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

A semicontinuous variable has a portion of responses equal to a single value (typically 0) and a continuous, often skewed, distribution among the remaining values. In cross-sectional analyses, variables of this type may be described by a pair of regression models; for example, a logistic model for the probability of nonzero response and a conditional linear model for the mean response given that it is nonzero. We extend this two-part regression approach to longitudinal settings by introducing random coefficients into both the logistic and the linear stages. Fitting a two-part random-effects model poses computational challenges similar to those found with generalized linear mixed models. We obtain maximum likelihood estimates for the fixed coefficients and variance components by an approximate Fisher scoring procedure 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 relationships to parental monitoring and rebelliousness.