Continuous optimal designs for generalised linear models under model uncertainty
Continuous optimal designs for generalised linear models under model uncertainty
We propose a general design selection criterion for experiments where a generalised linear model describes the response. The criterion allows for several competing aims, such as parameter estimation and model discrimination, and also for uncertainty in the functional form of the linear predictor, the link function and the unknown model parameters. A general equivalence theorem is developed for this criterion. In practice, an exact design is required by experimenters and can be obtained by numerical rounding of a continuous design. We derive bounds on the performance of an exact design under this criterion which allow the efficiency of a rounded continuous design to be assessed.
exponential family, general equivalence theorem, logistic regression, nonlinear regression, optimal design.
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Woods, David C. and Lewis, Susan M.
(2008)
Continuous optimal designs for generalised linear models under model uncertainty.
Journal of Statistical Theory and Practice.
(Submitted)
Abstract
We propose a general design selection criterion for experiments where a generalised linear model describes the response. The criterion allows for several competing aims, such as parameter estimation and model discrimination, and also for uncertainty in the functional form of the linear predictor, the link function and the unknown model parameters. A general equivalence theorem is developed for this criterion. In practice, an exact design is required by experimenters and can be obtained by numerical rounding of a continuous design. We derive bounds on the performance of an exact design under this criterion which allow the efficiency of a rounded continuous design to be assessed.
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63323-01.pdf
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Submitted date: 2 October 2008
Keywords:
exponential family, general equivalence theorem, logistic regression, nonlinear regression, optimal design.
Identifiers
Local EPrints ID: 63323
URI: http://eprints.soton.ac.uk/id/eprint/63323
ISSN: 1559-8608
PURE UUID: 9fec3f03-1bca-43a4-9978-b7ea4cb74eee
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Date deposited: 03 Oct 2008
Last modified: 16 Mar 2024 03:14
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Author:
Susan M. Lewis
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