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OPTIMAL DESIGNS FOR GENERALIZED LINEAR MODELS WITH MULTIPLE DESIGN VARIABLES

Min Yang, Bin Zhang and Shuguang Huang
Statistica Sinica
Vol. 21, No. 3 (July 2011), pp. 1415-1430
Stable URL: http://www.jstor.org/stable/24309568
Page Count: 16
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
OPTIMAL DESIGNS FOR GENERALIZED LINEAR MODELS WITH MULTIPLE DESIGN VARIABLES
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Abstract

Binary response experiments are common in scientific studies. However, the study of optimal designs in this area is in a very underdeveloped stage. Sitter and Torsney (1995a) studied optimal designs for binary response experiments with two design variables. In this paper, we consider a general situation with multiple design variables. A novel approach is proposed to identify optimal designs for the commonly used multi-factor logistic and probit models. We give explicit formulas for a large class of optimal designs, including D-, A-, and E-optimal designs. In addition, we identify the general structure of optimal designs, which has a relatively simple format. This property makes it feasible to solve seemingly intractable problems. This result can also be applied in a multi-stage approach.

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