Optimal crossover designs in a model with self and mixed carryover effects

We consider a variant of the usual model for crossover designs with carryover e ects. Instead of assuming that the carryover e ect of a treatment is the same regardless of the treatment in the next period, the model assumes that the carryover e ect of a treatment on itself is di erent from the carryover e ect on other treatments. For the traditional model optimal designs tend to have pairs of consecutive identical treatments; for the model considered here they tend to avoid such pairs. Practitioners have long expressed reservations about designs that exhibit such pairs, resulting in reservations about the traditional model. Our results provide support for these reservations if the carryover e ect of a treatment depends also on the treatment in the next period.