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Biometrika 1996 83(2):447-452; doi:10.1093/biomet/83.2.447
© 1996 by Biometrika Trust
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MISCELLANEA

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

EDWARD F. VONESH

Applied Statistics Center, Baxter Healthcare Corporation P. O. Box 490, Round Lake, Illinois 60073, U. S.A

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.

Key Words: First-order method • Maximum likelihood • Nonlinear random effects


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