Locally D-Optimal Designs for Generalized Linear Models with Group Effects and a Covariate

• Activity Number: 507
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Xijue Tan*+ and John Stufken
• Companies: University of Georgia and University of Georgia
• Keywords: D-optimality ; generalized linear model ; orthogonal array ; logistic model ; probit model

Abstract

Optimal design considerations for generalized linear models involve an information matrix that depends on unknown parameters. Locally optimal designs, in which best guesses of parameter values are used, overcome this difficulty. Among different optimality criteria, D-optimality is commonly studied. However, most results are for models with only group effects or only continuous variables. Results that do allow group effects and continuous variables require observations in all or most groups. We consider models with both group effects and a continuous covariate. Focusing on probit and logistic models, we derive locally D-optimal designs for certain design regions. We also study the use of orthogonal arrays to obtain locally D-optimal designs with fewer design points.