CRRUCS Report 2001
A Better Kind of High: How Religious Commitment Reduces Drug Use Among Poor Urban Teens
APPENDIX C: ANALYTIC MODEL
In the present study, multilevel models, specifically, Bryk and Raudenbush’s (1992) hierarchical linear models (HLM) are used to examine the influence of neighborhood disorder and religious commitment on use of illicit drugs among adolescents. When multiple observations are made over time on a group of individuals for longitudinal research, such data can be viewed as having a multilevel data structure where the “higher” level (level 2) units are individuals and the “lower” level (level 1) units are occasions of measurement (waves in a panel design like the NYS). The multilevel modeling does not require the standard data structure in which the spacing and number of repeated observations are the same for each individual (Bryk and Raudenbush, 1992).
Let Y_{i,t} represent the measure of the dependent variable, illicit drug use, for individual i at time t. In our withinindividual (i.e., level1) model, the individual’s illicit drug use measured at time t can be represented as a linear function of timevarying predictors measured at time t plus random error (r_{i,t}). First, to test whether neighborhood disorder has significant positive effects on adolescent use of illicit drugs before the hypothesized mediating variables are included in the model, we begin with a simple level1 equation that includes only an intercept and age variables (i.e., linear and quadratic terms) as follows:
Y_{i,t} = b_{0,i} + b_{1,i}Age_{i,t} + b_{2,i}Age^{2}_{i,t} + r_{i,t} (1)
where r_{i,t} is the residual for individual i at time t, and assumed to be normally distributed with homogeneous variance across individuals. One caveat is that the level1 model is a randomintercept model where only the intercept (b_{0,i} in Equation 1) is specified as a random coefficient because of the limited number of waves.
On the other hand, the level2 model includes the key predictor of perceived neighborhood disorder and sociodemographic controls of underclass, intact family, number of children, sex (male), and race (white). In addition, given that the NYS data are from an “accelerated” longitudinal design in which cohort effects tend to confound with age effects, and recent studies providing evidence of significant agecohort interactions (Jang 1999; Lauritsen 1998; Raudenbush and Chan 1992), it is necessary to control for such interaction effects. It was necessary, therefore, to construct six cohort dummy variables (cohorts 12 through 17 where the number refers to the age of a respondent at the time of the first interview) with the youngest cohort (cohort 11) as the reference category and added them to the level2 model. Therefore, the following level2 model is estimated for the random intercept (Equation 2a) and two fixed age effects (Equation 2b).
b_{0,i} = g_{0,0} + g_{0,1}Disorder_{i} + g_{0,2}Underclass_{i} + g_{0,3}Intact_{i} + g_{0,4}Children_{i} + g_{0,5}Male_{i} + g_{0,6}White_{i} + g_{0,7}Cohort12_{i} + g_{0,8}Cohort13_{i} + g_{0,9}Cohort14_{i} + g_{0,10}Cohort15_{i} + g_{0,11}Cohort16_{i} + g_{0,12}Cohort17_{i} + u_{0,i} (2a)
b_{k,i} = g_{k,}_{0} + g_{k,}_{1}Cohort12_{i} + _{gk,2}Cohort13_{i} + _{gk,3}Cohort14_{i} + _{gk,4}Cohort15_{i} + _{gk,5}Cohort16_{i} + _{gk,6}Cohort17_{i} (2b)
where k refers to the age variables (k = 1, 2). In Equations 2a and 2b, g_{0,0} and g_{k,}_{0} are the mean intercept and mean slope for the age variables, whereas u_{0,i} and u_{k,i} represent conditional residual or random variation of individuals around the mean intercept and slope, respectively.
Second, to see whether the neighborhood effects, if found significant, are mediated by individual religious commitment as hypothesized, we add individual religious commitment and two interaction terms involving age and religious commitment to the level1 equation (Equation 1) as follows:
Y_{i,t} = b_{0,i} + b_{1,i}Age_{i,t} + b_{2,i}Age^{2}_{i,t} + b_{3,i}Religious commitment_{i,t} + b_{4,i}Age_{i,t}Religious commitment_{i,t} + b_{5,i}Age^{2}_{i,t}Religious commitment_{i,t} + r_{i,t} (3)
As a result of adding the three variables to the level1 equation, the following equations are added to the level2 model (Equations 2a and 2b).
b_{l,i} = g_{l,}_{0} (2c)
b_{m,i} = g_{m,}_{0} (2d)
where l and m refer to individual religious commitment (l = 3) and the interactions between age and religious commitment (m = 4 and 5), respectively. This second model (Equations 3 and 2a through 2d) is intended not only to examine the role which religious commitment plays in mediating the neighborhood effects but also to estimate the “total” effects of religious commitment on illicit drug use before controlling for the social bonding and social learning variables hypothesized to mediate the religious effects. In addition, we test whether the total effects of religious commitment increase with age.
Third, before we test whether the social bonding and social learning variables (i.e., family bonding, school bonding, association with drugusing peers, prodrug attitudes) mediate the effects of religious commitment on illicit drug use, however, religious commitment and its interaction variables are replaced with the social bonding and social learning variables in our level1 model as shown below. This third model is intended to test whether the social bonding and social learning variables mediate the effects of perceived neighborhood disorder on adolescent use of illicit drug use.
Y_{i,t} = b_{0,i} + b_{1,i}Age_{i,t} + b_{2,i}Age^{2}_{i,t} + b_{6,i}Family_{i,t} + b_{7,i}School_{i,t} + b_{8,i}Peers_{i,t} + b_{9,i}Attitudes_{i}_{,t} + r_{i,t } (4)
For this level1 model, our level2 model now includes a slightly changed Equation 2d, which we call now Equation 2d1, as well as Equations 2a and 2b as shown below.
b_{m,i} = g_{m,}_{0} (2d1)
where m now refers to the social bonding and social learning variables (m = 6, 7, 8, 9).
Fourth, religious commitment and its interactions are placed with age back into the level1 equation to estimate the effects of religious commitment on illicit drug use independent of the mediating variables (i.e., the social bonding and social learning variables), and is called the “direct” effects of religious commitment, as follows:
Y_{i,t} = b_{0,i} + b_{1,i}Age_{i,t} + b_{2,i}Age^{2}_{i,t} + b_{3,i}Religious commitment_{i,t} + b_{4,i}Age_{i,t}Religious commitment_{i,t} + b_{5,i}Age^{2}_{i,t}Religious commitment_{i,t} + b_{6,i}Family_{i,t} + b_{7,i}School_{i,t} + b_{8,i}Peers_{i,t} + b_{9,i}Attitudes_{i}_{,t} + r_{i,t} (5)
In the corresponding level2 model Equations 2a through 2c remain the same as above, while Equation 2d1 now represents the interactions between individual religious commitment and age as well as the social bonding and social learning variables, being called Equation 2d2, as shown below:
b_{m,i} = g_{m,}_{0} (2d2)
where m refers to level1 predictors other than the age and religious commitment variables (m = 4, ..., 9). This fourth model enables us not only to test whether the direct effects of religious commitment on illicit drug use increase with age, but also to see whether the effects of perceived neighborhood disorder on adolescent use of illicit drugs remain significant after controlling for individual religious commitment and the social bonding and social learning variables simultaneously.
Finally, to test whether individual religious commitment negatively interacts with or buffers the effects of perceived neighborhood disorder on adolescent use of illicit drugs, the neighborhood disorder variable is included in the level2 model, specifically, Equation 2c, which becomes Equation 2c1, as shown below.
b_{l,i} = g_{l,}_{0}+ g _{l,}_{1}Disorder_{i} (2c1)
where g_{ l,}_{1} estimates the interaction between neighborhood disorder and religious commitment. In sum, combining the level1 model (Equation 5) and the level2 model (Equations 2a, 2b, 2c1, and 2d2) yields a full model which specifies that illicit drug use at time t is a linear function of: the overall intercept (g_{0,0}); the main effects of perceived neighborhood disorder (g0,1), individual background characteristics (g_{0,2}, ..., g_{0,12}), age (g_{1,0} and g_{2,0}), individual religious commitment (g_{3,0}), and social bonding and social learning variables (g_{6,0}, ..., g_{9,0} for the directeffect model); two interaction terms involving the age and individual religious commitment (g_{4,0} and g_{5,0}); and the interactions involving not only the age and cohort variables (g_{1,1}, ..., g_{1,6} and g_{2,1}, ..., g_{2,6}) but also individual religious commitment and perceived neighborhood disorder (g_{3,1}) plus random error (u_{0,i} + r_{i,t}).
