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The Importance of Marginal Likelihood Estimation Applied to Mixed-Effects Modeling

Abstract
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.}

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