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

SUMMARY 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 appiled only to the random effects of the integ...

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Bibliographic Details
Published in:Biometrika 1996-06, Vol.83 (2), p.447-452
Main Author: Vonesh, Edward F.
Format: Article
Language:English
Subjects:
Approximation
Biometrics
Consistent estimators
Covariance matrices
Drug design
Exact sciences and technology
First-order method
Least squares
Linear inference, regression
Mathematics
Maximum likelihood
Maximum likelihood estimation
Maximum likelihood estimators
Miscellanea
Nonlinear random effects
Pharmacokinetics
Probability and statistics
Sciences and techniques of general use
Statistical variance
Statistics
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Summary:SUMMARY 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 appiled 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.
ISSN:0006-3444
1464-3510
DOI:10.1093/biomet/83.2.447