^{1} Non-Hispanic whites and non-Hispanic blacks are referred to as "whites" and "blacks" in this report. "Other" indicates those other than whites, blacks, and Hispanics (i.e., Asians, American Indians or Alaska Natives, and Native Hawaiians or other Pacific Islanders).

^{2} Comparisons between the 1997 and the 1999 NHSDAs were limited to factors included in both years of the survey that were measured using identical questions. The 1999 NHSDA paper-and-pencil interviewing (PAPI) data, adjusted for field interview experience, were used for comparisons with data from the 1997 NHSDA. For more information, see ** Chapter 5** of this report.

^{3} Because the analyses are based on separate logistic regression models for each domain, summing the explained variation for each domain would add to more than 100 percent.

^{4} There were 38 questions directly relevant to risk and protective factors for youth substance use in the 1997 NHSDA compared with 60 such questions in the 1999 NHSDA.

^{5} Some aspects of hierarchical modeling are addressed in more detail in ** Chapter 4** of this report.

^{6} Because of the expansion of the number of questions between 1997 and 1999, as well as improvements made to the wording and response options to some questions, the discussion of change between 1997 and 1999 was limited to factors included in both years of the survey using comparable questions.

^{7} Single-item factors were measured using a single question in the NHSDA questionnaire. Each of these single items contained two or more response options. Multiple-item scales are factors that were measured using two or more questions in the NHSDA questionnaire, with each question having the same scale of response items.

^{8} Cronbach's coefficient alpha is a measure of internal consistency of multiple-item scales. The alphas for these scales ranged from 0.59 to 0.89, with most scales having alphas over 0.70. These alphas indicate that these scales have reasonable internal consistency.

^{9} Care should be taken in interpreting statistically significant differences between these demographic groups. When sample sizes are large, very small differences between groups can reach statistical significance. For this reason, group differences are only discussed if the scale scores or distributions show sizable differences between groups.

^{10} For more information about distributions of risk and protective factors in the family domain by gender and age, see ** Appendix C**.

^{11} These response options were reverse coded for the question about wearing a seatbelt when riding in the front passenger seat of a car.

^{12} For more information about distributions of risk and protective factors in the peer/individual domain by gender and age, see ** Appendix C**.

^{13} Approximately 25 percent of youths aged 12 to 17 did not answer the questions for the school domain risk and protective factors and thus are not included in these analyses. Analyses in which revised sample weights were computed for the subsample who did complete these questions indicated that these missing cases did not have a significant effect on these measures. See ** Appendix B** for a fuller discussion of these missing values for the school domain questions.

^{14} Approximately 2.3 percent of youths attended schools that did not give letter grades.

^{15} For more information about distributions of risk and protective factors in the school domain by gender and age, see ** Appendix C**.

^{16} Approximately 25 percent of youths aged 12 to 17 did not answer the questions covering the school domain risk and protective factors and thus are not included in these analyses. Analyses in which revised sample weights were computed for the subsample who did complete these questions indicated that these missing cases did not have a significant effect on these measures. See ** Appendix B** for a fuller discussion of these missing values for the school domain questions.

^{17} Other work (Wright & Zhang, 1999) has indicated that the family and neighborhood levels can account for 20 to 25 percent of the overall variation in drug use (the remainder being attributed to the person level). In this situation, treating the analysis as a person-level analysis could result in somewhat different estimates of the association between risk and protective factors and past year marijuana use.

^{18} For risk and protective factors focused specifically on substance use, the questions specific to marijuana use (rather than the use of other substances) were used in these models.

^{19} If* p _{i}* indicates the probability that

^{20} The first measure is Cox and Snell's R^{2}, a measure of the fit of the model defined as where *L*(*O*) is the likelihood of the intercept-only model, is the likelihood of the full model, and *n* is the sample size. For further information, refer to SUDAAN Manual 7.5 (Shah et al., 1998) and Cox and Snell (1989). The second measure is Nagelkerke's R_{N}^{2}. Recognizing that Cox and Snell's R^{2} reaches a maximum for discrete models that depends on the value of the estimated percentage, Nagelkerke (1991) proposed dividing the Cox and Snell measure by the maximum. In this sense, R_{N}^{2} measures the absolute percentage of variation explained by the model.

^{21} For risk and protective factors focused specifically on substance use, the questions specific to cigarette or tobacco use (rather than the use of other substances) were used in these models.

^{22} For factors focused specifically on substance use, the questions specific to alcohol use were used in these models.

^{23} Note that Cox and Snell's R^{2} for the final model predicting past year alcohol use was slightly higher (0.34) than Cox and Snell's R^{2} for the final model predicting past year marijuana use (0.33). The Nagelkerke adjustment led to a greater increase in the R^{2} for the marijuana model than the alcohol model because the prevalence rates among youths were considerably lower for past year marijuana use compared with past year alcohol use.

^{24} Analyses presented in the earlier chapters have utilized SUDAAN software (Shah et al., 1998), which can address the special circumstances of complex survey data, including the use of stratification, sampling weights, and the clustering of observations. Given a two-level structure (e.g., persons nested within neighborhoods), SUDAAN can provide unbiased estimates for person-level characteristics, including estimates of precision. However, it cannot estimate the separate variance components, nor can it be used to estimate separate models for each hierarchical level.

^{25} Snijders and Bosker (1999) provided some approximations for this that work well when the prevalence rate of the dependent variable is not too small.

^{26} These estimates are based on the 1999 NHSDA from responses of 3,902 pairs of youths aged 12 to 17 residing in eligible households in a total of 2,774 segments (groups of contiguous Census blocks). This analysis does not address youths in households in which there was only a single child in the age range. Of all youths aged 12 to 17 in 1999, approximately 49 percent were in households that included at least two youths aged 12 to 17.

^{27} In Gfroerer et al. (2002), specifically see Chapter 7 (Chromy, Davis, Packer, & Gfroerer, 2002) and Chapter 8 (Hughes, Chromy, Giacoletti, & Odom, 2002).

^{28} Several questions had their wording or response options altered in the 1999 survey in order to improve them. The principal reasons for these changes were that (a) respondents had expressed difficulty in comprehending the meaning of the questions or (b) statistical properties, such as a lack of discrimination between response options, or correlations with other items in the same construct were either excessively high (indicating redundancy) or low (indicating a lack of reliability).

^{29} The regression coefficients for main effects in 1997 are found in the "" column under Model 2 in ** Table 5.5**. The regression coefficients for main effects in 1999 are equal to the main effect regression coefficients from Model 2 plus the regression coefficients for the year-by-factor interactions. For example, for easy availability, the regression coefficient for 1999 was 2.03 + (-0.52) = 1.51. The seven variables that changed in a direction consistent with a decrease in marijuana use between 1997 and 1999 were easy availability of marijuana, approached by a drug seller in the past 30 days, perceived risk of using marijuana once or twice a week, youths get a kick out of doing things that are a little dangerous, youths wear a seatbelt when riding in the passenger seat of a car, youths' religious beliefs are very important part of their life, and religious beliefs influence how youths make decisions in their life.

^{30} The probability (*p*) of past year marijuana use for youths who were in the "high-risk" group for a specified subset of risk and protective factors was determined using the formula *p* = [*e*^{Χ} / (*e*^{Χ} + 1)]. In 1997, Χ = the sum of the beta for the intercept and the betas for the main effects of the specified subset of risk and protective factors (the relevant betas are in Model 2 of ** Table 5.5**). In 1999, Χ = the sum of the betas from the intercept and the year effect, as well as the betas from the main effects and year-by-factor interaction effects for the specified subset of risk and protective factors.

^{31} The equation used to disaggregate the change due to changes in their distributions and changes in s is a modification of this equation that further partitions the changes in model parameters into changes due to the intercept (_{0}) and changes due to the remainder of the variables (referred to as the slope). The purpose of separating out the impact of the change in intercept is that a change in intercept can occur when there has been no change in the relationship between substance use prevalence and risk and protective factors.

^{32} The family domain risk factor "low parental monitoring" contains questions about whether parents check on whether youths complete their homework and whether parents help youths with their homework when needed. The skip pattern for answering "no" to the school enrollment question included these items, which explains why the sample size for this factor is similar to the sample size for the school domain factors.

^{33} Because the survey data were collected continuously throughout the year and age is determined as age at the time of interview, individuals who were 12 years old at the time of the survey can be separated in birth date by as much as 2 years. That is, an individual born in late January 1986 could be interviewed at 12 years of age in early January 1999; and an individual born nearly 2 years later in mid-December 1987 could be interviewed at 12 years old in late December 1999. The age groups are therefore not clean successive birth cohorts. In addition, although there are differences in substance use by birth cohort, these differences are, for the measures used in this discussion, overshadowed by the degree of change associated with age alone.

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