摘要：We discuss inference for repeated fractional data, with outcomes between 0 to 1, includ- ing positive probability masses on 0 and 1. The point masses at the boundaries prevent the routine use of logit and other commonly used transformations of (0, 1) data. We introduce a model augmentation with latent variables that allow for the desired positive probability at 0 and 1 in the model. A linear mixed e.ect model is imposed on the latent variables. We propose a Bayesian semiparametric model for the random e.ects distribu- tion. Speciˉcally, we use a Polya tree prior for the unknown random e.ects distribution. The proposed model can capture possible multimodality and skewness of random e.ect distribution. We discuss implementation of posterior inference by Markov chain Monte Carlo simulation. The proposed model is illustrated by a simulation study and a cancer study in dogs.
关键词：Fractional data ￠ Linear mixed model ￠ MCMC algorithm ￠ Polya tree;￠ Repeated measurement data ￠ Semiparametric Bayesian inference.
