Large Modelling Conditional Covariance in the Linear Mixed Model

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					Large Modelling Conditional Covariance in the Linear Mixed Model Jianxin Pan and Gilbert MacKenzie May 2006

MIMS EPrint: 2006.76

Manchester Institute for Mathematical Sciences School of Mathematics The University of Manchester

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ISSN 1749-9097

Large Modelling Conditional Covariance in the Linear Mixed Model
Jianxin Pan & Gilbert MacKenzie
First version: 6 January 2006

Research Report No. 1, 2006, Probability and Statistics Group School of Mathematics, The University of Manchester

Modelling Conditional Covariance in the Linear Mixed Model
Jianxin Pan
1

School of Mathematics, University of Manchester, UK

and Gilbert MacKenzie
Department of Mathematics and Statistics, University of Limerick, Ireland Summary. 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 (BIC). We also conduct a simulation study which confirms our observational findings. The paper extends our previous covariance modelling 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.

1 Address for correspondence: Dr. Jianxin Pan, School of Mathematics, University of Manchester, PO Box 88, Sackville Street, Manchester M60 1QD, UK. Email: jianxin.pan@manchester.ac.uk

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