Abstract
Optimum experimental designs for generalized linear models are found by applying the methods for normal theory regression models to the information matrix for weighted least squares. The weights are those in the iterative fitting of the model. Examples for logistic regression with two variables illustrate the differences between design for normal theory models and that for other GLMs.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Atkinson, A.C. (1996). The usefulness of optimum experimental designs (with discussion). Journal of the Royal Statistical Society B, 58, (to appear).
Atkinson, A.C., C.G.B. Demetrio and S. Zocchi (1995). Optimum dose levels when males and females differ in response. Applied Statistics, 44, 213–226.
Atkinson, A.C. and A.N. Donev (1992). Optimum Experimental Designs. Oxford university Press.
Burridge, J. and P. Sebastiani (1995). D-optimal designs for generalised linear models with variance proportional to the square of the mean. Biometrika,81, 295–304.
Chaloner, K. and K. Larntz (1987). Optimal Bayesian design applied to logistic regression experiments.Journal of Statistical Planning and Inference,21, 191–208.
Ford, I., B. Torsney and C.F.J. Wu (1997). The use of a canonical form in the construction of locally optimal designs for non-linear problems. Journal of the Royal Statistical Society B, 54, 569–583.
McCullagh, P. and J.A. Nelder (1989). Generalized Linear Models.. Chapman and Hall, London
Ponce de Leon, A.M. and A.C. Atkinson (1992). The design of experiments to discrirriinate between two rival generalized linear models. In: Fahrmeir, L., B. Francis, R. Gilchrist and G. Tutz (eds). Advances in GLIM and Statistical Modelling: Proceedings of the GLIM92 Conference, Munich,pp.159–164. Springer, New York.
Ponce de Leon, A.M. and A.C. Atkinson (1993). Designing optimal experiments for the choice of link function for a binary data model. In: Müller, W.G., H.P. Wynn and A.A. Zhigljaysky (eds). Model-Oriented Data Analysis, pp.25–36. Physica-Verlag, Heidelberg.
Pukelsheim, F. (1993). Optimal Design of Experiments. Wiley, New York
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1995 Springer Science+Business Media New York
About this paper
Cite this paper
Atkinson, A.C. (1995). Some Topics in Optimum Experimental Design for Generalized Linear Models. In: Seeber, G.U.H., Francis, B.J., Hatzinger, R., Steckel-Berger, G. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0789-4_2
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0789-4_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94565-1
Online ISBN: 978-1-4612-0789-4
eBook Packages: Springer Book Archive