Optimal one and two-stage designs for the logistic regression model

Binary response data is often modeled using the logistic regression model, a well known nonlinear model. Designing an optimal experiment for this nonlinear situation poses some problems not encountered with a linear model. The application of several optimality design criteria to the logistic regression model is explored, and many resulting optimal designs are given. The implementation of these optimal designs requires the parameters of the model to be known. However, the model parameters are not known. If they were, there would be no need to design an experiment. Consequently the parameters must be estimated prior to implementing a design. Standard one-stage optimal designs are quite sensitive to parameter misspecification and are therefore unsatisfactory in practice. A two-stage Bayesian design procedure is developed which effectively deals with poor parameter knowledge while maintaining high efficiency. The first stage makes use of Bayesian design as well as Bayesian estimation in order to cope with parameter misspecification. Using the parameter estimates from the first stage, the second stage conditionally optimizes a chosen design optimality criterion. Asymptotically, the two-stage design procedure is considerably more efficient than the one-stage design when the parameters are misspecified and only slightly less efficient when the parameters are known. The superiority of the two-stage procedure over the one-stage is even more evident for small samples.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Statistics

Department dc:contributor.department

Statistics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

1995

Author dc:creator

• Letsinger, William C. II

Chair dc:contributor.committeechair

• Myers, Raymond

Committee members dc:contributor.committeemember

• Arnold, Jesse C.
• Hinkelmann, Klaus
• Reynolds, Marion R. Jr.
• Birch, Jeffrey B.

• nonlinear logistic regression model

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Language dc:language.iso

en

Dc Identifier Other

etd-02132009-171953

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/37354