A Further Study of Predictions in Linear Mixed Models

Abstract

This article is concerned with the prediction problems in linear mixed models (LMM). Both biased predictors and restricted predictors are introduced. It was found that the mean square error matrix (MSEM) of a predictor strongly depends on the MSEM of corresponding estimator of the fixed effects and precise formulas are obtained. As an application, we propose three new predictors to improve the best linear unbiased predictor (BLUP). The performance of the new predictors can be examined easily with the help of vast literature on the linear regression models (LM). We also illustrate our findings with a Monte Carlo simulation and a numerical example.

Keywords:

• Linear mixed model
• Best linear unbiased predictor
• Mean square error matrix
• Mixed predictor
• Biased predictor

Mathematics Subject Classification:

• Primary 62J99
• Secondary 62J99

Acknowledgments

The authors gratefully acknowledged the anonymous referees for their useful comments which enabled us to make this article more readable.

Additional information

Funding

The research was supported by National Natural Science Foundation of China (Grant No. 11171361) and Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110191110033).