A two-part random-effects model for semicontinuous longitudinal data

A semicontinuous variable has a portion of responses equal to a single valu e (typically 0) and a continuous, often skewed, distribution among the rema ining values. In cross-sectional analyses, variables of this type may be de scribed by a pair of regression models; for example, a logistic model for t he probability of nonzero response and a conditional linear model for the m ean response given that it is nonzero. We extend this two-part regression a pproach to longitudinal settings by introducing random coefficients into bo th the logistic and the linear stages. Fitting a two-part random-effects mo del poses computational challenges similar to those found with generalized linear mixed models. We obtain maximum likelihood estimates for the fixed c oefficients and variance components by an approximate Fisher scoring proced ure based on high-order Laplace approximations. To illustrate, we apply the technique to data from the Adolescent Alcohol Prevention Trial, examining reported recent alcohol use for students in grades 7-11 and its relationshi ps to parental monitoring and rebelliousness.