Simultaneous modelling of the Cholesky decomposition of several covariance matrices

Mohsen Pourahmadi, Michael J. Daniels, Trevor H Park

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)568-587
Number of pages20
JournalJournal of Multivariate Analysis
Volume98
Issue number3
DOIs
StatePublished - Mar 1 2007
Externally publishedYes

Fingerprint

Cholesky Decomposition
Covariance matrix
Decomposition
Modeling
Growth Hormone
Variance Components
Incomplete Data
Expectation-maximization Algorithm
Maximum Likelihood Estimate
Clinical Trials
Parameterization
Parameter Space
Hormones
Regression
Iterative methods
Maximum likelihood
Eigenvalue
Iteration
Decompose

Keywords

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

ASJC Scopus subject areas

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

Cite this

Simultaneous modelling of the Cholesky decomposition of several covariance matrices. / Pourahmadi, Mohsen; Daniels, Michael J.; Park, Trevor H.

In: Journal of Multivariate Analysis, Vol. 98, No. 3, 01.03.2007, p. 568-587.

Research output: Contribution to journalArticle

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