Model-Based Adjustment

A model-based method of computing adjustments that would account for the changes in the NHSDA methodology was used for estimates of the use of the more prevalent drugs, including lifetime, past year, and past month use of alcohol, marijuana, cigarettes, and any illicit drug, as well as past month binge drinking and past month heavy drinking. The model that was used is based on a constrained exponential model originally proposed by Deville and Särndal (1992). Similar to the ratio adjustment, this method of adjusting previous estimates models the combined effect of all measurement error differences between the new and old methodologies. This model offers the primary advantages of allowing (a) a greater number of potentially significant explanatory variables in the adjustment and (b) bounding the resulting adjustment between predetermined thresholds. This a priori bounding eliminates extreme adjustments that might otherwise occur, particularly for small subpopulations. Additionally, the model-fitting procedure used to compute the adjustment forces the adjusted 1994-A estimates to equal the 1994-B estimates within the subpopulations represented by the dummy variables in the vector of model predictors. Mathematically, this model can be expressed as follows:



where the ratio adjustment R _I can be interpreted as



In equation (1), the constant A is simply a scale factor set equal to [U-L]/[ (1-L)(U-1)], beta are the model coefficients, and Xi is a vector of explanatory variables. The explanatory variables considered in the models consisted of the categorical indicator variables for age group and race/ethnicity. The parameters L and U are the predetermined constants that force the estimated Ri to be

Notice that if the constant L is set equal to zero and U approaches 4 , then the constant A approaches 1, and equation (1) reduces to the familiar, unconstrained exponential model:



The model parameter vector beta in (1) was estimated by solving the generalized raking equations:



 
subject to the constraints.

Notice from the above raking equations that the estimated adjustment R_i
forces the 1994-A estimate to equal the 1994-B estimate for any subpopulation represented by an indicator variable in Xi. Therefore, for example, if an appropriate indicator for the age group = 12 to 17 year olds was included in Xi, then the model-based estimate of the R_i's would produce an adjusted prevalence estimate using the 1994-A sample that exactly equaled the prevalence estimate generated from the 1994-B sample for the 12 to 17 age group.