Universally Optimal Network Balanced Designs for Agroforestry Trials

The need for improvement in agroforestry systems experiments necessitates the development of appropriate designs to provide more precise estimates of effects of interest in agroforestry trials. This is attainable through the development of optimal or at least highly efficient designs. Optimal designs constitute one of the most desired but hard-to-obtain concepts in design theory. They have the advantages of yielding more precise estimates, and reducing cost of experimentation as fewer experimental units would be required to estimate the underlying statistical models. This study aimed to develop and characterize designs that would be suitable for use in agroforestry trials. Based on a linear network effects model, a class of network balanced designs accounting for effects of trees from adjacent plots has been developed for use in agroforestry experiments. A study of the characterization properties of this class of network balanced designs showed that the designs are variance balanced for estimation of direct effects of trees. They are also shown to be universally optimal under a linear network effects model and could be used for agroforestry experiments involving even number of tree species.