Degree Type

Dissertation

Date of Award

1993

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Mervyn G. Marasinghe

Abstract

When designing an experiment, it is often assumed that the response to be measured can be modelled as a linear function of a vector of parameters plus an error term, y = X[beta] + [epsilon]. Using this model several properties of the design can be defined in terms of the matrix X[superscript]' X, including A-, D-, E- and G-optimality. In this dissertation we review some common design properties and develop new graphical methods for displaying them using dynamic graphics techniques, including interactive updating, linking, animation and rotation. The effects of perturbations to the design on these properties are also displayed, and a new graphical search technique for improving designs is introduced. Our results indicate that these graphs can help to verify the stability of standard experimental designs, highlight weaknesses present in non-standard designs, and suggest possible remedies;In addition, an adaptation of Cook's method for assessing local influence is developed to examine the effects of local perturbations to the model and to the design on selected design properties. Perturbations are made to case weights, design variables, and added variables not included in the assumed model. The design properties examined are D-optimality and the mean squared error of estimating the response at selected points in the design region. Graphical displays are used to interpret the results.

DOI

https://doi.org/10.31274/rtd-180813-12253

Publisher

Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/

Copyright Owner

Philip W. Iversen

Language

en

Proquest ID

AAI9321172

File Format

application/pdf

File Size

242 pages

Share

COinS