A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models

Djalil Chafai (1, 2) , Didier Concordet (1, 2)

1 UPTE - Physiopathologie et Toxicologie Expérimentales
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We propose a new method for the Maximum Likelihood Estimator (MLE) of nonlinear mixed effects models when the variance matrix of Gaussian random effects has a prescribed pattern of zeros (PPZ). The method consists in coupling the recently developed Iterative Conditional Fitting (ICF) algorithm with the Expectation Maximization (EM) algorithm. It provides positive definite estimates for any sample size, and does not rely on any structural assumption on the PPZ. It can be easily adapted to many versions of EM.

Mots clés: Maximum likelihood; Mixed effects models; EM algorithm; Parametric estimation; ICF algorithm; Stuctured covariance matrix

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Djalil Chafai, Didier Concordet. A new method for the estimation of variance matrix with prescribed zeros in nonlinear mixed effects models. Statistics and Computing, 2009, 19 (2), pp.129-138. ⟨10.1007/s11222-008-9076-9⟩. ⟨hal-00169189v2⟩