A Two-Part Random-Effects Model for Semicontinuous Longitudinal Data

TLDR

Semicontinuous variables combine a point mass at zero with a skewed continuous distribution and are typically modeled by separate logistic and linear regressions, but extending this two‑part approach to longitudinal data introduces computational challenges similar to those in generalized linear mixed models. The study extends the two‑part regression model to longitudinal data by incorporating random coefficients in both the logistic and linear components. The authors estimate fixed effects and variance components via an approximate Fisher‑scoring algorithm using high‑order Laplace approximations, and illustrate the method on Adolescent Alcohol Prevention Trial data on students’ recent alcohol use and its links to parental monitoring and rebelliousness. Application to the trial data shows the model can capture associations between.

Abstract

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.