A new class of criteria for optimal designs in random coefficient regression (RCR) models with r responses is presented, which is based on the integrated mean squared error (IMSE) for the prediction of random effects. This class, referred to as \(\textrm{IMSE}_{r,L}\) -class of criteria, is invariant with respect to different parameterizations of the model and contains \(\textrm{IMSE}\) - and G-optimality as special cases for the prediction in univariate response situations. General equivalence theorems for \(\textrm{IMSE}_{r,L}\) -criteria are established for \(L\in [1,\infty )\) and \(L=\infty \) , respectively, which are used to check \(\textrm{IMSE}_{r,L}\) -optimality of designs. \(\textrm{IMSE}_{r,L}\) -optimal designs for linear and quadratic bi-response RCR models are given for illustration.
