Nonlinear mixed-effects model

Nonlinear mixed-effects models make up a class of statistical models generalizing linear mixed-effects models.

Definition

While any statistical model containing both fixed effects and random effects is an example of a nonlinear mixed-effects model, the most commonly used class of models is the class of nonlinear mixed-effects models for repeated measures

${y}_{ij}=f(\phi _{ij},{v}_{ij})+\epsilon _{ij},\quad i=1,\ldots ,M,\,j=1,\ldots ,n_{i}$

where

• $M$ is the number of groups/subjects,
• $n_{i}$ is the number of observations for the $i$th group/subject,
• $f$ is a real-valued differentiable function of a group-specific parameter vector $\theta _{ij}$ and a covariate vector $v_{ij}$
• $\phi _{ij}$ is modeled as a linear mixed-effects model $\phi _{ij}={\boldsymbol {A}}_{ij}\beta +{\boldsymbol {B}}_{ij}{\boldsymbol {b}}_{ij},$

Estimation

Reference Lindstrom & Bates ´? stochastic EM

See also

• Fixed effects model

• Fixed effects model
• Generalized linear mixed model
• Linear regression
• Mixed-design analysis of variance
• Multilevel model
• Random effects model
• Repeated measures design