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REML estimation of variance parameters in nonlinear mixed effects models using the SAEM algorithm.

Cristian Meza1, Florence Jaffrézic, Jean-Louis Foulley

  • 1Laboratoire de Mathématiques, Université Paris-Sud, Bât. 425, 91405 Orsay Cedex, France. cristian.meza@math.u-psud.fr

Biometrical Journal. Biometrische Zeitschrift
|July 20, 2007
PubMed
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This study introduces a new REML method for nonlinear mixed effects models, improving accuracy in biometrical studies. The approach reduces bias and enhances individual profile predictions compared to traditional ML methods.

Area of Science:

  • Biometrics
  • Statistical Modeling

Background:

  • Nonlinear mixed effects models are crucial in biometrical studies like pharmacokinetics and growth trait analysis.
  • Maximum Likelihood (ML) estimation, commonly used, is known for downward bias.
  • Existing REML extensions for these models often rely on approximations.

Purpose of the Study:

  • To present an exact REML estimation scheme for nonlinear mixed effects models.
  • To implement this via a stochastic EM algorithm (SAEM).
  • To evaluate its performance against ML estimation.

Main Methods:

  • Developed an exact REML estimation procedure.
  • Integrated fixed effects and employed a stochastic estimation process.
  • Utilized the Stochastic Approximation Expectation-Maximization (SAEM) algorithm for implementation.

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Main Results:

  • The proposed REML method significantly reduced bias in variance parameter estimation compared to ML.
  • Residual mean squared error for variance parameters was notably decreased, especially in unbalanced data.
  • While fixed effect estimates were similar, REML improved individual profile predictions over ML.

Conclusions:

  • The presented REML implementation offers a less biased and more accurate estimation for nonlinear mixed effects models.
  • This method provides superior individual profile predictions, beneficial for applications like growth modeling in chickens.