Sugasawa, Shonosuke and Tatsuya Kubokoawa

The Box-Cox transformation is applied to linear mixed models for analyzing positive and clustered data. The problem is that the maximum likelihood estimator of the transformation parameter is not consistent. To fix it, we suggest a simple and consistent estimator for the transformation parameter based on the moment method. The consistent estimator is used to construct consistent estimators of the parameters involved in the model and to provide an empirical predictor of a linear combination of both fixed and random effects. Second-order accurate prediction intervals for measuring uncertainty of the predictor are derived. Finally, the performance of the proposed procedure is investigated through simulation and empirical studies.