Drug Use and Health: Guide to Substate

Tables and Summary of Small Area

Estimation Methodology

The model is given by the equation: log of pi sub a, i, j, k divided by 1 minus pi sub a, i, j, k and is equal to the sum of three terms. The first term is given by x transpose sub a, i, j, k times beta sub a. The second term is eta sub a, i. And the third term is nu sub a, i, j. Here, pi sub a, i, j, k is the probability of engaging in the behavior of interest by person-k belonging to age group-a in substate region-j of State-i. The x sub a, i, j, k denotes a vector of auxiliary variables associated with age group-a, and the beta sub a denotes the associated vector of regression parameters. The eta sub a, i and the nu sub a, i, j denote, respectively, the vectors of random effects at the State and substate region levels.

Return to equation B.1-1.

The average annual incidence rate is calculated as the number of marijuana initiates in the past 24 months times 0.5, divided by the number of marijuana initiates in the past 24 months times 0.5 plus the number of persons who have never used marijuana. This rate is then multiplied by 100 to get a percentage.

Return to equation B.8-1.

The logit of pi hat is equivalent to the logarithm of pi hat divided by the quantity 1 minus pi hat, which is equal to the sum of the following six quantities: negative 5.972664, the product of 0.0873416 and capital X sub k, the product of 0.3385193 and capital X sub w, the product of 1.9552664 and capital X sub s, the product of 1.1267330 and capital X sub m, and the product of 0.1059137 and capital X sub a.

or

Pi hat is equal to the ratio of two quantities. The numerator is 1. The denominator is 1 plus e raised to the negative value of the sum of the following six quantities: negative 5.972664, the product of 0.0873416 and capital X sub k, the product of 0.3385193 and capital X sub w, the product of 1.9552664 and capital X sub s, the product of 1.1267330 and capital X sub m, and the product of 0.1059137 and capital X sub a.

Return to equation (1).

The logit of pi hat is equivalent to the logarithm of pi hat divided by the quantity 1 minus pi hat, which is equal to the sum of the following five quantities: negative 5.7736246, the product of 0.1772067 and capital X sub k, the product of 1.8392433 and capital X sub s, the product of 1.6428623 and capital X sub m, and the product of 0.1231266 and capital X sub a.

or

Pi hat is equal to the ratio of two quantities. The numerator is 1. The denominator is 1 plus e raised to the negative value of the sum of the following five quantities: negative 5.7736246, the product of 0.1772067 and capital X sub k, the product of 1.8392433 and capital X sub s, the product of 1.6428623 and capital X sub m, and the product of 0.1231266 and capital X sub a.

Return to equation (2).