0.00 | 0.27 | 0.04 | 0.03 | 0.86 |
Married | 0.76 | 0.81 | 0.53 | 0.73 | 0.72 | 0.91 | 0.63 | 0.61 | 0.83 | 0.68 | 0.58 | 0.28 | 0.60 | 0.70 | 0.29 |
Number of drinks consumed in the past 30 days | 19.68 | 10.60 | 0.06 | 22.08 | 17.00 | 0.52 | 10.31 | 19.75 | 0.11 | 11.60 | 7.65 | 0.43 | 18.21 | 19.47 | 0.90 |
Social Context |
Neighborhood danger and drugs | 2.48 | 2.40 | 0.71 | 2.75 | 2.78 | 0.82 | 2.80 | 2.93 | 0.51 | 3.03 | 2.95 | 0.68 | 3.41 | 3.13 | 0.16 |
Advertisement on newspapers/magazines (low exposure) | 0.37 | 0.57 | 0.04 | 0.45 | 0.35 | 0.18 | 0.25 | 0.18 | 0.32 | 0.22 | 0.19 | 0.77 | 0.14 | 0.30 | 0.02 |
Advertisement on newspapers/magazines (moderate exposure) | 0.37 | 0.24 | 0.17 | 0.31 | 0.34 | 0.63 | 0.36 | 0.45 | 0.33 | 0.37 | 0.42 | 0.63 | 0.43 | 0.33 | 0.32 |
Advertisement on newspapers/magazines (high exposure) | 0.26 | 0.19 | 0.35 | 0.24 | 0.30 | 0.34 | 0.39 | 0.38 | 0.88 | 0.41 | 0.39 | 0.81 | 0.43 | 0.37 | 0.48 |
Advertisement on television (low exposure) | 0.34 | 0.43 | 0.38 | 0.26 | 0.32 | 0.37 | 0.16 | 0.21 | 0.44 | 0.24 | 0.10 | 0.08 | 0.12 | 0.13 | 0.83 |
Advertisement on television (moderate exposure) | 0.24 | 0.27 | 0.70 | 0.39 | 0.30 | 0.20 | 0.36 | 0.36 | 0.95 | 0.26 | 0.29 | 0.76 | 0.31 | 0.37 | 0.55 |
Advertisement on television (high exposure) | 0.42 | 0.30 | 0.21 | 0.35 | 0.38 | 0.68 | 0.48 | 0.43 | 0.59 | 0.50 | 0.61 | 0.24 | 0.57 | 0.50 | 0.48 |
Observations (n) | 38 | 70 | -- | 84 | 96 | -- | 80 | 56 | -- | 129 | 31 | -- | 300 | 30 | -- |
After confirming that the two groups were reasonably homogeneous within each stratum we estimated the differential associations between peer drinking and youth drinking. For each stratum, we estimated the relationship between peer drinking and youth drinking using a negative binomial regression model. We found differences in the associations between peer and youth alcohol consumption patterns after accounting for some level of variability.
Table 5 summarizes Level-1 and Level-2 results. Comparison of Level-1 slopes indicated that youths who were most likely to socialize with drinking friends (stratum 5) showed a larger response to peer drinkers (β = 3.36,
p < 0.001) relative to youths who were least likely (stratum 1; β = 1.46,
p = 0.198). These values provide a more accurate range of parameters of the relationship between peer and youth drinking, in contrast with the single relationship parameter of 2.40 under the homogeneity assumption. The Level-2 slope of 0.51, trending toward significance (
p = 0.052), suggested that the size of the association between peer and youth drinking may increase linearly across strata (
Figure 2). When assuming heterogeneous relationship sizes, the role of peers on youth drinking increased, with greater levels of risk of associating with friends who drink. Evidence of such heterogeneous relationship sizes substantiated the idea that youth alcohol consumption proliferates when youth are more likely to socialize with peer drinkers.
Table 5.
Relationship between Peer-Drinking and Youth-Drinking under Heterogeneity Assumption.
Table 5.
Relationship between Peer-Drinking and Youth-Drinking under Heterogeneity Assumption.
Stratum | Coefficient | Standard Error | p-Value | Significance | Observations |
---|
Level-1 |
1 | 1.46 | 1.13 | 0.198 | | 108 |
2 | 1.66 | 0.66 | 0.012 | * | 180 |
3 | 2.85 | 0.92 | 0.002 | *** | 136 |
4 | 2.75 | 0.90 | 0.002 | *** | 160 |
5 | 3.36 | 0.70 | 0.000 | *** | 330 |
Level-2 |
Slope | 0.51 | 0.26 | 0.052 | † | 914 |
Constant | 0.83 | 0.91 | 0.361 | | |
Figure 2.
Graphical Representation of Heterogeneous Size of Peer-Drinking and Youth-Drinking Relationship (N = 914).
Figure 2.
Graphical Representation of Heterogeneous Size of Peer-Drinking and Youth-Drinking Relationship (N = 914).
Finally, we also investigated a rich set of behavioral measures to check the plausibility of invoking the strongly ignorable treatment assumption (
Table 6). Behavioral measures can reflect latent dispositions of individuals who are more susceptible to negative peer influence and are likely to actively seek out associations with similar friends. Rule-breaking behavior, aggression, and risk-taking behavior have been found to characterize antisocial youth [
1].
Table 6 illustrates that individuals with the lowest probability of engaging with drinking peers (stratum 1) did in fact have significantly lower problem behavior scores (
p < 0.001) relative to youth with the highest estimated propensity scores (stratum 5). There was no variability, however, in self-esteem—a finding different from some studies that have highlighted its protective nature [
11]. The self-esteem measure employed in our study provides a less-representative understanding of the dispositions of adolescents who increase their exposure to other peers.
Table 6.
Evidence of Selection-Based Stratification (N = 914).
Table 6.
Evidence of Selection-Based Stratification (N = 914).
Variables | Stratum 1 | Stratum 2 | Stratum 3 | Stratum 4 | Stratum 5 | (1)–(5) |
---|
Mean | Mean | Mean | Mean | Mean | p-Value a |
---|
Rule-Breaking | 4.26 | 4.46 | 4.36 | 5.01 | 5.90 | <0.001 |
Aggression | 6.44 | 7.65 | 7.69 | 9.26 | 8.90 | <0.001 |
Risk-Taking | 15.61 | 16.16 | 16.59 | 17.03 | 17.71 | <0.001 |
Self-esteem and Satisfaction | 28.19 | 28.36 | 28.45 | 26.86 | 28.02 | 0.746 |