D-optimal designs for logistic models with three and four parameters

Logistic functions are used in different applications, including biological growth studies and assay data analysis. Locally D-optimal designs for logistic models with three and four parameters are investigated. It is shown that these designs are minimally supported. Efficiencies are computed for equally spaced and uniform designs.

[1]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[2]  P. Whittle Some General Points in the Theory of Optimal Experimental Design , 1973 .

[3]  A. S. Hedayat,et al.  Modeling and Identifying Optimum Designs for Fitting Dose-Response Curves Based on Raw Optical Density Data , 1997 .

[4]  S. Silvey Optimal Design: An Introduction to the Theory for Parameter Estimation , 1980 .

[5]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[6]  H. Chernoff Locally Optimal Designs for Estimating Parameters , 1953 .

[7]  Paola Sebastiani,et al.  A note on D-optimal designs for a logistic regression model , 1997 .

[8]  Holger Dette,et al.  Optimal designs for a class of nonlinear regression models , 2002 .

[9]  C. F. Wu,et al.  Optimal designs for binary response experiments: Fieller, D, and A criteria , 1993 .

[10]  L. White An extension of the General Equivalence Theorem to nonlinear models , 1973 .

[11]  J. Kiefer General Equivalence Theory for Optimum Designs (Approximate Theory) , 1974 .

[12]  L. Skovgaard NONLINEAR MODELS FOR REPEATED MEASUREMENT DATA. , 1996 .

[13]  M Davidian,et al.  Some general estimation methods for nonlinear mixed-effects models. , 1993, Journal of biopharmaceutical statistics.

[14]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[15]  J. Kiefer,et al.  The Equivalence of Two Extremum Problems , 1960, Canadian Journal of Mathematics.

[16]  I. Ford,et al.  The Use of a Canonical Form in the Construction of Locally Optimal Designs for Non‐Linear Problems , 1992 .

[17]  K. Chaloner,et al.  Optimal Bayesian design applied to logistic regression experiments , 1989 .

[18]  Kathryn Chaloner,et al.  D- and c-optimal designs for exponential regression models used in viral dynamics and other applications , 2003 .

[19]  Holger Dette,et al.  Bayesian D-optimal designs for exponential regression models , 1997 .