Optimality of designs with generalized group divisible structure

Abstract

The generalized group divisible designs with s groups, or GGDD( s)s, are defined in terms of the elements of the information matrix, rather than in terms of the elements of the concurrence matrix as has been done previously. This definition extends the class of designs to include nonbinary members, and allows for broader optimality results. Several sufficient conditions are derived for the designs to be E- and MV-optimal. It is further shown how augmentation of additional blocks to certain GGDD( s)s produces infinite series of other nonbinary, unequally replicated E- and MV-optimal block designs. Where nonbinary designs are found, they can be preferable to binary designs in terms of interpretability as well as one or more formal optimality criteria.