Locally Optimal Designs for Generalized Linear Models with a Single-Variable Quadratic Polynomial in the Vertex Form as the Predictor

• Activity Number: 334
• Type: Contributed
• Date/Time: Tuesday, August 5, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Biometrics Section
• Author(s): Hsin-Ping Wu*+ and John Stufken
• Companies: University of Georgia and University of Georgia
• Keywords: Generalized linear models ; Optimal designs

Abstract

Finding optimal designs for generalized linear models is a challenging problem. Recent research has identified the structure of optimal designs for generalized linear models with a single or multiple independent explanatory variables that appear as first-order terms in the predictor. In this study, we focus on a popular family of optimality criteria and consider alternative cases when the predictor is a single-variable quadratic polynomial in the vertex form. When the design region is unrestricted, our results establish that optimal designs can be found within a subclass of designs based on a small support with symmetric structure. We show that the same conclusion holds with certain restrictions on the design region, but in other cases a larger subclass may have to be considered. In addition, we derive explicit expressions for some D-optimal designs.