Abstract

Abstract

I will talk about mixture median and quantile models for describing latent growth curves of longitudinal outcomes. The models exhibit the different latent classes of evolution of the underlying outcome process. The mixture median model can be used as a robust alternative to the Gaussian likelihood based latent class model for skewed data, and the quantile models provide a complete regression picture for investigating the latent class structure at different quantiles. The within-subject correlation is incorporated by a marginal approach based on the idea of weighting. The weighted estimating equations for the model parameters are given, and the asymptotic distribution of the resultant estimates is established to approximate the standard errors of the parameter estimates. A penalized weighted loss function is defined to select the optimal number of latent classes. The proposed methods are illustrated with data from 418 arthritis patients recruited between 1990-1994.