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

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.