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Design selection criteria for discrimination/estimation for nested models and a binomial response

Design selection criteria for discrimination/estimation for nested models and a binomial response
Design selection criteria for discrimination/estimation for nested models and a binomial response
The aim of an experiment is often to enable discrimination between competing forms for a response model. We investigate the selection of a continuous design for a non-sequential strategy when there are two competing generalized linear models for a binomial response, with a common link function and the linear predictor of one model nested within that of the other.

A new criterion, TE-optimality, is defined, based on the difference in the deviances from the two models, and comparisons are made with T-, Ds- and D-optimality. Issues are raised through the study of two examples in which designs are assessed using simulation studies of the power to reject the null hypothesis of the smaller model being correct, when the data are generated from the larger model. Parameter estimation for discrimination designs is also discussed and a simple method is investigated of combining designs to form a hybrid design in order to achieve both model discrimination and estimation. This method has a computational advantage over the use of a compound criterion and the similar performance of the designs obtained from the two approaches is illustrated in an example.
binary response, deviance, D-optimality, Ds-optimality, hybrid designs, likelihood ratio test, T-optimality
0378-3758
132-144
Waterhouse, T.H.
957510d9-ecfe-416b-ad40-cf662fb06746
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Eccleston, J.A.
8d0ae072-0870-4302-a54d-af9ec88e42b8
Lewis, S.M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Waterhouse, T.H.
957510d9-ecfe-416b-ad40-cf662fb06746
Woods, D.C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Eccleston, J.A.
8d0ae072-0870-4302-a54d-af9ec88e42b8
Lewis, S.M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8

Waterhouse, T.H., Woods, D.C., Eccleston, J.A. and Lewis, S.M. (2008) Design selection criteria for discrimination/estimation for nested models and a binomial response. [in special issue: International Conference on Design of Experiments (ICODOE)] Journal of Statistical Planning and Inference, 138 (1), 132-144. (doi:10.1016/j.jspi.2007.05.017).

Record type: Article

Abstract

The aim of an experiment is often to enable discrimination between competing forms for a response model. We investigate the selection of a continuous design for a non-sequential strategy when there are two competing generalized linear models for a binomial response, with a common link function and the linear predictor of one model nested within that of the other.

A new criterion, TE-optimality, is defined, based on the difference in the deviances from the two models, and comparisons are made with T-, Ds- and D-optimality. Issues are raised through the study of two examples in which designs are assessed using simulation studies of the power to reject the null hypothesis of the smaller model being correct, when the data are generated from the larger model. Parameter estimation for discrimination designs is also discussed and a simple method is investigated of combining designs to form a hybrid design in order to achieve both model discrimination and estimation. This method has a computational advantage over the use of a compound criterion and the similar performance of the designs obtained from the two approaches is illustrated in an example.

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More information

e-pub ahead of print date: 13 May 2007
Published date: 1 January 2008
Keywords: binary response, deviance, D-optimality, Ds-optimality, hybrid designs, likelihood ratio test, T-optimality
Organisations: Southampton Statistical Research Inst.

Identifiers

Local EPrints ID: 151265
URI: http://eprints.soton.ac.uk/id/eprint/151265
ISSN: 0378-3758
PURE UUID: e27c8fcd-7060-46fe-bfdf-d441f8aaf5d9
ORCID for D.C. Woods: ORCID iD orcid.org/0000-0001-7648-429X

Catalogue record

Date deposited: 10 May 2010 09:55
Last modified: 14 Mar 2024 02:44

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Contributors

Author: T.H. Waterhouse
Author: D.C. Woods ORCID iD
Author: J.A. Eccleston
Author: S.M. Lewis

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