An algorithm for restricted maximum likelihood estimation in balanced multivariate variance components models

James Arthur Calvin

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Restricted maximum likelihood (REML) estimation of variance components in multivariate linear models is a computationally intensive task. Calvin and Dykstra (1991a) have developed a general maximum likelihood estimation algorithm for a product of Wishart densities when the parameter matrices of the Wishart distributions follow a partial order of the Lowner type (Lowner, 1934). The algorithm is iterative in nature and does not require the computation of derivatives. It is guaranteed to converge to the correct solution and, for an important class of models, can be applied to the problem of REML estimation of variance components. In this paper, we define the class of models for which the algorithm is applicable. This class includes all two-factor models and all nested models as special cases. We also relate the general algorithm to the problem of REML estimation for balanced multivariate variance components models. An implementation is supplied in the Appendix and computational aspects of the algorithm are also discussed.

Original languageEnglish (US)
Pages (from-to)233-246
Number of pages14
JournalJournal of Statistical Computation and Simulation
Volume40
Issue number3-4
DOIs
StatePublished - Apr 1 1992

Keywords

  • Isotonic regression. Fenchel duality
  • REML
  • multivariate linear model

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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