"Estimation and Prediction Intervals in Transformed Linear Mixed Models"

Sugasawa, Shonosuke and Tatsuya Kubokawa

For analyzing positive or bounded data, this paper suggests parametrically transformed nested error regression models (TNERM), which not only include the log-transformed model, but also adjust flexibly the transformation parameter to fit the data to a normal linear regression. Conditions on the transformation are derived for consistency of the maximum likelihood estimator for the transformation parameter. The conditions are satisfied by the dual power transformation for positive data and the dual power logistic transformation for bounded data. In order to calibrate uncertainty of the transformed empirical best linear unbiased predictor (TEBLUP), the paper derives prediction intervals with second-order accuracy based on the parametric bootstrap method. Conditional prediction intervals given data in the area of interest are also constructed. The proposed methods are investigated through simulation and empirical studies.