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

TL;DR

This paper introduces a novel estimation method combining ICF and EM algorithms to accurately estimate variance matrices with prescribed zeros in nonlinear mixed effects models, ensuring positive definiteness regardless of sample size.

Contribution

It presents a new approach that guarantees positive definite estimates for variance matrices with prescribed zero patterns without structural assumptions.

Findings

Provides positive definite estimates for any sample size

Does not rely on structural assumptions on the PPZ

Easily adaptable to various EM algorithm versions

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 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.