Designs for Discriminating Between Linear and Cubic Regression Models

• Activity Number: 470
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Santanu Dutta*+ and Subir Ghosh
• Companies: University of California at Riverside and University of California at Riverside
• Keywords: Model Discrimination ; T-optimality ; I and J criteria ; Linear and Cubic Models ; Optimal Design

Abstract

We consider the identification and discrimination between two competing regression models, a linear and a cubic, with the response variable y and the explanatory variable x. The four distinct design points x1, x2, x3, and x4 are replicated n1, n2, n3, and n4 times respectively, satisfying n1 + n2 + n3 + n4 = n, n1 = n4 and n2 = n3. For a fixed value of n, we compare designs optimum with respect to two criteria, J (equivalent to T-optimality) and a proposed I. We obtain a class of designs that are better than the Dette-Titoff T-optimal (equivalently J-optimal) design (Dette and Titoff (2009)) under the criterion I in their setup where the quadratic coefficient is zero in the cubic model. However, the Dette-Titoff design is better than our class of designs under the criterion J. We also obtain optimal designs when the quadratic coefficient is not zero.