A note on the use of Laplace's approximation for nonlinear mixed-effects models

Biometrika

Volumn 83, Issue 2, 1996, Pages 447-452

  Vonesh, Edward F ^a  

^a BAXTER HEALTHCARE CORPORATION   (United States)

Author keywords

First order method; Maximum likelihood; Nonlinear random effects

Indexed keywords

EID: 0000474486     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/83.2.447     Document Type: Article

References (15)

1. BARNDORFF-NIELSEN, O. E. (1983). On a formula for the distribution of the maximum likelihood estimator. Biometrika 70, 343-65.
2. BEAL, S. L. & SHEINER, L. B. (Ed.) (1992). NONMEM User's Guide. University of California, San Francisco: NONMEM Project Group.
3. BRESLOW, N. E. & CLAYTON, D. G. (1993). Approximate inference in generalized linear mixed models. J. Am. Statist. Assoc. 88, 9-25.
4. COX, D. R. & REID, N. (1987). Parameter orthogonality and approximate conditional inference (with Discussion). J. R. Statist. Soc. B 49, 1-39.
5. DAVIDIAN, M. & GILTINAN, D. M. (1993). Some simple methods for estimating intra-individual variability in nonlinear mixed effects models. Biometrics 49, 59-73.
6. LINDSTROM, M. J. & BATES, D. M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics 46, 673-87.
7. PRENTICE, R. L. & ZHAO, L. P. (1991). Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics 47, 825-39.
8. RACINE-POON, A. (1985). Bayesian approach to nonlinear random effects models. Biometrics 41, 1015-23.
9. SHEINER, L. B. & BEAL, S. L. (1980). Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-Menten model: routine clinical pharmacokinetic data. J. Pharmacokin. Biopharmac. 8, 553-71.
10. SHEINER, L. B. & BEAL, S. L. (1985). Pharmacokinetic parameter estimates from several least squares procedures: superiority of extended least squares. J. Pharmacokin. Biopharmac. 13, 185-201.
11. SOLOMON, P. J. & COX, D. R. (1992). Nonlinear component of variance models. Biometrika 79, 1-11.
12. STIRATELLI, R., LAIRD, N. M. & WARE, J. H. (1984). Random-effects models for serial observations with binary response. Biometrics 40, 961-71.
13. VONESH, E. F. (1992). Nonlinear models for the analysis of longitudinal data. Statist. Med. 11, 1929-54.
14. VONESH, E. F. & CARTER, R. L. (1992). Mixed-effects nonlinear regression for unbalanced repeated measures. Biometrics 48, 1-17.
15. WOLFINGER, R. (1993). Laplace's approximation for nonlinear mixed models. Biometrika 80, 791-5.