Maximum likelihood estimation in nonlinear mixed effects models. (English) Zbl 1429.62279

Summary: A stochastic approximation version of EM for maximum likelihood estimation of a wide class of nonlinear mixed effects models is proposed. The main advantage of this algorithm is its ability to provide an estimator close to the MLE in very few iterations. The likelihood of the observations as well as the Fisher Information matrix can also be estimated by stochastic approximations. Numerical experiments allow to highlight the very good performances of the proposed method.


62J02 General nonlinear regression
62F10 Point estimation


Full Text: DOI


[1] Concordet, D.; Nunez, O.G., A simulated pseudo-maximum likelihood estimator for nonlinear mixed models, Comput. statist. data anal., 39, 2, 187-201, (2002) · Zbl 1132.62337
[2] Delyon, B.; Lavielle, M.; Moulines, E., Convergence of a stochastic approximation version of the EM algorithm, Ann. statist., 27, 1, 94-128, (1999) · Zbl 0932.62094
[3] Dempster, A.P.; Laird, N.M.; Rubin, D.B., Maximum likelihood from incomplete data via the EM algorithm, J. roy. statist. soc. ser. B, 39, 1, 1-38, (1977), (with discussion) · Zbl 0364.62022
[4] Kuhn, E.; Lavielle, M., Coupling a stochastic approximation version of EM with a MCMC procedure, ESAIM probability and statistics, 8, 115-131, (2004) · Zbl 1155.62420
[5] Lavielle, M.; Moulines, E., A simulated annealing version of the EM algorithm for non-Gaussian deconvolution, Statist. comput., 7, 4, 229-236, (1997)
[6] Louis, T.A., Finding the observed information matrix when using the EM algorithm, J. roy. statist. soc. ser. B, 44, 2, 226-233, (1982) · Zbl 0488.62018
[7] Pinheiro, J.C.; Bates, D.M., Mixed-effects models in S and S-PLUS, (2000), Springer Berlin · Zbl 0953.62065
[8] Racine-Poon, A., A Bayesian approach to nonlinear random effects models, Biometrics, 41, 4, 1015-1023, (1985) · Zbl 0655.62102
[9] Sheiner, L.; Hashimoto, Y.; Beal, S., A simulation study comparing designs for dose ranging, Statist. med., 10, 303-321, (1991)
[10] Vonesh, E.F., A note on the use of Laplace’s approximation for nonlinear mixed-effects models, Biometrika, 83, 2, 447-452, (1996) · Zbl 0878.62019
[11] Wakefield, J., The Bayesian analysis of population pharmacokinetic models, J. amer. statist. assoc., 91, 433, 62-75, (1996) · Zbl 0925.62474
[12] Wakefield, J.; Smith, A.; Racine-Poon, A.; Gelfand, A., Bayesian analysis of linear and nonlinear population models by using the Gibbs sampler, J. roy. stat. soc. ser. C, 43, 1, 201-221, (1994) · Zbl 0825.62410
[13] Walker, S., An EM algorithm for nonlinear random effects models, Biometrics, 52, 3, 934-944, (1996) · Zbl 0868.62058
[14] Wei, G.C.G.; Tanner, M.A., A Monte Carlo implementation of the EM algorithm and the poor’s Man’s data augmentation algorithms, J. amer. statist. assoc., 85, 411, 699-704, (1990)
[15] Wu, C.-F.J., On the convergence properties of the EM algorithm, Ann. statist., 11, 1, 95-103, (1983) · Zbl 0517.62035
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.