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Risk and Protective Factors for Adolescent Drug Use:
Findings from the 1999 National Household Survey on Drug Abuse

Chapter 5. Changes in Risk and Protective Factors Between 1997 and 1999

5.1 Introduction

The focus of the previous chapters was on the results of the 1999 National Household Survey on Drug Abuse (NHSDA), which included questions addressing an expanded set of risk and protective factors and an expanded sample relative to previous years of the survey. The discussion updated and extended a previous report on risk and protective factors based upon the 1997 NHSDA (Lane et al., 2001). The focus of this chapter is on changes in the risk and protective factors between 1997 and 1999 and how these changes may be related to observed changes in the prevalence of past year marijuana use among youths during this time period. This chapter addresses the following issues:

A question might be asked, "What is to be gained by determining the extent to which, if any, the reported prevalence of risk and protective factors has changed over time?" Prevention researchers have concluded that a number of risk and protective factors are mediating variables in changes in the usage of substances among youths. The changes in youth substance use over time have been conjectured by various researchers to be attributable to different sets of risk and protective factors (Bachman, Johnston, & O'Malley, 1998). Such factors as the perceived risk of a substance have been shown to be highly (negatively) correlated at the national level with levels of youth substance use; however, substance use and perceived risk do not always move in opposite directions. For example, past month use of marijuana among youths decreased between 1997 and 1999 (9.4 percent in 1997, 8.3 percent in 1998, and 7.0 percent in 1999), but perceived (great) risk of using marijuana once a month also decreased during the same period (32.6 percent in 1996, 30.9 percent in 1997, 30.8 percent in 1998, and 29.0 percent in 1999). So, it is clear that trends in prevalence are not always directly related to changes in a single risk factor. The relationship may be further complicated by a lagged relationship between changes in risk factors and changes in prevalence rates. Therefore, it is informative to know whether changes in the prevalence of youth substance use are accompanied by a general shift of the risk and protective factors in a given direction. It also is informative to know which risk and protective factors experience the greatest amount of change over time.

In addition, the final model of past year marijuana use in Chapter 4 (Table 4.6) suggests that a large amount of variation is unexplained by the risk and protective factors included in the 1999 NHSDA. Perhaps other variables need to be included in the model to obtain a better fit of the data. An implication of this is that these other variables may better explain the trends. A related question about change in risk and protective factors over time is whether the strength of the associations between (some) factors and youth substance use may change over time, due to changing perspectives and behaviors of the population. If this is the case, some factors may not be as predictive of youth substance use in 1999 as they were in 1997, whereas other factors may be more predictive. If those variables that have changed substantially and are significantly associated with the trends in substance use can be identified, they would represent plausible variables to focus on in the design of programs to reduce substance use among youths.

5.2 Comparison of Estimates of Marijuana Use for 1997 and 1999

Exhibit 5.1 displays estimates of marijuana use for the past month and past year from the 1997 NHSDA as well as estimates from the various versions of the survey from 1999. The 1997 paper-and-pencil interviewing (PAPI) estimates are not comparable with the 1999 CAI estimates because of differences in data collection methodology, and they are not comparable with the 1999 PAPI estimates because of significant differences found in the field interviewer (FI) experience levels between those 2 years. These issues are discussed in detail elsewhere (Gfroerer, Eyerman, & Chromy, 2002).27 For this reason, the most valid comparison with the prevalence rates from 1997 is made using the 1999 PAPI after adjusting for FI experience.

Exhibit 5.1 Sample Sizes and Percentages Reporting Past Month and Past Year Marijuana Use among Youths Aged 12 to 17 in the 1999 NHSDA PAPI, 1999 NHSDA CAI, 1999 NHSDA PAPI, and 1999 NHSDA PAPI Adjusted for Field Interviewer Experience

Year and Data Collection Mode of Survey1 Sample Size Percent Used Marijuana in Past Month
(Standard Error)
Percent Used Marijuana in Past Year
(Standard Error)
1997 NHSDA PAPI 7,844 9.4
(0.56)
15.8
(0.74)
1999 NHSDA CAI 25,357 7.2
(0.20)
14.2
(0.29)
1999 NHSDA PAPI 3,449 8.1
(0.64)
14.7
(0.90)
1999 NHSDA PAPI (FI adjusted)2 3,449 7.0
(0.66)
13.0
(0.97)
1 PAPI = paper-and-pencil interviewing method; CAI = computer-assisted interviewing method.
2 Adjusted for differences in experience between field interviewers.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1999.

Looking at the FI-adjusted 1999 PAPI estimates, it is clear that the youth prevalence rates declined between 1997 and 1999 for both past month and past year use of marijuana. Unless noted otherwise, all references to the 1999 NHSDA in this chapter refer to the 1999 PAPI with the FI adjustment. More information about the methodological differences between the 1997 and 1999 NHSDAs, as well as the adjustments made for FI experience, is presented in Appendix D.

5.3 Risk and Protective Factors Common to Both the 1997 and 1999 NHSDAs

The assessment of change in the prevalence and influence of risk and protective factors between the 1999 and 1997 NHSDAs can be made only between comparable questions in both years of the survey.28 Of the 60 items used to measure risk and protective factors in the 1999 NHSDA, only 11 were identical to the questions asked in the 1997 survey. These 11 comparable questions were as follows:

Community Domain

  1. the ease of availability of marijuana to the youth


  2. whether the youth had been approached by a drug seller in the past 30 days

Family Domain

  1. parents as a source of social support for the youth

Peer/Individual Domain

  1. perception of risk from using marijuana once a month


  2. perception of risk from using marijuana once or twice a week


  3. how often youths get a kick out of doing things a little dangerous


  4. how often youths test themselves by doing something a little risky


  5. how often youths wear a seatbelt when riding in the front seat of a car


  6. the importance of religious beliefs to youths


  7. the degree to which religious beliefs influence the youths' decisions


  8. how important it is that youths' friends share their religious beliefs

These 11 questions are the focus of the presented comparisons between the 1997 and 1999 NHSDAs. Note that no questions from the school domain were comparable between 1997 and 1999. The distributions for these 11 questions in both 1997 and 1999 are presented in Table 5.1. (For the exact wording and format of these questions, see Appendix A.) Table 5.1 also contains the distributions for some of the demographic items that were measured using identical items in 1997 and 1999.

In addition to these 11 items, a small number of questions measured similar constructs but were asked using slightly different questions between the 1997 and 1999 surveys. One example is the question about use of marijuana by friends:

Here, one can see changes in both the question and in the answer options. The 1997 question talks about close friends trying marijuana, which implies occasional use. The 1999 question talks about a broader group of friends (not just close friends) using marijuana or hashish, which implies a more regular usage. In addition, the 1999 question has a response option of "all of them" that was not present in 1997. Because of these types of changes, it is not possible to tell whether differences in the distribution of friends' use of marijuana between 1997 and 1999 were due to actual differences in youths' perceptions of marijuana use among their friends or to changes in the wording of the questions. For this reason, questions that were similar but not identical in the 1997 and 1999 surveys were not included in the comparisons presented in this chapter. A more complete discussion of the questions that were asked using similar but not identical questions in the 1997 and 1999 surveys is presented in Appendix E. Selected analyses also are presented.

5.4 Comparison of Risk and Protective Factors Between 1997 and 1999

For the 11 comparable questions between 1997 and 1999, two dimensions of comparison across the 2 years are especially relevant: the distribution of answers among the response categories, and the strength of the association of the responses with substance use (here, the past year use of marijuana). The purpose of the first comparison is to show whether there were significant changes in the percentage of youths indicating they had the risk or protective factor (i.e., changes in answers that youths gave to the questions related to risk and protective factors) between 1997 and 1999. The second comparison's purpose is to show whether the associations between each of the comparable risk and protective questions and past year marijuana use were stronger or weaker in 1999 compared with 1997.

5.4.1 Distributions of Factors Between 1997 and 1999

Table 5.1 presents, for the comparable questions, percentages of youths who selected each response category in both 1997 and 1999, as well as a test of whether the differences in responses between the 2 years are statistically significant (values of p < .05). The table also includes comparisons of the distributions of a set of demographic variables. Note that there were no statistically significant differences in the age, gender, or race/ethnicity distributions of youths over the 2–year period.

It is clear from Table 5.1 that there were a number of statistically significant differences in the distributions of these variables between 1997 and 1999. However, except for cases in which there were only two categories (e.g., whether the youth was approached by someone selling drugs), it is difficult to determine from Table 5.1 whether the 1999 distribution of a factor indicates a higher or lower level of risk (or protection) than in 1997. Because the goal is to determine whether the decrease in youth marijuana use can be associated with a corresponding decrease in the prevalence of risk factors or a decrease in the strength of the association between risk factors and youth marijuana use, it is important to be able to describe the "direction" of the associated changes. For this purpose, the categories of each of the 11 common risk and protective factors have been collapsed into two categories. These results are presented in Table 5.2.

These findings indicate that none of the questions related to risk and protective factors that were directly comparable between the 1997 and 1999 NHSDAs showed statistically significant change in prevalence between the 2 years. If one looks at the direction of the changes in these factors between 1997 and 1999 (discounting statistical significance), Table 5.2 indicates that about half of the 11 variables changed in the direction of decreased risk of substance use (e.g., compared with 1997, youths in 1999 were more likely to report that marijuana was difficult to obtain and less likely to have been approached by a drug seller in the past 30 days), and the remaining questions changed in the direction of increased risk of substance use (e.g., compared with 1997, youths in 1999 were less likely to talk to their parents about a serious problem and were less likely to perceive a great risk from using marijuana).

5.4.2 Associations with Marijuana Use in 1997 and 1999

Table 5.3 presents the associations with past year marijuana use of the dichotomized risk and protective factors that were measured using comparable items in 1997 and 1999, as well as a test of whether the difference in associations between the 2 years was statistically significant. As was the case with the distributions seen in Table 5.1, the associations between all three demographic variables and past year marijuana use indicate no significant changes between 1997 and 1999. This lack of change can also be seen in the similar betas and odds ratios (ORs) for most of these factors between the 2 years.

Within the community domain, there was a significant change between 1997 and 1999 in the association between past year marijuana use and being approached by a drug seller in the past month. The OR for 1997 was 10.90, which indicates that youths who had been approached by a drug seller in the past month had odds of using marijuana in the past month that were nearly 11 times higher than other youths. The comparable OR for 1999 was only 5.83, which indicates that being approached by a drug seller was less closely associated with past year marijuana use in 1999 when compared with 1997. There were no significant differences in the associations with past year marijuana use between 1997 and 1999 for any of the other risk and protective factors in the community or family domain. Within the peer/individual domain, there was a significant change between 1997 and 1999 in the association between the importance of religious beliefs in the youths' lives and use of marijuana in the past year. In 1997, youths who agreed that their religious beliefs were a very important part of their life had odds of marijuana use that were less than half of the odds of use for youths who did not agree with this statement (OR = 0.48). In 1999, this association was stronger; youths in 1999 who agreed that their religious beliefs were a very important part of their lives had odds of marijuana use that were less than one third of the odds of use for youths who did not agree with this statement (OR = 0.30). There were no other significant differences in associations between 1997 and 1999. Note that the associations presented in Table 5.3 are unadjusted, meaning that they have not been adjusted for demographic variables or for other risk and protective factors.

5.4.3 Comparisons of the Predictiveness of the Final Models from 1997 and 1999

In Chapter 4, prediction models were presented in which the risk and protective factors were combined into a single model in order to determine how much variation in past year marijuana use could be explained by these factors (see Table 4.6 in Chapter 4). Similar prediction models were presented in the previous report using the 1997 NHSDA (Lane et al., 2001). These data indicate that the final model from 1997 accounted for slightly more variation in past year marijuana use (R2 = 0.35; RN2 = 0.61) than the final model from the 1999 CAI (R2 = 0.33; RN2 = 0.56). This slight drop in the amount of variance explained was surprising giving the larger number of risk and protective factors included in the 1999 NHSDA.

Several reasons for this drop in explanatory power are possible. First, many constructs in the 1999 model were measured using multiple-item scales, whereas all constructs in 1997 were measured using single items. Combining single items into scale scores to measure a construct has the effect of improving the accuracy of item as a "true" measure of the construct; however, the resulting scale scores, which in this case were the mean responses to the individual items, are often less predictive than the set of individual items. Second, different decision rules were used in 1997 and 1999 regarding the variables to be included in these final models. In 1999, factors specific to substance use were included in the multiple regression models predicting marijuana use only if the questions asked specifically about the use of marijuana. In 1997, questions were included in the marijuana prediction models that were specific to cigarettes, alcohol, and illicit drugs other than marijuana. Although questions specific to marijuana are typically the best predictors of marijuana use, the inclusion of these other questions in 1997 may have had the effect of increasing the predictiveness of that model. Third, it could be that in general, risk and protective factors were not as predictive of past year marijuana use in 1999 as they were in 1997.

A number of other noteworthy comparisons between the multiple regression models were conducted on the 1997 NHSDA and the 1999 NHSDA CAI. First, the results from both years show that the peer/individual domain had the highest number of statistically significant risk and protective factors and accounted for the highest amount of variation in past year marijuana use among all the domains. The amount of variance explained by the peer/individual domain alone in 1997 (R2 = 0.32; RN2 = 0.55) and in 1999 (R2 = 0.30; RN2 = 0.53) was nearly as high as the variance explained by the full model in each of those years. Second, demographics by themselves accounted for a relatively small, but consistent amount of variation relative to the risk and protective factor domains in both 1997 (R2 = 0.07; RN2 = 0.12) and in 1999 (R2 = 0.09; RN2 = 0.12). One notable difference between the models in the 2 years is that in 1999, the school domain accounted for more variation in past year marijuana use (R2 = 0.18; RN2 = 0.32) compared with the 1997 model (R2 = 0.10; RN2 = 0.18). This seems to indicate that the expanded set of questions included in the school domain in the 1999 NHSDA were an improvement on the smaller set of school domain questions included in 1997.

5.4.4 Comparison of the Predictiveness of the Items Included in Both 1997 and 1999

Another method of comparing the predictiveness of the set of risk and protective factors between 1997 and 1999 is to compare the results of multiple regression models that include only the questions that were included in both the 1997 and 1999 surveys. Because these models include the same items for both years of the survey, they provide a more direct comparison of whether the associations between risk and protective factors and youth past year marijuana use changed appreciably between 1997 and 1999 than does the comparison of the "final" models from these 2 years.

Table 5.4 presents the results of these prediction models for both the 1997 NHSDA and the 1999 NHSDA PAPI. Each of these models included a set of demographic variables (age, gender, and race/ethnicity) as well as the set of 11 questions that were directly comparable between the 2 years of the survey. Consistent with the results from the final models for 1997 and 1999, the 1997 model accounted for slightly more variation in past year marijuana use (R2 = 0.31; RN2 = 0.53) than the 1999 model (R2 = 0.25; RN2 = 0.47). As previously stated, there are a number of possible explanations for the seemingly reduced explained variation in 1999 compared with 1997. One is that the association between use of marijuana and risk and protective factors in general was weaker in 1999 than in 1997. Second, the 1999 PAPI sample size was significantly smaller than the 1997 PAPI sample, and this may have led to a lower percentage of explained variation for 1999. Third, the 11 risk and protective factors that were common to both survey years may not have been representative of the full set of factors; perhaps a different set of factors could have resulted in more explained variation for 1999 than for 1997.

The adjusted ORs presented in Table 5.4 indicate that there were some differences in the associations between the individual questions and past year marijuana use between 1997 and 1999. For example, the odds of past year marijuana use in 1997 were more than 4 times higher for youths who had been approached by a drug seller in the past month compared with youths who had not (OR = 4.04). In 1999, the odds of past year marijuana use were only about 2 times higher for those who had been approached by a drug seller (OR = 1.92). This indicates that after adjusting for the other variables in the model, marijuana use was not as strongly associated with being approached by a drug seller in 1999 as it was in 1997. Another significant change was found for the risk-taking proclivity question that asked how often youths wore a seatbelt when riding in the front passenger seat of a car. In 1997, the odds of past year marijuana use were lower for those who reported that they were more likely to wear a seatbelt (OR = 0.80), whereas there was no significant association between these variables in 1999.

For a discussion of the comparison of predictiveness of the items that were measured using similar but not identical questions in the 1997 and 1999 surveys, see Appendix E.

5.5 Disaggregating the Change in the Prevalence of Past Year Marijuana Use Between 1997 and 1999

The purpose of the discussion in this chapter so far has been to suggest possible explanations for the observed drop in the national prevalence of youth marijuana use between 1997 and 1999 in terms of changes in the mediating factors associated with youth marijuana use. It is important to note that the samples for the 2 years reflect two different cohorts of youths aged 12 to 17. As such, the phenomenon of interest, namely, the decrease in prevalence rates of marijuana among youths aged 12 to 17 over the 2–year period, can be estimated most effectively from repeated cross-sectional surveys such as the NHSDA. A traditional longitudinal survey, which measures how a single cohort changes over time, would at most measure the "cohort" change component (maturation) if the 2 years compared were sufficiently close in time. For example, in a longitudinal survey of youths aged 12 to 17 with a 2–year delay between the baseline and follow-up surveys, only youths aged 12 to 15 in the baseline survey could be included in estimates of youth marijuana use during the follow-up survey 2 years later because older youths (those aged 16 or 17 at the time of the baseline survey) would be older than 17 at the time of the follow-up survey. Similarly, youths aged 12 or 13 at the time of the follow-up survey would have only been 10 or 11, respectively, at the time of the baseline survey.

5.5.1 A Standard Methodology for Measuring Change

One traditional method of examining changing parameters over time (e.g., over 2 years) is to combine the data for both years and specify a model that includes the explanatory variables that are common to the 2 years, a dummy variable for the year, and a set of year-by-explanatory variable interaction terms. This traditional approach was applied with two different models, which are presented in Tables 5.5 and 5.6. In Table 5.5, each of the 11 questions related to risk and protective factors of youth substance use that were common to 1997 and 1999 were coded as dichotomous variables. This was done to increase the sample size within individual year-by-predictor domains, which increases the ability to detect statistically significant differences. Using dichotomous predictors also facilitates a discussion of the direction of any changes between 1997 and 1999. In Table 5.6, all response categories for each of the 11 variables are reflected in the modeling. An advantage of using all response categories is the possibility of explaining more variation, but a disadvantage is the reduced sample size in individual response categories.

The results presented in Model 1 of each table (Tables 5.5 and 5.6) were derived from a model that contained only the main effects of the 11 variables. The results from Model 2 in each table were derived from a model that included all main effects plus all of the variable by year interaction effects. In general, the tables showed similar results in going from Model 1 to Model 2. In both the model with the full set of response options and the model with the dichotomous responses, adding the interaction effects, to a slight degree, reduced the lack of fit statistic and increased the explained variation. Both for the main effects model and the full model with interactions, inclusion of the full set of response options for the explanatory variables explained somewhat more of the variation than did the models based on the dichotomized responses. This can be seen in the increase in the Nagelkerke R2 from RN2 = 0.40 in the dichotomous model to RN2 = 0.47 in the model with the full set of response options.

In the model with all of the response categories that contained only the main effects (Model 1 of Table 5.6), a number of the risk and protective main effect variables and their categories were significant. However, the "year" main effect was not significant, either in the model with only the main effects (Model 1) or in the model with the added interaction terms (Model 2). Only a single interaction term was significant (year of survey by having been approached by a drug seller in the past year; p = .0035).

In the dichotomous model with only the main effects (Model 1 in Table 5.5), the "year" variable was statistically significant, as were many of the risk and protective factors. The fact that the "year" variable was statistically significant implies that the risk and protective factors alone have not fully explained the increase in the prevalence level between 1997 and 1999. When the "year" interaction terms were added (Model 2 in Table 5.5), the "year" main effect was no longer significant, although most of the risk and protective factor main effects maintained their significance. Only 1 out of the 11 interaction terms was significant (year of survey by having been approached by a drug seller in the past year; p = .0047), although a second interaction (year of survey by testing yourself by doing something risky) approached significance (p = .0511). Together, the combined contribution of all of the interaction effects was significant (likelihood ratio test, p < .0001), although the amount of extra explained variation was small (1 percent).

An additional method of determining whether the distributions of risk and protective factors changed substantially between 1997 and 1999 is a comparison of the unadjusted year effect that can be determined from the prevalence rates presented in Exhibit 5.3 (see Section 5.5.2) with the adjusted year effect from Model 1 in Table 5.5. If the 1997 and 1999 risk and protective factor distributions were significantly different, the adjusted year effect in Model 1 would be substantially reduced or partially explained away by the risk and protective factors. This reduction in the log-odds ratio for year would result from the model's indirect standardization to a common risk and protective factor distribution. The unadjusted odds ratio between the 2 years (based on the actual distributions of the risk and protective factors in 1997 and 1999, respectively) can be calculated from the prevalence rates presented in Exhibit 5.3 for those years:

[Prevalence99 / (100 - Prevalence99)] / [Prevalence97 / (100 - Prevalence97)] = 0.7916.

The adjusted odds ratio between the 2 years, adjusted to the average (across 1997 and 1999 combined) distribution of each of the 11 risk and protective factors, can be calculated by exponentiating the "year" effect beta found in Model 1 of Table 5.5. The "year" effect beta in Model 1 equals -0.27, which translates into an odds ratio of e-0.27 = 0.7634. The small reduction in the adjusted odds ratio compared with the unadjusted odds ratio suggests that the distribution of the risk and protective factors did not change substantially between 1997 and 1999.

One question that is not addressed in this standard methodology is how much these changes, though perhaps small, contributed to the decrease in the youth marijuana prevalence rate during that period. Although the changes in all but one interaction effect were nonsignificant, it can be noted from the interaction terms in Table 5.5 that for 7 out of the 11 factors measured, the association with marijuana use changed between 1997 and 1999 in a direction that is consistent with a decrease in marijuana prevalence. This is most readily indicated by the negative signs associated with seven of the interaction terms. Thus, for example, the coefficient for "easy availability of marijuana" was 2.03 in 1997, but only 1.51 (2.03 + [-0.52]) in 1999. Those coefficients translate into conditional odds ratios of 7.61 (e2.03) and 4.53 (e1.51) in 1997 and 1999, respectively. That is, in 1997, the conditional odds (conditional on the other factors in the model) of having used marijuana in the past year for youths who indicated that it was "fairly easy to obtain marijuana" were 7.61 times greater than for youths who indicated that marijuana was not fairly easy to obtain.29 In 1999, the conditional odds ratio was lower, 4.53. The other four factors evidenced changes in the opposite direction, as indicated by the positive coefficients of those interaction terms. Combined, the sizes of the changes for the seven variables that went in the direction consistent with the decrease in marijuana prevalence were larger than the sizes of the changes for the four variables that went in the opposite direction.

Because these changes in coefficient sizes are from a national model fitted to the population of youths aged 12 to 17, they represent the average change across all youths. To see the impact of these changes on youths with different combinations of the risk and protective factors present, it is instructive to estimate the probability of use for youths who had few of the risk factors present and contrast them with youths having a larger number of risk factors present. For youths who reported that it was fairly easy or very easy to obtain marijuana, who perceived a moderate (or less) risk in using marijuana once a month, and who never or seldom wore a seatbelt when in the front seat of a car (and who were not in the "high-risk" group for the remaining factors [i.e., they did not exhibit the other risk factors, but they did exhibit the remaining protective factors]), the probability of past year use of marijuana was similar between the 2 years (0.054 in 1997 vs. 0.045 in 1999).30 By contrast, for youths who additionally reported that they had been approached by a drug seller in the past month, who perceived moderate (or less) risk of using marijuana once or twice a week, and who somewhat or strongly disagreed that religious beliefs are a very important part of their life, the probability of having used marijuana in the past year was 0.587 in 1997, but only 0.378 in 1999. This indicates that the probability of marijuana use based on the model decreased dramatically between 1997 and 1999 for the youths in the "high-risk" group (exhibiting more risk factors and fewer protective factors), but only slightly for youths in the lower risk group (exhibiting fewer risk factors and more protective factors). The result that youths in the "high-risk" group have a much higher probability of use in the past year than youths with fewer of the risk factors is consistent with other research indicating that multiple risk factors are typically associated with an increased likelihood of illicit drug use (Newcomb, Maddahian, & Bentler, 1986).

5.5.2 A New Methodology for Measuring Change

From the discussion in Section 5.4 that focused on the changes in both the distributions of the individual variables and in their association with youth marijuana use (or their Betas), it is still not possible to obtain a single measure of all of the changes in these distributions or of all the changes in these associations, nor can the relative role that both sources play in the decreased marijuana rate be assessed. Therefore, to attempt to quantify these two factors, a second method of analyzing aggregate trends from repeated surveys also was utilized. This method is similar to various methods suggested by Firebaugh (1997, p. 39). However, the new derivation (Ralph E. Folsom, personal communication, August 2001) is quite different in that it is applicable to logistic regression models for which the predictor variables are categorical. The goal is to partition the aggregate change between prevalence rates for 2 different years into the portion due to changes in distribution of the independent variables as well as to that due to changes in the associated regression coefficients.

5.5.2.1 Methodology

Assume that logistic regression models have been fitted to data from two different surveys, t = 1,2. Further assume that the set of predictor variables X is the same for the two surveys and that each predictor variable is categorical. Assume also that the population can be cross-classified by all combinations of X into D domains. Denote the number of persons in the population domain d on occasion t by (d = 1, ..., D, t = 1, 2) and their share of the total population as f sub d,t is the proportion of domain d at time t in the population and equals the ratio of the size of the domain at time t, denoted by N sub d,t over the sum of all the domain sizes N sub d,t, as d ranges from 1 to D

If rd,t is the associated expected prevalence rate,

r sub d,t is defined as the expectation at time t of y, given the covariates x sub d. It equals 1 over the sum of 1 plus the exponential of minus the transpose of beta sub t times x sub d

Thus, the overall prevalence for occasion t is P (prevalence) sub t is equal to the sum as d ranges from 1 to D of the product of f sub d, t and r sub d,t, and the change between two occasions is P (prevalence) sub 2 minus P sub 1 is equal to Delta sub 1 plus Delta sub 2, where Delta sub 1 is the sum as d ranges from 1 to D of the product of the difference f sub d,2 minus f sub d,1, times r bar sub d and Delta sub 2 is the sum as d ranges from 1 to D of the product of the difference r sub d,2 minus r sub d,1, times f bar sub d, with r bar sub d is the mean of r sub d,1 and r sub d,2 and f bar sub d similarly defined. Therefore, Delta sub 1 represents the portion of the change due to changes in the distribution of the independent variables (Χs), and Delta sub 2 represents the portion of change due to changes in regression coefficients (Betas).31

5.5.2.2 Caveats

Although the preceding equation clearly partitions the change between two occasions into a part due to changes in the prevalence of risk and protective factors and a part due to changes in the direction and degree of association of those risk and protective factors with marijuana use, it is important for several reasons not to overinterpret the results.

First, this partitioning is based on cross-sectional data, and inferences about causality cannot be easily established—if at all—with only cross-sectional data.

Second, an underlying assumption in all of this is that various sources of response and nonresponse bias (e.g., underreporting of marijuana use among youths), as well as sampling errors, have been constant across the 2 years.

Third, given the nature of this equation, one could use any set of variables in the regression, even a set in which no variables were related to marijuana use, and the equation would still partition the change in marijuana use into a part due to changes in distribution of independent variables and a part due to changes in the regression coefficients. Note, however, that if this were the case, the partitioning would indicate a large effect for the intercept, with little change attributed to changes in the betas or in the distribution of the independent variables. It also is possible that a set of variables may be associated with marijuana use but not be substantively informative (e.g., there is typically a positive association between height and marijuana use among youths because both variables increase with age among youths).

Related to this, note the following general comment from Firebaugh (1997, p. 42):

A decomposition is only as informative as the explanatory variables on which it is based. For example, we could "account for" the decline in voter turnout ["prevalence rate" for this report's purpose] by applying the decomposition equation to any variables that are correlated with voting [i.e., "prevalence rates"] and have exhibited an upward or downward trend over the past three decades [i.e., "time period"]. Such mechanical applications of the method might well yield statistically significant results yet tell us nothing useful about the social world.

Relevant to the above comment, using the Nagelkerke (1991) adjusted R2, the full set of X variables used in the final multiple regression models (see Chapter 4) were shown to account for approximately 60 and 56 percent of the total variation in past year marijuana use for 1997 and 1999, respectively. The reduced set of explanatory variables—those that are the same for the 2 years and can be used in the partitioning—account for a somewhat smaller amount of variation: approximately 53 percent of the variation in past year use of marijuana in the 1997 model and 47 percent in 1999 (PAPI adjusted). Therefore, any conclusions about the importance of changes in the independent variables or changes in the regression coefficients (Betas) relative to their impact on changes in the prevalence rate between 1997 and 1999 should be tempered by this reduced explanatory power. Of course, showing that a set of variables explains a significant amount of the total variation in the prevalence of youth marijuana use tells little about whether those variables can explain a similar amount of the variation in change between 1997 and 1999.

Fourth, a number of technical questions and issues still remain unresolved. One issue is that, at present, there is no estimate of the variability associated with the partitioning. A second issue is that the crossing of the response categories of the set of risk and protective factors used in the equation creates a large number of "domains," or cells formed by the intersection of the categories of all 11 questions. The number of these domains depends on how the questions are coded. If the questions are dichotomized, there are approximately 2,000 domains (two categories for each of the 11 questions, or 211). However, if the full set of response options is used for each of the 11 questions, there are more than 1.3 million domains. Although the inclusion of the undichotomized questions could result in better model fit and therefore a more accurate partition, the inclusion of the undichotomized questions also results in a large number of domains that have no sample records in them either from 1997 or 1999. In addition, the cross-categorization results in a significant number of domains that contain data from only 1 of the 2 years. Although the equation accounts for these records in the net partitioning result and, therefore, still holds true, there is a question whether the results can be interpreted as desired when there are more domains that have observations from only 1 year's data than there are with data from both years. This was especially true when using the full set of response options. In addition, the results using the full set of response options were significantly different from those using the dichotomous categorization, and it is not clear whether this was caused by the variability of the estimates or some other factor.

Therefore, the only results presented here are for the situation in which the responses to the set of comparable questions were dichotomized. For that case, approximately 80 percent of all observations were in domains in which both years were represented. Other issues relevant to the interpretation of these results include (a) separating out the impact of the change in model parameters to changes from the intercept and changes from the risk and protective factors (or slopes), (b) the consistency of the results for both past year and past month marijuana use, and (c) interpretation of counterintuitive findings (e.g., effects of the change from one component that are larger in absolute value than the total change in the prevalence rates).

5.5.2.3 Results

The set of 11 questions identified as being the same or comparable between the 1997 and 1999 NHSDAs were included in these disaggregation analyses. To better isolate the cause of the change, a partitioning was first done to quantify the contribution of any changes in demographics across the 2 years. Chapter 4 discusses the relatively small amount of variation explained by demographics in models predicting the prevalence level for a given year. Exhibit 5.2 shows that although the prevalence of past year marijuana use decreased 2.80 percent between 1997 and 1999 ([12.98 - 15.78] = -2.80 percent), the changes in demographic characteristics between those 2 years would have increased the prevalence 0.24 percent during this time. Therefore, it is clear that the changes in demographics did not play a significant role in the decrease in marijuana use between 1997 and 1999 because, if anything, those changes would have served to increase the prevalence rate. Looking at the change that way, these analyses suggest that the observed decrease in past year marijuana use between 1997 and 1999 would have been greater (-3.04 percent) had there been no shift in demographics. The results for past month use of marijuana are similar.

Exhibit 5.2 Partitioning Change in Prevalence of Past Month and Past Year Marijuana Use from 1997 to 1999, with Age Group, Gender, and Race/Ethnicity

  Past Month
Marijuana Use
(percent)1
Past Year
Marijuana Use
(percent)1
Prevalence, 1997 (P97) 9.38 15.78
Prevalence, 1999 (P992) 7.01 12.98
Change from demographic factors (Delta sub 1) 0.20 0.24
Change from model parameters (Delta sub 2) -2.57 -3.04
Note: Delta sub 1 represents the portion of change in prevalence from 1997 to 19992 that can be attributed to changes in the distribution of demographic variables (age, gender, and race/ethnicity). Delta sub 2 represents the portion of change in the prevalence from 1997 to 19992 that can be attributed to changes in model parameters. P99 - P97 = Delta sub 1 + Delta sub 2.

1 Prevalence rates may differ from previously published rates for these surveys because only records that contained nonmissing data for each covariate included in the model were used in creating these prevalence rates.
2 The 1999 paper-and-pencil interviewing (PAPI) method.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999 PAPI.

Exhibit 5.3 shows the decomposition between changes in the distributions of the factors and changes in Betas when the response options were constrained to be dichotomous. Note that these prevalence rates differ somewhat from those in Exhibit 5.1. The reason for the difference is that the only records that could be used were those for members of the sample who had nonmissing data for all of the covariates included in the model. For this set of variables, most of the approximately 3 percent drop in prevalence of past year marijuana use ([13.06 - 15.95] H 100 = -2.87 percent) was accounted for by changes in the Betas (-2.39), and only a very small part was a result of changes in the distributions (-0.50). Note that the impact of the intercept rounded to 0 for both past year use of marijuana and for past month use. In both cases, the effect of the change in distribution of the factors between 1997 and 1999 was quite small.

Exhibit 5.3 Partitioning Change in Prevalence of Past Month and Past Year Marijuana Use from 1997 to 1999, with Risk and Protective Variables

  Past Month
Marijuana Use
(percent)1
Past Year
Marijuana Use
(percent)1
Prevalence, 1997 (P97) 9.49 15.95
Prevalence, 1999 (P992) 7.01 13.06
Change from risk and protective factors (Delta sub 1) -0.25 -0.50
Change from model parameters (Delta sub 2) -2.23 -2.39
Change in intercept 0.00 0.00
Change in slope -2.23 -2.39
Note: Delta sub 1 represents the portion of change in prevalence from 1997 to 19992 that can be attributed to changes in the distribution of risk and protective factors. Delta sub 2 represents the portion of change in the prevalence from 1997 to 19992 that can be attributed to changes in model parameters. P99 - P97 = Delta sub 1 + Delta sub 2.

The dataset was partitioned using the following risk and protective factors: availability of marijuana, approached by drug seller in past 30 days, parents as source of social support, perceived risk of using marijuana once a month, perceived risk of using marijuana once or twice a week, gets a kick out of dangerous things, tests self by doing something risky, used seatbelt as front seat passenger, religious beliefs important to life, religious beliefs influence decision, and important for my friends to share my religious beliefs.

1 Prevalence rates may differ from previously published rates for these surveys because only records that contained nonmissing data for each covariate included in the model were used in creating these prevalence rates.
2 The 1999 paper-and-pencil interviewing (PAPI) method.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999 PAPI.

The data in Exhibit 5.3 imply that the decrease in the prevalence of youth marijuana use between 1997 and 1999 was due more to changes in the associations between the risk and protective factors and marijuana use than to changes in the distributions (i.e., the percentage of youths indicating the presence of each risk and protective factor in those 2 years). Combined, the changes in the distributions of risk and protective factors between 1997 and 1999 were associated with only about 17 percent (-0.50 / -2.89) of the decrease in past year use of marijuana between those years. The remainder of the decrease was due to changes in the associations between marijuana use and both risk factors and protective factors.

Again, it must be emphasized that these results do not allow for the conclusion of causal relationships. However, they do supply some evidence that the decrease in youth marijuana use between 1997 and 1999 could well have been the net result of attenuation in the relationship between risk factors and marijuana use and a strengthening in the relationship between protective factors and marijuana use. There is an implicit assumption in these comparisons that this set of 11 risk and protective factors that were measured in both 1997 and 1999 are not only "responsible" for the change, but also represent the totality of risk and protective factors that are relevant for change. However, it is known that there are many more risk and protective factors that are also associated with youth marijuana use that could not be included in these comparisons. Therefore, the set of 11 factors used in these comparisons can probably best be viewed more as a representative, rather than a comprehensive, set of risk and protective factors.

Table 5.1 Comparison of Distributions of Risk and Protective Variables and Demographics Measured Using Identical Questions in the 1997 and 1999 NHSDAs

Variable 1997 1999 Test of Difference Between 1997 and 1999
% % X2 p value
Demographics        
Age group        
     12 to 14 49.8 48.3 0.65 .4203
     15 to 17 50.2 51.7    
Gender        
     Male 51.0 51.2 0.02 .9024
     Female 49.0 48.8    
Race/ethnicity        
     White 67.3 67.4 1.22 .7486
     Black 14.3 14.5    
     Hispanic 13.3 14.0    
     Other 5.1 4.0    
Community Domain        
Availability of Marijuana        
     Probably impossible 19.3 19.2 12.21 .0176
     Very difficult 11.1 13.1    
     Fairly difficult 11.7 13.3    
     Fairly easy 21.2 24.0    
     Very easy 36.7 30.5    
Approached by Drug Seller in Last 30 Days?        
     No 85.4 86.8 1.44 .2312
     Yes 14.6 13.2    
Family Domain        
Parents as Source of Social Support        
     Would not talk to parent(s) about serious problems 20.1 22.3 1.81 .1793
     Would talk to parent(s) about serious problems 79.8 77.7    
Peer/Individual Domain        
Perceived Risk of Marijuana Use        
Risk of using marijuana once a month        
     Great risk 30.9 29.5 2.19 .5342
     Moderate risk 30.6 32.7    
     Slight risk 27.2 27.6    
     No risk 11.3 10.3    
Risk of using marijuana once or twice a week        
     Great risk 54.0 52.2 7.11 .0711
     Moderate risk 26.1 30.2    
     Slight risk 13.7 11.7    
     No risk 6.2 5.9    
Risk-Taking Proclivity        
How often do you get a kick out of doing things that are a little dangerous?        
     Never 40.1 39.0 0.90 .8251
     Seldom 23.8 23.1    
     Sometimes 30.1 31.4    
     Always 6.0 6.4    
How often do you test yourself by doing something a little risky?        
     Never 39.1 36.0 2.27 .5191
     Seldom 28.7 30.2    
     Sometimes 27.0 28.5    
     Always 5.2 5.3    
How often do you wear a seatbelt when you ride in the front passenger seat of a car?        
     Never 8.7 8.2 5.66 .1321
     Seldom 8.7 6.9    
     Sometimes 21.8 19.8    
     Always 60.8 65.2    
Religiosity        
My religious beliefs are a very important part of my life        
     Strongly disagree 2.6 4.4 11.48 .0105
     Somewhat disagree 13.1 11.9    
     Somewhat agree 53.1 47.7    
     Strongly agree 31.2 36.1    
My religious beliefs influence how I make decisions in my life        
     Strongly disagree 3.4 6.2 15.86 .0015
     Somewhat disagree 20.8 16.8    
     Somewhat agree 50.0 48.6    
     Strongly agree 25.8 28.3    
It is important that my friends share my religious beliefs        
     Strongly disagree 15.6 21.1 17.47 .0007
     Somewhat disagree 52.1 43.5    
     Somewhat agree 25.1 27.5    
     Strongly agree 7.3 7.9    
Note 1: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.
Note 2: No questions from the school domain were identical in the 1997 and 1999 NHSDAs.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

Table 5.2 Comparison of Distributions of Dichotomous Risk and Protective Variables Measured Using Identical Questions in the 1997 and 1999 NHSDAs

Variable 1997 1999 Test of Difference Between 1997 and 1999
% % T p value
Community Domain        
Availability of Marijuana        
     Probably impossible / Very-Fairly difficult 42.1 45.5 -1.83 .0685
     Fairly easy/ Very easy 57.9 54.5    
Approached by Drug Seller in Last 30 Days?        
     No 85.4 86.8 -1.20 .2305
     Yes 14.6 13.2    
Family Domain        
Parents as Source of Social Support        
     Would not talk to parent(s) about serious problems 20.2 22.3 -1.35 .1771
     Would talk to parent(s) about serious problems 79.8 77.7    
Peer/Individual Domain        
Perceived Risk of Marijuana Use        
Risk of using marijuana once a month        
     Great risk 30.9 29.5 0.81 .4173
     Moderate / Slight/ No risk 69.1 70.5    
Risk of using marijuana once or twice a week        
     Great risk 54.0 52.2 0.94 .3501
     Moderate / Slight / No risk 46.0 47.8    
Risk-Taking Proclivity        
How often do you get a kick out of doing things that are a little dangerous?        
     Never / Seldom 63.9 62.1 0.94 .3480
     Sometimes / Always 36.1 37.9    
How often do you test yourself by doing something a little risky?        
     Never / Seldom 67.8 66.2 0.83 .4057
     Sometimes / Always 32.2 33.8    
How often do you wear a seatbelt when you ride in the front passenger seat of a car?        
     Never / Seldom 17.4 15.1 1.49 .1369
     Sometimes / Always 82.6 85.0    
Religiosity        
My religious beliefs are a very important part of my life        
     Strongly - Somewhat disagree 15.7 16.3 -0.39 .6992
     Somewhat - Strongly agree 84.3 83.8    
My religious beliefs influence how I make decisions in my life        
     Strongly - Somewhat disagree 24.2 23.1 0.61 .5394
     Somewhat - Strongly agree 75.8 76.9    
It is important that my friends share my religious beliefs        
     Strongly - Somewhat disagree 67.7 64.5 1.47 .1424
     Somewhat - Strongly agree 32.3 35.5    
Note 1: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.
Note 2: No questions from the school domain were identical in the 1997 and 1999 NHSDAs.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

Table 5.3 Comparison of Unadjusted Associations with Past Year Marijuana Use of Dichotomized Risk and Protective Factors and Demographics Measured Using Identical Questions in the 1997 and 1999 NHSDAs

Variable 1997 NHSDA   1999 NHSDA   Test of Difference Between 1997 and 1999
Beta Odds
Ratio
95% CI p value Beta Odds
Ratio
95% CI p value t-test
value1
df p value
Demographics                      
Age (15 to 17 vs. 12 to 14) 1.51 4.52 (3.62, 5.65) <.0001 1.78 5.95 (3.99, 8.89) <.0001 1.19 1 .2358
Gender (males vs. females) -0.03 0.97 (0.81, 1.17) .7694 -0.06 1.06 (0.75, 1.51) .7259 0.45 1 .6549
Race/ethnicity                      
     Black vs. white -0.23 0.79 (0.60, 1.04) .0958 -0.17 0.85 (0.57, 1.25) .3939 0.27 1 .7869
     Hispanic vs. white -0.20 0.82 (0.64, 1.04) .1076 -0.13 0.88 (0.58, 1.33) .5414 0.30 1 .7682
     Other vs. white 0.26 1.30 (0.74, 2.30) .3587 -0.24 0.79 (0.36, 1.71) .5449 -1.03 1 .3022
Community Domain                      
Marijuana fairly/very easy to obtain 2.70 14.87 (10.8, 20.4) <.0001 2.34 10.38 (6.05, 17.8) <.0001 -1.14 1 .2562
Approached by drug seller in past 30 days (yes vs. no) 2.39 10.90 (8.67, 13.7) <.0001 1.76 5.83 (3.84, 8.86) <.0001 -2.60 1 .0100
Family Domain                      
Parents as source of social support
(yes vs. no)
-1.22 0.30 (0.25, 0.36) <.0001 -1.09 0.34 (0.24, 0.48) <.0001 0.66 1 .5086
Peer/Individual Domain                      
Perceived Risk of Marijuana Use                      
Less than great risk of using marijuana once a month 2.12 8.30 (5.84, 11.8) <.0001 2.11 8.23 (3.97, 17.0) <.0001 -0.02 1 .9832
Less than great risk of using marijuana once or twice a week 2.23 9.34 (7.09, 12.3) <.0001 1.99 7.29 (4.25, 12.5) <.0001 -0.81 1 .4180
Peer/Individual Domain (continued)                      
Risk-Taking Proclivity                      
Sometimes / always get a kick out of doing things that are a little dangerous 1.28 3.60 (2.97, 4.37) <.0001 1.12 3.05 (2.26, 4.11) <.0001 -0.92 1 .3597
Sometimes / always test yourself by doing something a little risky 1.02 2.76 (2.28, 3.35) <.0001 1.01 2.75 (2.07, 3.66) <.0001 -0.02 1 .9819
Never / seldom wear a seatbelt when you ride in the front passenger seat of a car 0.75 2.12 (1.72, 2.61) <.0001 0.70 2.01 (1.40, 2.90) .0002 -0.24 1 .8108
Religiosity                      
My religious beliefs are a very important part of my life -0.73 0.48 (0.38, 0.61) <.0001 -1.20 0.30 (0.22, 0.42) <.0001 -2.33 1 .0207
My religious beliefs influence how I make decisions in my life -0.80 0.45 (0.37, 0.54) <.0001 -1.11 0.33 (0.24, 0.45) <.0001 -1.63 1 .1035
It is important that my friends share my religious beliefs -0.83 0.44 (0.34, 0.56) <.0001 -0.81 0.44 (0.30, 0.65) <.0001 0.06 1 .9529
Note 1: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.
Note 2: No questions from the school domain were identical in the 1997 and 1999 NHSDAs.

1 Significance tests indicate whether the interaction terms (factor x year) are significantly different from zero.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

Table 5.4 Comparison of Adjusted Associations with Past Year Marijuana Use of Risk and Protective Factors and Demographics Measured Using Identical Questions in the 1997 and 1999 NHSDAs

Variable 1997 NHSDA   1999 NHSDA   Test of Difference Between 1997 and 1999
Beta Odds
Ratio
95% CI p value Beta Odds
Ratio
95% CI p value t-test
value1
df p value
Demographics                      
Age (15 to 17 vs. 12 to 14) 0.90 2.46 (1.86, 3.25) <.0001 1.26 3.54 (1.95, 6.44) .0001 1.09 1 .2774
Gender (males vs. females) 0.36 1.43 (1.11, 1.84) .0068 0.28 1.33 (0.79, 2.23) .2797 -0.24 1 .8079
Race/ethnicity                      
     Black vs. white -0.38 0.68 (0.49, 0.95) .0230 0.33 1.38 (0.79, 2.42) .2518 2.16 1 .0321
     Hispanic vs. white -0.15 0.86 (0.60, 1.24) .4189 -0.07 0.93 (0.56, 1.55) .7900 0.26 1 .7980
     Other vs. white 0.77 2.16 (1.23, 3.80) .0081 0.33 1.38 (0.73, 2.62) .3156 -1.03 1 .3037
Community Domain                      
Easy availability of marijuana 0.71 2.03 (1.77, 2.33) <.0001 0.69 1.98 (1.63, 2.42) <.0001 -0.18 1 .8546
Approached by drug seller in past 30 days (yes vs. no) 1.40 4.04 (3.03, 5.38) <.0001 0.65 1.92 (1.18, 3.14) .0094 -2.58 1 .0104
Family Domain                      
Parents as source of social support
(yes vs. no)
-0.57 0.56 (0.43, 0.75) .0001 -0.33 0.72 (0.46, 1.12) .1394 0.91 1 .3662
Peer/Individual Domain                      
Perceived Risk of Marijuana Use                      
Low risk of using marijuana once a month 0.43 1.54 (1.29, 1.85) <.0001 0.38 1.46 (1.05, 2.01) .0229 -0.31 1 .7534
Low risk of using marijuana once or twice a week 0.68 1.98 (1.63, 2.40) <.0001 0.69 1.99 (1.36, 2.89) .0004 0.02 1 .9880
Risk-Taking Proclivity                      
How often do you get a kick out of doing things that are a little dangerous? 0.36 1.43 (1.24, 1.65) <.0001 0.34 1.40 (1.07, 1.83) .0158 -0.14 1 .8887
How often do you test yourself by doing something a little risky? -0.12 0.89 (0.76, 1.05) .1657 0.18 1.20 (0.89, 1.63) .2316 1.72 1 .0866
How often do you wear a seatbelt when you ride in the front passenger seat of a car? -0.23 0.80 (0.70, 0.92) .0015 0.08 1.08 (0.87, 1.35) .4910 2.31 1 .0219
Religiosity                      
My religious beliefs are a very important part of my life 0.10 1.11 (0.83, 1.49) .4820 -0.32 0.73 (0.53, 1.01) .0562 -1.90 1 .0583
My religious beliefs influence how I make decisions in my life -0.12 0.88 (0.68, 1.16) .3688 -0.13 0.88 (0.61, 1.25) .4628 -0.05 1 .9629
It is important that my friends share my religious beliefs -0.11 0.89 (0.75, 1.06) .2080 -0.04 0.96 (0.70, 1.34) .8293 0.40 1 .6863
Sample size 7,169 3031  
R2 (see footnote 1) 0.31 0.25  
RN2 (see footnote 2) 0.53 0.47  
Note: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.

1 Cox and Snell (1989) R2 is a measure of the fit of the model, defined as 1 minus a certain quantity raised to the power of 2 over n, where n is the sample size. The aforementioned quantity is the ratio of the likelihood of the intercept-only model to the likelihood of the full model where L(O) is the likelihood of the intercept-only model, The likelihood of the full model is the likelihood of the full model, and n is the sample size.
2 Recognizing that the Cox and Snell R2 reaches a maximum for models that depend on the value of the estimated percentage, Nagelkerke (1991) proposed dividing the Cox and Snell measure by the maximum. In this sense, RN2 measures the absolute percentage of variation explained by the model.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

Table 5.5 Main Effects and Interactions (Year x Factor) in the Associations Between Dichotomous Risk and Protective Factors and Past Year Marijuana Use in 1997 and 1999: Combined 1997 and 1999 NHSDAs

Covariates Model 1
(Main Effects Only)
Model 2
(Main Effects + Interactions)
Beta p value Beta p value
Intercept -4.37 <.0001 -4.93 <.0001
Main Effects        
Year        
     1999 vs. 1997 -0.27 .0499 0.68 .2293
Easy availability of marijuana        
     Fairly easy/Very easy vs. Probably impossible/Very-Fairly difficult 1.74 <.0001 2.03 <.0001
Approached by drug seller in past 30 days        
     Yes vs. No 1.25 <.0001 1.69 <.0001
Parents as source of social support        
     Yes vs. No -0.48 .0004 -0.69 <.0001
Perceived risk of using marijuana once a month        
     Moderate-Slight-No risk vs. Great risk 0.80 .0002 0.69 .0020
Perceived risk of using marijuana once or twice a week        
     Moderate-Slight-No risk vs. Great risk 1.36 <.0001 1.55 <.0001
How often do you get a kick out of doing things that are a little dangerous        
     Always/Sometimes vs. Seldom/Never 0.48 <.0001 0.52 <.0001
How often do you test yourself by doing something a little risky        
     Always/Sometimes vs. Seldom/Never 0.13 .3152 -0.12 .3031
How often do you wear a seatbelt when you ride in the front passenger seat of a car        
     Never/Seldom vs. Sometimes/Always 0.19 .2087 0.46 .0012
My religious beliefs are a very important part of my life        
     Strongly-Somewhat agree vs. Somewhat-Strongly disagree -0.26 .1143 0.02 .9227
My religious beliefs influence how I make decisions in my life        
     Strongly-Somewhat agree vs. Somewhat-Strongly disagree -0.24 .1336 -0.08 .6494
It is important that my friends share my religious beliefs        
     Strongly-Somewhat agree vs. Somewhat-Strongly disagree -0.18 .1909 -0.37 .0062
Interactions (Year x Factor)        
Year x Ease of obtaining marijuana -0.52 .1312
Year x Approached by drug seller -0.83 .0047
Year x Parents as source of social support 0.37 .1563
Year x Risk of using marijuana once a month - 0.25 .5754
Year x Risk of using marijuana once or twice a week -0.33 .3722
Year x Get a kick of doing things that are a little dangerous -0.12 .6264
Year x Test yourself by doing something a little risky 0.51 .0511
Year x How often wear seatbelt when riding in passenger seat of a car -0.46 .1184
Year x Importance of religious beliefs -0.50 .1178
Year x Religious beliefs influence decisions -0.37 .2683
Year x Important that friends share religious beliefs 0.36 .1912
R2 (see footnote 1) 0.22 0.23
RN2 (see footnote 2) 0.40 0.41
Note: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.

1 Cox and Snell (1989) R2 is a measure of the fit of the model, defined as 1 minus a certain quantity raised to the power of 2 over n, where n is the sample size. The aforementioned quantity is the ratio of the likelihood of the intercept-only model to the likelihood of the full model where L(O) is the likelihood of the intercept-only model, The likelihood of the full model is the likelihood of the full model, and n is the sample size.
2 Recognizing that the Cox and Snell R2 reaches a maximum for models that depend on the value of the estimated percentage, Nagelkerke (1991) proposed dividing the Cox and Snell measure by the maximum. In this sense, RN2 measures the absolute percentage of variation explained by the model.

Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

Table 5.6 Main Effects and Interactions (Year x Factor) in the Associations Between Risk and Protective Factors and Past Year Marijuana Use in 1997 and 1999: Combined 1997 and 1999 NHSDAs

Covariates Model 1
(Main Effects Only)
Model 2
(Main Effects + Interactions)
Beta p value Beta p value
Intercept -5.53 <.0001 -6.13 <.0001
Main Effects        
Year        
     (1) 1999 vs. (2) 1997 -0.15 .2484 0.50 .5937
Easy availability of marijuana        
     (1) Probably impossible 0.00 0.00
     (2) Very difficult 0.69 .1497 0.20 .6830
     (3) Fairly difficult 2.05 <.0001 1.72 .0001
     (4) Fairly easy 2.53 <.0001 2.54 <.0001
     (5) Very easy 3.35 <.0001 3.19 <.0001
Approached by drug seller in past 30 days        
     (2) Yes vs. (1) No 1.01 <.0001 1.43 <.0001
Parents as source of social support        
     (2) Yes vs. (1) No -0.50 .0001 -0.63 <.0001
Perceived risk of using marijuana once a month        
     (1) Great risk 0.00 0.00
     (2) Moderate risk 0.53 .0314 0.36 .1482
     (3) Slight risk 0.95 <.0001 0.96 .0001
     (4) No risk 1.49 <.0001 1.33 <.0001
Perceived risk of using marijuana once or twice a week        
     (1) Great risk 0.00 0.00
     (2) Moderate risk 0.62 .0017 0.76 .0001
     (3) Slight risk 1.32 <.0001 1.37 <.0001
     (4) No risk 1.65 <.0001 1.80 <.0001
How often do you get a kick out of doing things that are a little dangerous        
     (1) Never 0.00 0.00
     (2) Seldom 0.64 .0013 0.41 .0365
     (3) Sometimes 0.74 .0001 0.76 <.0001
     (4) Always 1.13 <.0001 1.00 .0006
How often do you test yourself by doing something a little risky        
     (1) Never 0.00 0.00
     (2) Seldom -0.01 .9640 0.03 .8928
     (3) Sometimes 0.05 .8038 -0.27 .1473
     (4) Always -0.20 .5131 -0.32 .3544
How often do you wear a seatbelt when you ride in the front passenger seat of a car        
     (1) Never 0.02 .9406 0.47 .0253
     (2) Seldom 0.23 .2688 0.43 .0532
     (3) Sometimes 0.19 .1695 0.33 .0317
     (4) Always 0.00 0.00
My religious beliefs are a very important part of my life        
     (1) Strongly disagree 0.00 0.00
     (2) Disagree -0.46 .3287 0.22 .6215
     (3) Agree -0.48 .3031 0.37 .4300
     (4) Strongly agree -0.56 .2586 0.38 .4575
My religious beliefs influence how I make decisions in my life        
     (1) Strongly disagree 0.00 0.00
     (2) Disagree -0.07 .8699 -0.21 .5536
     (3) Agree -0.12 .7753 -0.17 .6770
     (4) Strongly agree -0.33 .4437 -0.48 .3241
It is important that my friends share my religious beliefs        
     (1) Strongly disagree 0.00 0.00
     (2) Disagree -0.10 .5432 0.02 .9011
     (3) Agree -0.25 .2231 -0.31 .1629
     (4) Strongly agree 0.01 .9718 -0.16 .6414
Interactions (Year x Factor)        
Year x Ease of obtaining marijuana (1) 0.00
Year x Ease of obtaining marijuana (2) 0.93 .2975
Year x Ease of obtaining marijuana (3) 0.71 .2824
Year x Ease of obtaining marijuana (4) 0.06 .9234
Year x Ease of obtaining marijuana (5) 0.46 .4081
Year x Approached by drug seller -0.80 .0035
Year x Parents as source of social support 0.23 .3822
Year x Risk of marijuana use once a month (1) 0.00
Year x Risk of marijuana use once a month (2) 0.40 .4309
Year x Risk of marijuana use once a month (3) 0.08 .8609
Year x Risk of marijuana use once a month (4) 0.35 .5596
Year x Risk of marijuana use once or twice a week (1) 0.00
Year x Risk of marijuana use once or twice a week (2) -0.25 .5587
Year x Risk of marijuana use once or twice a week (3) 0.05 .9235
Year x Risk of marijuana use once or twice a week (4) -0.19 .7552
Year x Get a kick of doing things that are a little dangerous (1) 0.00
Year x Get a kick of doing things that are a little dangerous (2) 0.32 .4443
Year x Get a kick of doing things that are a little dangerous (3) -0.15 .7111
Year x Get a kick of doing things that are a little dangerous (4) 0.19 .7354
Year x Tests self by doing things that are a little risky (1) 0.00
Year x Tests self by doing things that are a little risky (2) -0.11 .7777
Year x Tests self by doing things that are a little risky (3) 0.70 .0779
Year x Tests self by doing things that are a little risky (4) 0.26 .6974
Year x How often wear seatbelt when riding in passenger seat of a car (1) -0.89 .0785
Year x How often wear seatbelt when riding in passenger seat of a car (2) -0.37 .3991
Year x How often wear seatbelt when riding in passenger seat of a car (3) -0.31 .2825
Year x How often wear seatbelt when riding in passenger seat of a car (4) 0.00
Year x Importance of religious beliefs (1) 0.00
Year x Importance of religious beliefs (2) -0.92 .2403
Year x Importance of religious beliefs (3) -1.18 .1316
Year x Importance of religious beliefs (4) -1.40 .1020
Year x Religious beliefs influence decisions (1) 0.00
Year x Religious beliefs influence decisions (2) 0.19 .7805
Year x Religious beliefs influence decisions (3) -0.03 .9729
Year x Religious beliefs influence decisions (4) 0.13 .8693
Year x Important that friends share religious beliefs (1) 0.00
Year x Important that friends share religious beliefs (2) -0.21 .5128
Year x Important that friends share religious beliefs (3) 0.12 .7644
Year x Important that friends share religious beliefs (4) 0.37 .5882
R2 (see footnote 1) 0.26 0.27
RN2 (see footnote 2) 0.47 0.48
Note: The 1999 NHSDA data were derived from the 1999 paper-and-pencil interviewing (PAPI) data, with weights adjusted for field interviewer experience.
1 Cox and Snell (1989) R2 is a measure of the fit of the model, defined as 1 minus a certain quantity raised to the power of 2 over n, where n is the sample size. The aforementioned quantity is the ratio of the likelihood of the intercept-only model to the likelihood of the full model where L(O) is the likelihood of the intercept-only model, The likelihood of the full model is the likelihood of the full model, and n is the sample size.
2 Recognizing that the Cox and Snell R2 reaches a maximum for models that depend on the value of the estimated percentage, Nagelkerke (1991) proposed dividing the Cox and Snell measure by the maximum. In this sense, RN2 measures the absolute percentage of variation explained by the model.
Source: SAMHSA, Office of Applied Studies, National Household Survey on Drug Abuse, 1997 and 1999.

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