Title page for ETD etd-07052002-105725

Type of Document Dissertation
Author Zahran, Alyaa R
Author's Email Address azahran@vt.edu
URN etd-07052002-105725
Title On the Efficiency of Designs for Linear Models in Non-regular Regions and the Use of Standard Desings for Generalized Linear Models
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Anderson-Cook, Christine M. Committee Co-Chair
Myers, Raymond H. Committee Co-Chair
Smith, Eric P. Committee Co-Chair
Morgan, John P. Committee Member
Ye, Keying Committee Member
  • non-regulare design spaces
  • design optimality
  • fraction of design space technique
  • gneralized linear models
  • linear models
Date of Defense 2002-07-01
Availability unrestricted
The Design of an experiment involves selection of levels of one or more factor in order to optimize one or more criteria such as prediction variance or parameter variance criteria. Good experimental designs will have several desirable properties. Typically, one can not achieve all the ideal properties in a single design. Therefore, there are frequently several good designs and choosing among them involves tradeoffs.

This dissertation contains three different components centered around the area of optimal design: developing a new graphical evaluation technique, discussing designs for non-regular regions for first order models with interaction for the two- and three-factor case, and using the standard designs in the case of generalized linear models (GLM).

The Fraction of Design Space (FDS) technique is proposed as a new graphical evaluation technique that addresses good prediction. The new technique is comprised of two tools that give the researcher more detailed information by quantifying the fraction of design space where the scaled predicted variance is less than or equal to any pre-specified value. The FDS technique complements Variance Dispersion Graphs (VDGs) to give the researcher more insight about the design prediction capability. Several standard designs are studied with both methods: VDG and FDS.

Many Standard designs are constructed for a factor space that is either a p-dimensional hypercube or hypersphere and any point inside or on the boundary of the shape is a candidate design point. However, some economic, or practical constraints may occur that restrict factor settings and result in an irregular experimental region. For the two- and three-factor case with one corner of the cuboidal design space excluded, three sensible alternative designs are proposed and compared. Properties of these designs and relative tradeoffs are discussed.

Optimum experimental designs for GLM depend on the values of the unknown parameters. Several solutions to the dependency of the parameters of the optimality function were suggested in the literature. However, they are often unrealistic in practice. The behavior of the factorial designs, the well-known standard designs of the linear case, is studied for the GLM case. Conditions under which these designs have high G-efficiency are formulated.

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