A hybrid estimator in nonlinear and generalised linear mixed effects models

Biometrika

Volumn 90, Issue 4, 2003, Pages 859-879

  Lai, Tze Leung ^a   Shih, Mei Chiung ^b  

^a STANFORD UNIVERSITY   (United States)

^b HARVARD SCHOOL OF PUBLIC HEALTH   (United States)

Author keywords

Laplace's method; Large sample theory; Mixed effects model; Monte Carlo integration; Sandwich variance estimator

Indexed keywords

EID: 3843119702     PISSN: 00063444     EISSN: None     Source Type: Journal    
DOI: 10.1093/biomet/90.4.859     Document Type: Article

References (32)

1. BEAL, S. L. & SHEINER, L. B. (1992). NONMEM User's Guide. University of California, San Francisco: NONMEM Project Group.
2. BRESLOW, N. E. & CLAYTON, D. G. (1993). Approximate inference in generalised linear mixed models. J. Am. Statist. Assoc. 88, 9-25.
3. CHOW, Y. S. & TEICHER, H. (1988). Probability Theory, 2nd ed. New York: Springer.
4. CROWDER, M. J. (1978). Beta-binomial ANOVA for proportions. Appl. Statist. 27, 34-7.
5. DAVIDIAN, M. & GILTINAN, D. M. (1995). Nonlinear Models for Repeated Measurement Data. New York: Chapman and Hall.
6. DEMIDENKO, E. (1997). Asymptotic properties of nonlinear mixed-effects models. In Modeling Longitudinal and Spatially Correlated Data: Methods, Applications and Future Directions, Ed. T. G. Gregoire et al., pp. 49-62. New York: Springer.
7. GELMAN, A., BOIS, F. & JIANG, J. (1996); Physiological pharmacokinetic analysis using population modeling and informative prior distributions. J. Am. Statist. Assoc. 91, 1400-12.
8. GEYER, C. J. & THOMPSON, E. A. (1992). Constrained maximum likelihood for dependent data (with Discussion). J. R. Statist. Soc. B 39, 657-99.
9. HENDERSON, C. R. (1975). Best linear unbiased estimation and prediction under a selection model. Biometrics 31, 423-48.
10. HOADLEY, B. (1971). Asymptotic properties of maximum likelihood estimators for the independent not identically distributed case. Ann. Math. Statist. 42, 1977-91.
11. JOHANSEN, S. (1984). Functional Relations, Random Coefficients and Nonlinear Regression with Application to Kinetic Data. New York: Springer.
12. KUK, A. Y. C. & CHENG, Y. W. (1999). Pointwise and functional approximations in Monte Carlo maximum likelihood estimation. Statist. Comp. 9, 91-9.
13. LAI, T. L. & SHIH, M. C. (2003). Nonparametric estimation in nonlinear mixed effects models. Biometrika 90, 1-13.
14. LEE, L. F. (1992). On efficiency of methods of simulated moments and maximum simulated likelihood estimation of discrete response models. Economet. Theory 8, 518-52.
15. LEE, L. F. (1995). Asymptotic bias in simulated maximum likelihood estimation of discrete choice models. Economet Theory 11, 437-83.
16. LEE, Y. & NELDER, J. A. (1996). Hierarchical generalized linear models (with Discussion). J. R. Statist. Soc. B 58, 619-78.
17. LINDSTROM, M. J. & BATES, D. M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics 46, 673-87.
18. MCCULLOCH, C. E. (1997). Maximum likelihood algorithms for generalized linear mixed models. J. Am. Statist. Assoc. 92, 162-70.
19. MCFADDEN, D. (1989). A method of simulated moments for estimation of discrete response models without numerical integration. Econometrica 57, 995-1026.
20. MÜLER, P. & ROSNER, G. L. (1997). A Bayesian population model with hierarchical mixture priors applied to blood count data. J. Am. Statist. Assoc. 92, 1279-92.
21. NEUHAUS, J. M., HAUCK, W. W. & KALBFLEISCH, J. D. (1992). The effects of mixture distribution misspecification when fitting mixed-effects logistic models. Biometrika 79, 755-62.
22. NEUHAUS, J. M., KALBFLEISCH, J. D. & HAUCK, W. W. (1994). Conditions for consistent estimation in mixed-effects models for binary matched-pairs data. Can. J. Statist. 22, 139-48.
23. PAKES, A. & POLLARD, D. (1989). Simulation and asymptotics of optimization estimators. Econometrica 51, 1027-57.
24. PINHEIRO, J. C. & BATES, D. M. (1995). Approximations to the log-likelihood function in the nonlinear mixed-effects model. J. Comp. Graph, Statist. 4, 12-35.
25. PRESS, W. H., TEUKOLAKV, S. A., VETTERLING, W. T. & FLANNERY, B. P. (1992). Numerical Recipes in C. The Art of Scientific Computing, 2nd ed. Cambridge University Press.
26. QUINTANA, F. A., LIU, J. S. & DEL PINO, G. E. (1999). Monte Carlo EM with importance reweighting and its applications in random effects models. Comp. Statist. Data Anal. 29, 429-44.
27. SHEINER, L. B. & BEAL, S. L. (1980). Evaluation of methods for estimating population pharmacokinetic parameters. I. Michaelis-Menten model: Routine pharmacokinetic data. J. Pharmacokin. Biopharm. 8, 553-71.
28. VONESH, E. F. (1996). A note on the use of Laplace's approximation for nonlinear mixed-effects models. Biometrika 83, 447-52.
29. WAKEFIELD, J. & BENNETT, J. (1996). The Bayesian modeling of covariates for population pharmacokinetic models. J. Am. Statist. Assoc. 91, 917-27.
30. WAKEFIELD, J. C., SMITH, A. F. M., RACINE-POON, A. & GELFAND, A. E. (1994). Bayesian analysis of linear and nonlinear population models by using the Gibbs sampler. Appl. Statist. 43, 201-21.
31. WOLFINGER, R. (1993). Laplace's approximation for nonlinear mixed models. Biometrika 80, 791-5.
32. ZEGER, S. L. & KARIM, M. R. (1991). Generalized linear models with random effects: a Gibbs sampling approach. J. Am. Statist. Assoc. 86, 79-86.