Design considerations for small experiments and simple logistic regression
Design considerations for small experiments and simple logistic regression
Inference for a generalized linear model is generally performed using asymptotic approximations for the bias and the covariance matrix of the parameter estimators. For small experiments, these approximations can be poor and result in estimators with considerable bias. We investigate the properties of designs for small experiments when the response is described by a simple logistic regression model and parameter estimators are to be obtained by the maximum penalized likelihood method of Firth [Firth, D., 1993, Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38]. Although this method achieves a reduction in bias, we illustrate that the remaining bias may be substantial for small experiments, and propose minimization of the integrated mean square error, based on Firth's estimates, as a suitable criterion for design selection. This approach is used to find locally optimal designs for two support points.
bias, generalized linear models, integrated mean square error, maximum penalized likelihood, optimality
81-91
Russell, Ken G.
71a66788-203b-4381-8b60-2f96f50ae775
Eccleston, J.A.
8d0ae072-0870-4302-a54d-af9ec88e42b8
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
2009
Russell, Ken G.
71a66788-203b-4381-8b60-2f96f50ae775
Eccleston, J.A.
8d0ae072-0870-4302-a54d-af9ec88e42b8
Lewis, Susan M.
a69a3245-8c19-41c6-bf46-0b3b02d83cb8
Woods, David C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Russell, Ken G., Eccleston, J.A., Lewis, Susan M. and Woods, David C.
(2009)
Design considerations for small experiments and simple logistic regression.
Journal of Statistical Computation and Simulation, 79 (1), .
(doi:10.1080/00949650701609006).
Abstract
Inference for a generalized linear model is generally performed using asymptotic approximations for the bias and the covariance matrix of the parameter estimators. For small experiments, these approximations can be poor and result in estimators with considerable bias. We investigate the properties of designs for small experiments when the response is described by a simple logistic regression model and parameter estimators are to be obtained by the maximum penalized likelihood method of Firth [Firth, D., 1993, Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38]. Although this method achieves a reduction in bias, we illustrate that the remaining bias may be substantial for small experiments, and propose minimization of the integrated mean square error, based on Firth's estimates, as a suitable criterion for design selection. This approach is used to find locally optimal designs for two support points.
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Published date: 2009
Keywords:
bias, generalized linear models, integrated mean square error, maximum penalized likelihood, optimality
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Local EPrints ID: 151263
URI: http://eprints.soton.ac.uk/id/eprint/151263
ISSN: 0094-9655
PURE UUID: 82b3147b-0e06-4b8e-bc7a-d4c0c05b2810
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Date deposited: 10 May 2010 09:30
Last modified: 14 Mar 2024 02:44
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Author:
Ken G. Russell
Author:
J.A. Eccleston
Author:
Susan M. Lewis
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