2015 QPRC

Title: Hidden Connections Between Different Projections under the Linear-Quadratic Parameterization

Abstract:
An important consideration for a fractional factorial design is its projection properties. Hidden projection, geometric projection, and projectivity are three important properties that at first appear to be concerned with different features of a design. However, these three properties can be connected based on the adopted parameterization system of factorial effects, and these connections can aid in the study of fractional factorials. We demonstrate strong connections between these properties under the linear-quadratic system for three-level designs with quantitative treatment factors. The connection between hidden and geometric projection is effectively applied to reduce the problem of designing a follow-up experiment to de-alias factorial effects into a simple exercise in integer linear programming. Furthermore, the connection between hidden projection and a model-based version of projectivity, known as eligibility, is employed to illuminate D-efficiency calculations for projections of a design. Ultimately, recognition of these connections is important, because it simplifies theory for the design and analysis of three-level fractional factorials.