⁸See for example the discussion by Malec, D. (1966) "Model Based State Estimates form the National Health Interview Survey," in Schaible (1996) op.cit.

Footnote #9:

⁹The subscript s indicates that the factor is a function of direct sample data.

Footnote #10:

¹⁰This square bracketed term is the logistic regression analog of the linear survey regression estimators commonly treated in sampling texts (see for example, Sarndal, C., Swensson, B., and Wertman, J. (1991) Model Assisted Survey Sampling. New York: Springer-Verlag) and is the "direct" component of the composite estimator.

Footnote #11:

¹¹If this is not done, post-hoc adjustments are needed to force State estimates to agree with national estimates.

 Footnote #12:

¹²Breslow, NE and Clayton, DG (1993). "Approximate Inference in Generalized Linear Mixed Models," Journal of the American Statistical Association, Vol. 88, No. 421, 9-25.

 Footnote #13:

¹³Self-administered questionnaires ensure that the answers given by respondents to the highly sensitive questions on drug use are anonymous. This has been shown to increase the accuracy of reports of drug use, particularly for illicit substances. See, for example, Turner, CF, Lessler, JT, and Gfroerer, JC (1992). "Survey Measurement of Drug Use: Methodological Studies," DHHS Publication No. (ADM) 92-1929. See Aquilino, WS (1994) "Interview Mode Effects in Surveys of Drug and Alcohol Use: A Field Experiment," Public Opinion Quarterly. Vol. 58, 210-240.

Footnote #14:

¹⁴From Summary Tape File 3, 1990 Census of Population and Housing.

Footnote #15:

¹⁵Further information on these long form Census data can be found in the technical documentation for Summary Tape File #3 of the 1990 Census of Population and Housing as well as in the booklet "1990 Census of Population and Housing Tabulation and Publication Program" prepared by the U.S. Bureau of Census.

Footnote #16:

¹⁶Claritas, Inc., 201 N. Union St. Suite 200, Alexandria, VA., 22314-2645, (703) 683-8300.

¹⁷Full descriptions of all of the evaluations can be found in Folsom, et al. (1996) op.cit.

 Footnote #18:

¹⁸A discussion of methods for assessing the fit of logistic regression models can be found in Hosmer, D and Lemeshow, S. (1989) Applied Logistic Regression, New York: John Wiley & Sons.

Footnote #19:

¹⁹the evaluation subgroups are formed using the distribution of the predicted substance abuse prevalence rates. Using the model, the predicted values were calculated for each person in the sample. This represents the model predicted probability of the person using the particular substance in question. Then these predicted values were used to order the sample from highest to lowest and evaluation subsamples were formed by starting at the top and dividing the sample into 40 subsamples each of which contained 2.5 percent of the population. Thus, the entire sample is partitioned into evaluation subsamples which are predicted to have similar levels for the prevalence of substance abuse.

Footnote #20:

²⁰This prediction subsamples span the entire set of evaluation subgroups.

Footnote #21:

²¹This cross-validation approach is done to eliminate an undesired correlation between the predicted estimates and the direct estimates in the evaluation subgroups. A fuller explanation of why this was done is given in Folsom, et.al (1996) op.cit.

Footnote #22:

²²A modification of the Hosmer-Lemeshow goodness-of-fit statistic (Hosmer and Lemeshow, 1989) was used to take into account the complex sample design. A full description is given in Folsom, et al. (1996).

Footnote #23:

²³Due to the cost of computations, these tests were restricted to a single age group (26-34) and the six estimates shown in the table.

Footnote #24:

²⁴For example, in a study that predicted college performance using a number of characteristics one might find that for the particular sample used to construct the model, people with red-hair did better in college. However, this might be an artifact in that by chance a number of very smart people with red-hair were in the first sample. Thus, if the model was evaluated in another sample, including hair color in the model would result in predictions of higher performance for red-haired people and lower performance for those who did not have red hair with the results that the estimated performance would have more variability than actually exists.

Footnote #25:

²⁵In areas were there was a large NHSDA sample, the full SAE model will do better because the estimation method was constructed so that it would take maximum advantage of the highly precise direct estimate in the areas with large samples. This is a desirable property of composite small area estimators and is called "shrinkage."

 Footnote #26:

²⁶Rank correlations are calculated by ranking the states according to prevalence and calculating the correlation of the ranks.

Footnote #27:

²⁷The range ratios in Exhibits 4.3 – 4.6 are different from as those in Exhibit 4.2 because, for a particular state, the estimates are averages across all levels of prevalence, whereas, in Exhibit 4.2 we used artificial subpopulations which were constructed to have widely divergent prevalence rates.

Footnote #28:

²⁸Aquilino (1994) op.cit.

Footnote #29:

²⁹For example, the ratio of range across states in the prevalence of cigarette use to the national mean for the BRFSS is about 0.45 whereas for the NDATUS estimates of drug treatment this range is 3.15. Thus, for treatment information there is wide variability across states in a very low prevalence characteristic which makes it more difficult to model this variability using the set of predictors that were chosen for this study.

Footnote #30:

³⁰And additional information on these evaluations in Folsom (1996).