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

Authors:
Djalil Chafaï;Didier Concordet
Affiliations:
UMR181, INRA, ENVT, Toulouse CEDEX 3, France 31076 and UMR CNRS 5219, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse CEDEX 9, France 31062;UMR181, INRA, ENVT, Toulouse CEDEX 3, France 31076 and UMR CNRS 5219, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse CEDEX 9, France 31062
Venue:
Statistics and Computing
Year:
2009

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Abstract

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 of 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 concerning the PPZ. It can be easily adapted to many versions of EM.