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Nonlinear Models and Regression

  • Peter L. Bonate
Chapter

Abstract

A model is nonlinear if any of the partial derivatives with respect to any of the model parameters are dependent on any other model parameter or if any of the derivatives do not exist or are discontinuous. This chapter expands on the previous chapter and introduces nonlinear regression within a least squares (NLS) and maximum likelihood framework. The concepts of minima, both local and global, and the gradient and Hessian are introduced and provide a basis for NLS algorithm selection. Ill-conditioning and its role in model instability are prominently discussed, as are influence diagnostics for the nonlinear problem and how to use prior information to obtain better model parameter estimates.

Keywords

Condition Number Singular Value Decomposition Model Parameter Estimate Newton Algorithm Taylor Series Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Recommended Reading

  1. Bates DM, Watts DG. Nonlinear Regression Analysis and its Applications. New York: John Wiley & Sons, 1988.CrossRefGoogle Scholar
  2. Donaldson JR, Schnabel RB. Computation experience with confidence regions and confidence intervals for nonlinear least squares. Technometrics 1987; 29:67-82.CrossRefGoogle Scholar
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Peter L. Bonate
    • 1
  1. 1.Astellas Pharma Global Development Pharmacokinetics, Modeling, and SimulationDeerfieldUSA

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