Modelling occurrence and quantity of longitudinal semicontinuous data simultaneously with nonparametric unobserved heterogeneity

Semicontinuous data frequently occur in longitudinal studies. The popular two-part modelling approach deals with longitudinal semicontinuous data by analyzing the occurrence of positive values and the intensity of positive values separately; however, this separation may break down the natural sequence of semicontinuous data within a subject and destroy its serial dependence structure. In this article, we introduce a Tweedie compound Poisson mixed model to study the occurrence of positive values and the quantity of the semicontinuous response simultaneously. In our approach, covariate effects on the semicontinuous response are assessed directly. The correlation within a subject and the unobserved heterogeneity are incorporated with serially correlated nonparametric random effects. Our model unifies subject-specific and population-averaged interpretations. We illustrate the approach with applications to a Brief Symptom Inventory study and an infants' fluoride intake study.