Abstract
This paper points out that so-called optimal designs for nonlinear regression models are often limited when the assumed model function is not known with complete certainty and argues that robust designs - near optimal designs but with extra support points - can be used to also test for lack of fit of the model function. A simple robust design strategy - which has been implemented with a popular software package - is also presented and illustrated.
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References
Atkinson, A.C. and Donev, A.N. (1992). Optimum Experimental Designs. Oxford: Clarendon Press.
Chaloner, K. and Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. J. Stat. Plann. Inf., 21 191–208.
Gaifke, N. (1987). On D-optimality of exact linear regression designs with minimum support. J. Stat. Plann. Inf., 15 189–204.
Gerig, T.M., Blum, U., Meier, K. (1989). Statistical analysis of the joint inhibitory action of similar compounds. J. Chem. Ecol., 15, 2403–2412.
Hamilton, D., Wiens, D. (1987). Correction factors for F ratios in nonlinear regression. Biometrika, 74, 423–5.
Kiefer, J., Wolfowitz, J. (1960). The equivalence of two extremum problems. Can. J. Math., 12, 363–6.
O’Brien, T.E. (1992). A note on quadratic designs for nonlinear regression models. Biometrika, 79, 847–9.
O’Brien, T.E. (1994). A new robust design strategy for sigmoidal models based on model nesting. In Dutter, R. and Grossmann, W., eds., Proceedings in Computational Statistics: Compstat, 1994, Heidelberg: Physica-Verlag, 97–102.
O’Brien, T.E. (1995). Obtaining and verifying optimal designs for nonlinear regression models using SAS software. To appear in Proceedings of SUGI 20.
Vølund, A. (1978). Application of the four-parameter logistic model to bioassay: comparison with slope ratio and parallel line models. Biometrics, 34, 357–65.
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© 1995 Springer Science+Business Media New York
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O’Brien, T.E. (1995). Optimal Design and Lack of Fit in Nonlinear Regression Models. In: Seeber, G.U.H., Francis, B.J., Hatzinger, R., Steckel-Berger, G. (eds) Statistical Modelling. Lecture Notes in Statistics, vol 104. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0789-4_25
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DOI: https://doi.org/10.1007/978-1-4612-0789-4_25
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94565-1
Online ISBN: 978-1-4612-0789-4
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