Alternative REML Estimation of Covariance Matrices in Linear Mixed-Effects Models with No Assumption on Random Effects

• Activity Number: 659
• Type: Contributed
• Date/Time: Thursday, August 4, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Erning Li*+ and Mohsen Pourahmadi
• Companies: Texas A & M University and Texas A & M University
• Keywords: Restricted or Residual Maximum Likelihood (REML) ; Longitudinal Data ; General Normal Linear Models ; Covariance Matrices ; Cholesky Decomposition

Abstract

Specifying the distribution of random effects, the covariance structure of random effects and the covariance matrices of within-subject deviations are among some of the most challenging problems in various applications of mixed-effects models. We propose a procedure for estimating the two competing covariance matrices while making no distributional assumption on the random effects. The main strategy is an alternative REML approach, in which we eliminate the random effects using a suitable linear transformation of the response variable, in contrast to the conventional REML method for linear mixed-effects models that focuses on removing the dependence on fixed effects and requires normality on random effects, then we proceed the estimation of the within-subject covariance matrix as in the standard REML for general normal linear models. This approach makes it possible for the first time to disentangle the two covariances matrices and model them separately with minimal assumptions on linear mixed-effects models. We rely on the modified Cholesky decomposition (Pourahmadi, 1999) to formulate models for the covariance matrices to accommodate unconstrained parameterisation and regression.