Estimation, prediction and interpretation of NGG random effects models: An application to Kevlar fibre failure times

We propose a class of Bayesian semiparametric mixed-effects models; its\r\ndistinctive feature is the randomness of the grouping of observations, which can be\r\ninferred from the data. The model can be viewed under a more natural perspective, as\r\na Bayesian semiparametric regression model on the log-scale; hence, in the original\r\nscale, the error is a mixture of Weibull densities mixed on both parameters by a\r\nnormalized generalized gamma random measure, encompassing the Dirichlet process.\r\nAs an estimate of the posterior distribution of the clustering of the random-effects\r\nparameters, we consider the partition minimizing the posterior expectation of a suitable\r\nclass of loss functions. As a merely illustrative application of our model we consider\r\na Kevlar fibre lifetime dataset (with censoring). We implement an MCMC scheme,\r\nobtaining posterior credibility intervals for the predictive distributions and for the\r\nquantiles of the failure times under different stress levels. Compared to a previous\r\nparametric Bayesian analysis, we obtain narrower credibility intervals and a better\r\nfit to the data. We found that there are three main clusters among the random-effects\r\nparameters, in accordance with previous frequentist analysis.