Understanding Scaled Prediction Variance Using Graphical Methods for Model Robustness, Measurement Error and Generalized Linear Models for Response Surface Designs

Graphical summaries are becoming important tools for evaluating designs. The need to compare designs in term of their prediction variance properties advanced this development. A recent graphical tool, the Fraction of Design Space plot, is useful to calculate the fraction of the design space where the scaled prediction variance (SPV) is less than or equal to a given value. In this dissertation we adapt FDS plots, to study three specific design problems: robustness to model assumptions, robustness to measurement error and design properties for generalized linear models (GLM). This dissertation presents a graphical method for examining design robustness related to the SPV values using FDS plots by comparing designs across a number of potential models in a pre-specified model space. Scaling the FDS curves by the G-optimal bounds of each model helps compare designs on the same model scale. FDS plots are also adapted for comparing designs under the GLM framework. Since parameter estimates need to be specified, robustness to parameter misspecification is incorporated into the plots. Binomial and Poisson examples are used to study several scenarios. The third section involves a special type of response surface designs, mixture experiments, and deals with adapting FDS plots for two types of measurement error which can appear due to inaccurate measurements of the individual mixture component amounts. The last part of the dissertation covers mixture experiments for the GLM case and examines prediction properties of mixture designs using the adapted FDS plots.

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

2004

Author dc:creator

• Ozol-Godfrey, Ayca

Chair dc:contributor.committeechair

• Anderson-Cook, Christine M.

Committee members dc:contributor.committeemember

• Woodall, William H.
• Ye, Keying
• Vining, G. Geoffrey
• Smith, Eric P.

• FDS Plots
• Design Optimality
• Generalized Linear Models

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-12202004-205209

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/30185