Restricted Maximum Likelihood Approaches for Linear Mixed Models: AREML and BREML

• Activity Number: 495
• Type: Contributed
• Date/Time: Wednesday, August 3, 2016 : 8:30 AM to 10:20 AM
• Sponsor: Biometrics Section
• Author(s): Erning Li* and Dale Zimmerman
• Companies: University of Iowa and University of Iowa
• Keywords: REML ; Linear Mixed Model ; Covariance Matrices ; Likelihood ; Estimating Equations ; Asymptotic Normality

Abstract

We investigate the properties of the alternative restricted maximum likelihood estimator (aREML, Li and Pourahmadi, 2013, Statistics and Probability Letters 83, 1071-1077) for within-subject measurement error covariance matrices in linear mixed models. We also propose a variant to the aREML. The proposed likelihood function focuses on parameters in within-subject measurement error covariances and is free of both fixed and random effects (hence we call this new approach bREML), leading to parameter space dimension reduction and computational benefits. No distributional assumption on random effects needs to be imposed. We compare the properties of the aREML and bREML to competing methods including full-maximum likelihood and conventional REML. We show that the aREML and bREML estimating equations are unbiased. The aREML and bREML estimators are asymptotically normal under suitable regularity conditions. We evaluate these methods via simulations and application.