Bayesian nonparametric hypothesis testing for longitudinal data analysis

Abstract

A Bayesian nonparametric procedure for longitudinal data analysis is proposed. The procedure simultaneously tests for the effects in the mean structure preserving the main effects when interactions are present. The method is highly flexible in that it does not assume a particular distribution for the errors and random effects, as is usually done in longitudinal data analysis. The correlation between the repeated measurements is captured via a Markovian time-dependent Dirichlet process mixture. Specifically, when this latter is represented via a species sampling model with stick-breaking weights, the effect of predictors is driven by the underlying atoms, and the time evolution driven by time-dependent weights. The performance of the proposed method is illustrated using both simulated and real data sets.