Statistical Modelling 7 (2007), 4971
Modelling conditional covariance in the linear mixed model
Jianxin Pan
School of Mathematics,
University of Manchester,
England
Gilbert MacKenzie
Centre of Biostatistics,
University of Limerick,
Ireland
eMail:
gilbert.mackenzie@ul.ie
Abstract:
We provide a data-driven method for modelling the conditional,
within-subject covariance matrix arising in linear mixed models
(Laird and Ware, 1982). Given an agreed structure for the
between-subject covariance matrix we use a regression equation
approach to model the within-subject covariance matrix.
Using an EM algorithm we estimate all of the parameters in
the model simultaneously and obtain analytical expressions for
the standard errors. By re-analyzing Kenward's (1987) cattle
data, we compare our new model with classical menu-selection-based
modelling techniques, demonstrating its superiority using the
Bayesian Information Criterion. We also conduct a simulation
study, which confirms our observational findings. The paper
extends our previous covariance modeling work
(Pan and MacKenzie, 2003, 2006) to the conditional
covariance space of the linear mixed model (LMM).
Keywords:
Cholesky decomposition; conditional covariance; EM algorithm;
joint mean-covariance models; linear mixed models;
longitudinal data
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