Optimal designs for quadratic regression with random block effects: The case of block size two

Optimal approximate designs for quadratic regression with random block effects in the case of block size two are considered. We obtain, with respect to the Schur ordering, an essentially complete class consisting of designs with a simple structure. The locally D- and A-optimal designs given in Cheng (1995a) and Atkins and Cheng (1999) belong to this class. We explicitly identify locally E-optimal designs and show that for each p, −∞≤p≤1, there is a unique ϕ_p-design in this class. Bayesian ϕ_p-optimal designs are also considered.