A note on the use of Laplace's approximation for nonlinear mixed-effects models

Edward F. Vonesh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

116 Scopus citations

Abstract

The asymptotic properties of estimates obtained using Laplace's approximation for nonlinear mixed-effects models are investigated. Unlike the restricted maximum likelihood approach, e.g. Wolfinger (1993), here the Laplace approximation is applied only to the random effects of the integrated likelihood. This results in approximate maximum likelihood estimation. The resulting estimates are shown to be consistent with the rate of convergence depending on both the number of individuals and the number of observations per individual. Conditions under which the leading term Laplace approximation should be avoided are discussed.

Original languageEnglish (US)
Pages (from-to)447-452
Number of pages6
JournalBiometrika
Volume83
Issue number2
DOIs
StatePublished - 1996

Keywords

  • First-order method
  • Maximum likelihood
  • Nonlinear random effects

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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