TY - JOUR

T1 - Design considerations for small experiments and simple logistic regression

AU - Russell., K.G.

AU - Eccleston, J.A.

AU - Lewis, S.M.

AU - Woods, D.C.

N1 - Imported on 12 Apr 2017 - DigiTool details were: month (773h) = January 2009; Journal title (773t) = Journal of Statistical Computation and Simulation. ISSNs: 0094-9655;

PY - 2009/1

Y1 - 2009/1

N2 - 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.

AB - 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.

KW - Bias

KW - Generalized linear models

KW - Integrated mean square error

KW - Maximum penalized likelihood

KW - Optimality

M3 - Article

SN - 0094-9655

VL - 79

SP - 81

EP - 91

JO - Journal of Statistical Computation and Simulation

JF - Journal of Statistical Computation and Simulation

IS - 1

ER -