Optimal designs for dual response systems for the normal and binomial case

Most research in design of experiments focuses on appropriate designs for a system with just one type of response, rather than multiple responses. In a decision-making process, relying on only one objective can lead to oversimplified, suboptimal choices that ignore important considerations. Consequently, the problem of constructing a design for an experiment when multiple types of responses are of interest often does not have a single definitive answer, particularly when the response variables have different distributions. Each of these response distributions imposes different requirements on the experimental design. Computer-generated optimal designs are popular design choices for less standard scenarios where classical designs are not ideal. This work presents a new approach to experimental designs for dual-response systems. The normal and binomial distributions are considered as potential responses. Using the D-criterion for the linear model and the Bayesian D-criterion for the logistic regression model, a weighted criterion is implemented in a coordinate-exchange algorithm. Designs are evaluated and compared across different weights. The sensitivity of the designs to the priors supplied for the Bayesian D-criterion is also explored.