Algorithms for the likelihood-based estimation of the random coefficient model

Statistics and Probability Letters

Volumn 32, Issue 2, 1997, Pages 189-199

  Shin, Chungyeol ^a   Amemiya, Yasuo ^a  

^a Iowa State University   (United States)

Author keywords

Maximum likelihood; Mixed effects; Proper covariance matrix estimate; REML

Indexed keywords

EID: 0031091901     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0167-7152(96)00072-7     Document Type: Article

References (26)

1. Amemiya, Y. (1985), What should be done when an estimated between-group covariance matrix is not nonnegative definite? The Amer. Statist. 39, 112-117.
2. Amemiya, Y. (1994), On multivariate mixed model analysis. Multivariate Analysis and Its Applications, IMS Lecture Notes, Monograph Ser. Vol. 24, pp. 83-95.
3. Anderson, B.M., T.W. Anderson and I. Olkin (1986), Maximum likelihood estimators and LR criteria in multivariate components of variance. The Ann. Statist. 14, 405-417.
4. Azzalini, A. (1987), Growth curve analysis for patterned covariance matrices, in: M.L. Puri, J.P. Vilaplana and W. Wertz, eds. New Perspectives in Theoretical and Applied Statistics (Wiley, New York) pp. 61-74.
5. Bhargava, A.K. and D. Disch (1982), Exact probabilities of obtaining estimated nonpositive definite between-group covariance matrices, J. Statist. Comput. and Simulation 15, 27-32.
6. Calvin, J.A. (1993), REML estimation in unbalanced multivariate variance components models using an EM algorithm, Biometrics 49, 691-701.
7. Carter, R.L. and M.C.K. Yang (1986), Large sample inference in random coefficient regression models, Commun. Statist. A, 15, 2507-2525.
8. Chi, E.M. and G.C. Reinsel (1989), Models for longitudinal data with random effects and AR(1) errors, JASA 84, 452-459.
9. Dempster, A.P., D.B. Rubin and R.K. Tsutakawa (1981), Estimations in covariance components models, JASA 76, 341-353.
10. Fuller, W.A. and R.M. Harter (1987), The multivariate components of variance model for small area estimation, in small area statistics, in: R. Platek, J.N.K. Rao, C.E. Sarnal and M.P. Singh, eds, An International Symposium, (Wiley, New York) pp. 103-123.
11. Goldstein, H. (1986), Multilevel mixed linear model analysis using iterative generalized least squares, Biometrika 73, 43-56.
12. Harville, D. (1977), Maximum likelihood approaches to variance component estimation and related problems, JASA 72, 320-340.
13. Hill, W.G. and R. Thompson (1978), Probabilities of non-positive definite between-group or genetic covariance matrics, Biometrics 34, 429-439.
14. Jennrich, R.I. and M.D. Schluchter (1986), Unbiased repeated measures models with structural covariance matrices, Biometrics 42, 805-820.
15. Laird, N.H. and J.H. Ware (1982), Random effects models for longitudinal data, Biometrics 38, 963-974.
16. Laird, N., N. Lange and D. Stram (1987), Maximum likelihood computations with repeated measures: Application of the EM algorithm, JASA 87, 97-105.
17. Lindstrom, M.J. and D.M. Bates (1988), Newton-Raphson and EM algorithm for linear mixed-effects model for repeated measures data, JASA 83, 1014-1022.
18. Liu, C. and D.B. Rubin (1994), The ECME algorithm: a simple extension of EM and ECM with faster monotone convergence, Biometrika 81, 633-648.
19. Potthoff, R.F. and S.N. Roy (1964), A generalized multivariate analysis of variance model useful especially for growth curve problems, Biometrika 51, 313-326.
20. Rao, C.R. (1965), The theory of least squares when the parameters are stochastic and its application to the analysis of growth curve, Biometrika 52, 447-458.
21. Remadi, S. and Y. Amemiya (1994), Asymptotic properties of the estimators for multivariate components of variance, J. Multivariate Anal. 49, 110-131.
22. Rochon, J. (1992), ARMA covariance structures with time heteroscedasticity for repeated measures experiments, JASA 87, 777-784.
23. Rochon, J. and R.W. Helms (1989), Maximum likelihood estimation for incomplete repeated-measures experiments under an ARMA covariance structure, Biometrics 45, 207-218.
24. Searle, S.R., G. Casella and C.E. McCulloch (1992), Variance Components (Wiley, New York).
25. Shin, C. (1995), On the multivariate random and mixed coefficient analysis, Ph.D. dissertation, Iowa State University, Ames, IA.
26. Shin, C. and Y. Amemiya (1995), Algorithms for the likelihood-based estimation of the random coefficient model, Preprint Series #95-15, Statistical Labarotory, Iowa State University, Ames, IA.