Simultaneous modelling of the Cholesky decomposition of several covariance matrices

Authors:
Mohsen Pourahmadi;Michael J. Daniels;Trevor Park
Affiliations:
Division of Statistics, Northern Illinois University, DeKalb, IL 60115, USA;Department of Statistics, University of Florida, Gainesville, FL 32611-8545, USA;Department of Statistics, University of Florida, Gainesville, FL 32611-8545, USA
Venue:
Journal of Multivariate Analysis
Year:
2007

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Abstract

A method for simultaneous modelling of the Cholesky decomposition of several covariance matrices is presented. We highlight the conceptual and computational advantages of the unconstrained parameterization of the Cholesky decomposition and compare the results with those obtained using the classical spectral (eigenvalue) and variance-correlation decompositions. All these methods amount to decomposing complicated covariance matrices into ''dependence'' and ''variance'' components, and then modelling them virtually separately using regression techniques. The entries of the ''dependence'' component of the Cholesky decomposition have the unique advantage of being unconstrained so that further reduction of the dimension of its parameter space is fairly simple. Normal theory maximum likelihood estimates for complete and incomplete data are presented using iterative methods such as the EM (Expectation-Maximization) algorithm and their improvements. These procedures are illustrated using a dataset from a growth hormone longitudinal clinical trial.