  This paper suggests parametrically transformed nested error regression models
(TNERM), which transform the data flexibly to follow the normal linear mixed
regression. We provide a procedure for estimating consistently the parameters
of the proposed model and a predictor based on the consistent estimators. Then,
in order to calibrate uncertainty of the transformed empirical best linear
unbiased predictor, we derive prediction intervals with second-order accuracy
based on the parametric bootstrap method. The proposed methods are investigated
through simulation and empirical studies.
