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Parameter expansion for estimation of reduced rank covariance matrices (Open Access publication)

By Karin Meyer


Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by restricted maximum likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme

Topics: Review
Publisher: BioMed Central
OAI identifier:
Provided by: PubMed Central

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  7. (1997). Acceleration of the EM algorithm using QuasiNewton methods,
  8. Advances in methodology for random regression analyses,
  9. (1995). ComputingmodifiedNewton directionsusing a partialCholeskyfactorization,SIAM
  10. (1993). Conjugate gradient acceleration of the EM algorithm,
  11. (2004). Convex Optimization,
  12. (2005). Estimation of quantitative genetic parameters,
  13. (1986). Estimation of variance components: What is missing in the EM algorithm?
  14. (1984). Estimation of variances and covariances under multiple trait models,
  15. (1998). Fast EM-type implementations for mixed-effects models,
  16. (2000). Fitting mixed-effects models using efficient EM-type algorithms,
  17. (1993). Genetic parameters for growth traits of Australian beef cattle from a multi-breed selection experiment,
  18. (1997). Harville D.A.,Matrix Algebrafroma Statistician’s Perspective,SpringerVerlag,
  19. (1977). Maximum likelihood approaches to variance component estimation and related problems,
  20. (1987). Maximum likelihood computations with repeated measures:
  21. (1977). Maximum likelihood from incomplete data via the EM algorithm,
  22. MeyerK.,Geneticprincipalcomponentsforliveultra-soundscan traitsofAngus cattle,
  23. (1988). Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data,
  24. (1976). Newton-Raphson and related algorithms for maximum likelihood variance component estimation,
  25. (1996). Numericalmethodsfor UnconstrainedOptimization and Nonlinear Equations,
  26. (1999). NumericalOptimization,SpringerSeriesin Operations Research,
  27. (1998). Parameter expansions to accelerate EM: The PX-EM algorithm,
  28. (2004). Perspectives of ANOVA, REML and a general linear mixed model, in:
  29. (2006). PX × AI: algorithmics for better convergence in restricted maximum likelihood estimation,
  30. (2000). Random regressions to model phenotypic variation in monthly weights of Australian beef cows,
  31. (1996). Restricted maximum likelihood estimation for animal models using derivatives of the likelihood,
  32. (1998). Restricted maximum likelihood estimation of covariance components in sparse linear models,
  33. (2005). Restricted maximum likelihood estimation of genetic principal components and smoothed covariance matrices,
  34. (2004). Simplified analysis of complex phenotypes: Direct estimation of genetic principal components,
  35. (1997). The EM algorithm and extensions,
  36. (1997). The EM algorithm- an old folk-songsung to a new fast tune,
  37. (2000). The PX-EM algorithm for fast stable fitting of Henderson’s mixed model,
  38. (1986). Unbalanced repeated-measures models with structured covariance matrices,
  39. (1996). Unconstrained parameterizations for variancecovariance matrices,

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