Growth mixture modeling with non-normal distributions.

A limiting feature of previous work on growth mixture modeling is the assumption of normally distributed variables within each latent class. With strongly non-normal outcomes, this means that several latent classes are required to capture the observed variable distributions. Being able to relax the assumption of within-class normality has the advantage that a non-normal observed distribution does not necessitate using more than one class to fit the distribution. It is valuable to add parameters representing the skewness and the thickness of the tails. A new growth mixture model of this kind is proposed drawing on recent work in a series of papers using the skew-t distribution. The new method is illustrated using the longitudinal development of body mass index in two data sets. The first data set is from the National Longitudinal Survey of Youth covering ages 12-23 years. Here, the development is related to an antecedent measuring socioeconomic background. The second data set is from the Framingham Heart Study covering ages 25-65 years. Here, the development is related to the concurrent event of treatment for hypertension using a joint growth mixture-survival model.