Distribution-free Prediction Intervals in Mixed Linear Models

This paper considers prediction intervals for a future observation in the context of mixed linear models. For such prediction problems, it is reasonable to assume that the future observation is independent of the current ones. Our approach is distribution-free, that is, we do not assume that the distributions of the random effects and errors are normal or specified up to a finite number of parameters. We show that for standard mixed linear models, a simple method based on the (regression) residuals works well for constructing prediction intervals. For nonstandard mixed linear models, however, a more complicated method may have to be used, based on estimation of the distribution of the random effects. Simulation studies compare prediction intervals based on the ordinary least squares estimators and those based on the empirical best linear unbiased estimators. We apply the method to a data set regarding lead contamination of soil.