Design considerations for small experiments and simple logistic regression

Russell, K. G., Eccleston, J. A., Lewis, S. M. and Woods, D. C. (2009) Design considerations for small experiments and simple logistic regression. Journal of Statistical Computation and Simulation, 79 1: 81-91. doi:10.1080/00949650701609006


Author Russell, K. G.
Eccleston, J. A.
Lewis, S. M.
Woods, D. C.
Title Design considerations for small experiments and simple logistic regression
Journal name Journal of Statistical Computation and Simulation   Check publisher's open access policy
ISSN 0094-9655
Publication date 2009-01-01
Sub-type Article (original research)
DOI 10.1080/00949650701609006
Volume 79
Issue 1
Start page 81
End page 91
Total pages 11
Editor Richard G. Krutchkoff
Place of publication United Kingdom
Publisher Taylor & Francis
Collection year 2010
Language eng
Subject C1
970101 Expanding Knowledge in the Mathematical Sciences
010405 Statistical Theory
Formatted 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.
Keyword Bias
Generalized linear models
Integrated mean square error
Maximum penalized likelihood
Optimality
Q-Index Code C1
Q-Index Status Confirmed Code

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
2010 Higher Education Research Data Collection
 
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Created: Thu, 03 Sep 2009, 19:11:58 EST by Mr Andrew Martlew on behalf of School of Mathematics & Physics