Some Considerations on the Fisher Information in Nonlinear Mixed Effects Models

Abstract

The inverse of the Fisher Information Matrix is a lower bound for the covariance matrix of any unbiased estimator of the parameter vector and, given this, it is important for the construction of optimal designs. For normally distributed observation vectors with known variance, the Fisher Information can be easily constructed. For nonlinear mixed effects models, the problem of the missing closed-form solution of the likelihood function carries forward to the calculation of the Fisher Information matrix. The often used approximation of the Fisher Information by linearizing the model-function in the fixed effects case is generally not reliable, as will be shown in this article.