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 personk belonging to age groupa in substate regionj of Statei. The x sub a, i, j, k denotes a vector of auxiliary variables associated with age groupa, 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 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 2.
The logit of pi hat sub w is equivalent to the logarithm of pi hat sub w divided by the quantity 1 minus pi hat sub w, which is equal to the sum of the following three quantities: negative 4.7500, the product of 0.2098 and capital X sub k, and the product of 0.3839 and capital X sub w.
Return to equation 3.
The logit of pi hat sub s is equal to the sum of the following three quantities: negative 4.4924, the product of 0.2960 and capital X sub k, and the product of 0.2242 and capital X sub s.
Return to equation 4.
Pi hat sub w 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 three quantities: negative 4.7500, the product of 0.2098 and capital X sub k, and the product of 0.3839 and capital X sub w.
Return to equation 5.
Pi hat sub s 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 three quantities: negative 4.4924, the product of 0.2960 and capital X sub k, and the product of 0.2242 and capital X sub s.
Return to equation 6.
