Optimal Design Through Weighting

• Activity Number: 4
• Type: Invited
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Memorial
• Author(s): John P. Morgan*+ and Jonathan W. Stallings
• Companies: Virginia Tech and North Carolina State University
• Keywords: experimental design ; factorial experiment ; design optimality ; weighted optimality criteria

Abstract

Conventional design optimality criteria, such as the popularly employed A, D, and E criteria, allocate equal weight to all estimable functions of model parameters. Not surprisingly, this can lead to designs that do not align with experimental goals. For example, in factorial experiments aimed primarily at estimating main effects, and secondarily at two-factor interactions, each main effect and interaction contrast exerts equal influence on any conventional criterion. Indeed, by dint of their greater number, interactions collectively exert greater influence than main effects. Shown here is how conventional criteria can be converted to weighted criteria, allowing functions of greater interest to be assigned greater weight, and thus leading to designs that estimate the targeted functions more efficiently. The basic theory for weighted optimality is delineated and applications to factorials are explored. It is shown that under a natural weighting regimen, in which main effects and two-factor interactions are accorded distinct weights, the balanced arrays introduced by I. M. Chakravarti are the designs of maximal symmetry. They thus provide maximal information in a fixed trace class.