### 2009-28

by Mielke, T., Schwabe, R..

**Series:** 2009-28, Preprints

- MSC:
- 62K05 Optimal designs
- 62J12 Generalized linear models

**Abstract:**

The Fisher Information is a lower bound for the covariance matrix of any unbiased estimator of the parameter vector and with 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 modelfunction

in the fixed effects is generally not reliable, as will be shown in this article.

**Keywords:**

nonlinear mexed model, maximum likelihood, Fisher information, weighted least squares, first order linearization