Affordable Access

Publisher Website

Simultaneous modelling of the Cholesky decomposition of several covariance matrices

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Publication Date
Volume
98
Issue
3
Identifiers
DOI: 10.1016/j.jmva.2005.11.002
Keywords
  • Common Principal Components
  • Longitudinal Data
  • Maximum Likelihood Estimation
  • Missing Data
  • Spectral Decomposition
  • Variance–Correlation Decomposition
Disciplines
  • Computer Science
  • Mathematics

Abstract

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.

There are no comments yet on this publication. Be the first to share your thoughts.