Weighting Procedures

The estimates of this report are based on sample survey data rather than on complete data for the population. This means that the data must be weighted to obtain unbiased estimates of drug use in the population represented by the 1997 NHSDA. The "final sampling weight" of the ith respondent, say w_i, can be interpreted as the number of persons in the NHSDA target population who are represented by the ith respondent. The sum of the weights over all respondents estimates the size of the total target population:

where the summation is over all NHSDA respondents in the 1997 NHSDA.

The final household and person-level sample weights for the 1997 NHSDA consist of a product of several factors, each representing either a probability of selection at some particular stage or some form of nonresponse or poststratification adjustment. The first seven factors are defined for all screener completedwelling units and reflect the fully adjusted dwelling unit sample weight. The latter five components reflect person-level selection within each screened dwelling unit, as well as any additional adjustments for person nonresponse and coverage error.

The first five components in the dwelling sample weight reflect the probability of selecting the dwelling unit. The five components are derived from (1) the probability of selecting the PSU, (2) the probability of selecting the geographic segment within each selected PSU, (3) a quarter segment weight adjustment, (4) a subsegmentation inflation factor, and (5) the probability of selecting a dwelling unit from within each counted, listed, and sampled segment. It should be noted that in the 1992 NHSDA, weight factor (3) was used for the calculation of independent, quarter-level sample weights, but as with the 1993 through 1996 NHSDAs, this factor was not needed for the 1997 survey. Subsequently, this factor has been set to one for all 1997 NHSDA selections. Also, when the field interviewers responsible for counting and listing traveled to a specified segment, occasionally they may have found that the number of potential dwelling units was much greater than what the sample frame (constructed from adjusted 1990 U.S. Census data) indicated. This error occurred either because of errors in the frame or, more commonly, due to rapid growth in a particular geographic area. When this occurred, the original segment was partitioned and a subsegment was randomly selected. The fourth weight component (the subsegmentation inflation factor) is an adjustment that accounts for the subselection process.

The sixth weight component is a dwelling unit smoothing adjustment. In previous NHSDAs, a dwelling unit post-stratification adjustment was applied to the sample weights associated with eligible and selected dwelling units. This factor was not applied for the 1997 NHSDA. Instead, the weights were normalized by strata and quarter in order to force equal weights for each strata by quarter combination. This adjustment serves as a measure to control for unequal weighting in the interest of reducing variance of estimates.

The seventh component of the weight is a dwelling unit nonresponse adjustment. After dwelling units were selected, a field interviewer was sent to the dwelling unit to screen the residence. Failure to obtain the screening interview from eligible dwelling units represents the first type of nonresponse in the study. Sample weights (computed as the product of the first five components) were adjusted for this type of nonresponse using an exponential regression model. This procedure uses exponential regression to model the expected value of a zero-one response indicator, given a set of predictor variables available for both respondents and nonrespondents. In 1997, the potential predictor variables included the State indicator (Arizona, California, or remainder of the United States), NHSDA field supervisor designation, quarter of the year when interview(s) in the dwelling unit were conducted, region, population density of the sample segment (e.g., segment located in a metropolitan area with 1 million or more persons), type of dwelling unit (dormitory, other group quarters, or not group quarters), and other variables based on 1990 Census block and enumeration district characteristics, including percentage Hispanic, percentage black, percentage owner-occupied households, median housing value, and median rent. The NHSDA field supervisor designation variable identified the areas covered by each supervisor, and was included to adjust for differential nonresponse among the field supervisors. After obtaining the final models, the adjustment factor was calculated as the inverse of the estimated response propensity.

After this adjustment was completed, the final dwelling unit weight was calculated as the product of weight adjustment components (1-7) described above. This adjusted weight can be used to compute household-level estimates from the screener data. In addition, these seven weight factors become the first seven weight components of the final interview respondent sample weight. The remaining five weight components discussed below account for the person probability of selection for those people from whom an NHSDA interview wassought, as well as account for the person-level nonresponse and coverage errors resulting from the last stages of the sample design.

The probability of selecting a person is accounted for by the eighth and ninth weight components. A screening interview was considered complete only after a member of the unit told the field interviewer certain demographic information (age, race, gender, ethnicity, and marital status) about all survey eligible residents of the dwelling unit. A subset of these variables (race, ethnicity, and age group) was used to form demographic groups. One or two age groups were randomly selected using a race/ethnicity-specific sampling rate predetermined during the design of the 1997 study. The inverse of this rate, or the inverse of the probability of selecting a particular age group within the dwelling unit, represents the eighth weight component, the age group selection weight. Within any particular selected age group, if more than one occupant of a dwelling unit was classified in this group, then only one of these persons was randomly selected for interview. The ninth weight component represents the inverse of this probability of selection.

The tenth weight component was a weight trimming factor. To minimize the effect of extreme weights on the unequal weighting effect observed on the sample weights, computed using previous weight adjustment factors (1-9), the largest sample weights were truncated or "trimmed." To accomplish this weight trimming, maximum weight thresholds were determined within classes defined by design strata, race/ethnicity, and age group. If the sample weight for any respondent was greater than this threshold within each group, then this adjustment factor was set to bring the sample weight down to equal the threshold.

The eleventh weight component was a combined roster and person nonresponse adjustment. The sample weights of the interview respondents were adjusted to the weighted demographic distributions based on the full roster sample and the associated final weights for screened eligible dwellings. This adjustment was created using an exponential regression model. The variables considered for this adjustment included a State indicator, age group, race, region, quarter, gender, population density, Hispanic indicator, relationship of person to householder, marital status, group quarters, segment characteristics (such as percentage Hispanic, percentage black, percentage owner-occupied dwelling units, and combined rent/housing value).

The twelfth and final adjustment was a person poststratification adjustment. This adjustment forced weighted respondent sample data to equal specified control totals obtained from the Census Bureau's projections of the civilian noninstitutionalized population aged 12 or older. The main effect control totals used for person poststratification were State indicator, age group, gender, quarter, Hispanic indicator, and race. Various two-way (such as age group by gender) and three-way (such as age group, gender, and Hispanic indicator) control totals also were used.

One additional weight variable was constructed for the Arizona and California supplemental sample. Because the supplemental sample of Arizona and California was introduced into the sample starting in quarter 2 of the 1997 NHSDA, a person-level weight was constructed for quarters 2 through 4. The weight was set to zero for the first quarter, and set to 4/3 for quarters 2, 3, and 4. This adjustment correctly weighted up the quarters 2, 3, and 4 samples to represent the total population.

 

Table D.1 Final Stratum Definitions and Sample Sizes for the Full Sample
Stratum	Description of Stratum	Number of Segments Allocated
1	Certainty high Hispanic	128
2	Certainty moderate Hispanic	300
3	Certainty low Hispanic	452
4	Certainty high black, non-Hispanic	124
5	Certainty high non-black, non-Hispanic	72
6	Noncertainty high black, non-Hispanic	103
7	Noncertainty high non-black, non-Hispanic	261
8	Noncertainty remainder	500
National Total		1,940
9	Certainty Arizona low non-black, non-Hispanic	130
10	Certainty Arizona high non-black, non-Hispanic	202
11	Noncertainty Arizona remainder	126
Arizona State Supplement Total		458
12	Certainty California low non-black, non-Hispanic	137
13	Certainty California high non-black, non-Hispanic	125
14	Noncertainty California remainder	36
California State Supplement Total		298
Total		2,696