Simultaneous modelling of the Cholesky decomposition of several covariance matrices

Mohsen Pourahmadi, Michael J. Daniels, Trevor Park

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)568-587
Number of pages20
JournalJournal of Multivariate Analysis
Issue number3
StatePublished - Mar 2007
Externally publishedYes


  • Common principal components
  • Longitudinal data
  • Maximum likelihood estimation
  • Missing data
  • Spectral decomposition
  • Variance-correlation decomposition

ASJC Scopus subject areas

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty


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