Unconstrained parametrizations for variance-covariance matrices

Statistics and Computing

Volumn 6, Issue 3, 1996, Pages 289-296

  Pinheiro, José C ^a   Bates, Douglas M ^b  

^a UNIVERSITY OF WISCONSIN MADISON   (United States)

^b University of Wisconsin Madison   (United States)

Author keywords

Cholesky factorization; Matrix logarithm; Unconstrained estimation; Variance covariance components estimation

Indexed keywords

EID: 21444460810     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF00140873     Document Type: Article

References (13)

1. Anderson, T. W., Olkin, I. and Underhill, L. G. (1987) Generation of random orthogonal matrices. SIAM Journal on Scientific and Statistical Computing, 8(4), 625-9.
2. Bates, D. M. and Watts, D. G. (1988) Nonlinear Regression Analysis and Its Applications. Wiley, New York.
3. Dennis, Jr., J. E. and Schnabel, R. B. (1983) Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice-Hall, Englewood Cliffs, NJ.
4. Jennrich, R. I. and Schluchter, M. D. (1986) Unbalanced repeated measures models with structural covariance matrices. Biometrics, 42(4), 805-20.
5. Jupp, D. L. B. (1978) Approximation to data by splines with free knots. SIAM Journal of Numerical Analysis, 15(2), 328-43.
6. Laird, N. M. and Ware, J. H. (1982) Random-effects models for longitudinal data. Biometrics, 38, 963-74.
7. Leonard, T. and Hsu, J. S. J. (1993) Bayesian inference for a covariance matrix. Annals of Statistics, 21, 1-25.
8. Lindstrom, M. J. and Bates, D. M. (1988) Newton-Raphson and EM algorithms for linear mixed-effects models for repeated-measures data. Journal of the American Statistical Association, 83, 1014-22.
9. Lindstrom, M. J. and Bates, D. M. (1990) Nonlinear mixed effects models for repeated measures data. Biometrics, 46, 673-87.
10. Pinheiro, J. C. (1994) Topics in Mixed Effects Models. PhD thesis, University of Wisconsin-Madison.
11. Pinheiro, J. C. and Bates, D. M. (1995) Model building for nonlinear mixed-effects models. Technical Report 91, Department of Biostatistics, University of Wisconsin-Madison.
12. Rao, C. R. (1973) Linear Statistical Inference and Its Applications, 2nd edn. Wiley, New York.
13. Thisted, R. A. (1988) Elements of Statistical Computing. Chapman & Hall, London.