Variance Models, Weighting, and Transformations

  • Peter L. Bonate


The previous chapters assumed that every observation carried equal weight in the estimation of the model parameters and that the assumptions of the model, e.g., normality of the residuals, were met. When the observations have nonconstant variance this is referred to as heteroscedasticity. This chapter introduces weighted least-squares (WLS) and variance models in the face of heteroscedasticity and how OLS estimates are biased when heteroscedasticity is not taken into account. An alternative to variance modeling are data transformations that force the resulting distributions to be normal or at least approximately normal. Data transformations, both with the dependent and independent variables, are introduced with particular emphasis on the transform-both-sides approach. Two case studies in WLS are presented: a compartmental model of DFMO and an E max model with XomaZyme-791.


Constant Variance Residual Plot Absorption Rate Constant Proportional Error Structural Model Parameter 
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Recommended Reading

  1. Carroll RJ, Ruppert D. Transformation and Weighting in Regression. New York: Chapman and Hall, 1988.CrossRefGoogle Scholar
  2. Davidian M, Carroll RJ. Variance function estimation. Journal of the American Statistical Association 1987; 82:1079-1091.CrossRefGoogle Scholar
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  5. Sakia RM. Box-Cox transformation: a review. The Statistician 1992; 41: 169-178.CrossRefGoogle Scholar

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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