Box-Cox Transformed Linear Mixed Models for Small-Area Estimation

• Activity Number: 445
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Shonosuke Sugasawa* and Tatsuya Kubokawa
• Companies: The University of Tokyo and The University of Tokyo
• Keywords: small area estimation ; Box-Cox transformation ; prediction interval ; consistency ; parametric bootstrap

Abstract

In this work, we consider inferences in linear mixed models when the observed values are transformed by the Box-Cox transformation, namely the Box-Cox transformed linear mixed models (BC-LMM) for positive valued and clustered data. We propose a simple and consistent estimating method for the transformation parameter. We also provide a procedure for estimating the whole parameters in the proposed model. Based on these estimators, we propose an empirical predictor of a linear combination of both fixed and random effects and second-order accurate prediction intervals for measuring uncertainty of the predictor. As an application of the proposed methodology, we focus on small area estimation. We investigate the proposed procedure through simulation experiments and empirical applications.