R-optimal designs for multi-response regression models with multi-factors

TL;DR

This paper develops theoretical properties and an efficient algorithm for R-optimal experimental designs in multi-response regression models with correlated errors, applicable to both linear and nonlinear cases.

Contribution

It introduces new theoretical results on R-optimal designs considering error correlation and proposes a flexible interior point algorithm for discrete design spaces.

Findings

Theoretical properties like scale invariance and symmetry are established.

An interior point method algorithm efficiently finds R-optimal designs.

Applicable to both linear and nonlinear multi-response models.

Abstract

We investigate R-optimal designs for multi-response regression models with multi-factors, where the random errors in these models are correlated. Several theoretical results are derived for Roptimal designs, including scale invariance, reflection symmetry, line and plane symmetry, and dependence on the covariance matrix of the errors. All the results can be applied to linear and nonlinear models. In addition, an efficient algorithm based on an interior point method is developed for finding R-optimal designs on discrete design spaces. The algorithm is very flexible, and can be applied to any multi-response regression model.