Optimal designs for binary response models with multiple nonnegative variables

Shih-Hao Huang, Mong-Na Lo Huang, and Cheng-Wei Lin

Department of Mathematics and Department of Applied Mathematics

National Central University and National Sun Yat-sen University

shhuang@math.ncu.edu.tw

In this work, we consider optimal approximate designs for binary response models with nonnegative explanatory variables. With respect to the Schur ordering, we construct an essentially complete class consisting of designs with a simple structure. In particular, we explicitly identify locally `D`-optimal designs within the class for logit and probit models. When the nonnegative explanatory variables have more restrictions, such as factorial and mixture experiments, we also provide an informative iteration algorithm to search an optimal design.Keyword: `\phi_p`-optimality, `D`-optimality, essentially complete class, logit model, probit model, schur ordering