Generalized prediction intervals for BLUPs in mixed models

A prediction interval is derived for the BLUP (Best Linear Unbiased Predictor) in mixed models involving a single random effect of interest, using the generalized inference approach. The resulting prediction interval is referred to as a generalized prediction interval. The solution in the case of the simplest balanced random effects model is first derived to provide better insight into the approach. Extensions to the unbalanced case as well as to a general model are then provided. A simulation study is carried out to show the advantage of the proposed interval compared to the ML and REML based intervals available from widely used software packages such as SAS and R/S+. The estimated coverage probabilities show that the generalized prediction interval exhibits substantially better performance compared to ML and REML based intervals; the latter intervals were found to be highly conservative.