R-optimal designs for multi-factor models with heteroscedastic errors

In this paper, we consider the R -optimal design problem for multi-factor regression models with heteroscedastic errors. It is shown that a R -optimal design for the heteroscedastic Kronecker product model is given by the product of the R -optimal designs for the marginal one-factor models. However, R -optimal designs for the additive models can be constructed from R -optimal designs for the one-factor models only if sufficient conditions are satisfied. Several examples are presented to illustrate and check optimal designs based on R -optimality criterion.