Equivalence theorems for compound design problems with application in mixed models

TL;DR

This paper develops equivalence theorems for compound design problems involving multiple designs, applying them to mixed models and illustrating with simple examples to identify optimal designs.

Contribution

It introduces new equivalence theorems for complex design criteria depending on multiple designs, especially in mixed models, expanding optimal design theory.

Findings

Derived equivalence theorems based on moment matrices and design regions

Applied the theorems to multiple-group random coefficient regression models

Provided illustrative examples demonstrating the application of the theorems

Abstract

In the present paper we consider design criteria which depend on several designs simultaneously. We formulate equivalence theorems based on moment matrices (if criteria depend on designs via moment matrices) or with respect to the designs themselves (for finite design regions). We apply the obtained optimality conditions to the multiple-group random coefficient regression models and illustrate the results by simple examples.