The Importance of Marginal Likelihood Estimation Applied to Mixed-Effects Modeling
We consider the problem of estimating deterministic
parameters in models that also have random parameters.
This is often referred to as
estimating fixed effects in mixed-effects models, and
the random parameters are called random effects.
These models lead to a direct representation of the
joint likelihood of the data and the random effects.
It is often difficult to obtain values of the
marginal likelihood, i.e., the integral of the
joint likelihood with respect to the random effects.
Nonetheless, the marginal likelihood is
often essential when estimating fixed effects
in a mixed-effects model.
We present a pharmacokinetic example
to illustrate the importance of
marginal likelihood estimates and their Laplace approximations
when applied to mixed-effects models.}