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

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 R-optimal 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 non-linear 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.