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2009-28

Some Considerations on the Fisher Information in Nonlinear Mixed Effects Models

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