Optimality regions for designs in multiple linear regression models with correlated random coefficients

TL;DR

This paper investigates optimal experimental designs for linear regression models with correlated random coefficients, introducing rhombic designs to simplify computations and characterizing their optimality based on correlation structures.

Contribution

It introduces rhombic designs for efficient computation and provides a semi-algebraic characterization of D-optimality in models with correlated random effects.

Findings

Rhombic designs reduce computational complexity.

Optimal design structure depends on correlation of random coefficients.

Semi-algebraic description of D-optimality established.

Abstract

This paper studies optimal designs for linear regression models with correlated effects for single responses. We introduce the concept of rhombic design to reduce the computational complexity and find a semi-algebraic description for the D-optimality of a rhombic design via the Kiefer-Wolfowitz equivalence theorem. Subsequently, we show that the structure of an optimal rhombic design depends directly on the correlation structure of the random coefficients.