TG‐compound optimal design for bivariate binary responses modelled via Copulas

Abstract

AbstractUnivariate data has been the focus of optimal design for generalized linear models. It is common practice to conduct experiments with multiple dependent responses that are modelled using regression techniques. To design the experiment for all these responses, one needs a multivariate distribution supporting a previously chosen data model. The T‐optimal criterion is used to discriminate between two competing models. The designs that are optimal for discrimination between two models may be unsuitable for describe the quality of predictions for test data. G‐optimal criterion overcomes this restriction by minimizing the maximum variance of the predicted values. The design of experiments with dependent bivariate binary data is a topic we discuss in this paper. For dependent bivariate binary data, a technique for deriving TG‐optimal experimental designs using Copula is shown. The new compound TG‐criterion satisfy the dual aim to selecting the true model and minimizing the maximum prediction variance. The equivalence theorem is demonstrated and proved for the new compound criterion. A numerical example is presented to show the properties of the new compound criterion for bivariate binary setting and its value in meeting the dual aims.