Optimal Block Designs With Interference Effects From Neighboring Units Under a Non Additive Model

Abstract

Here, the optimality of block design with interference effect from neighboring unit under a general non additive model is investigated, which allows for the presence of interactions among the treatments applied in the adjacent plots. A non additive model with interference × direct effects of treatments is considered as these effects contribute significantly to the response. A class of complete block designs balanced for interference effects from left neighboring unit is shown to be universally optimal for the estimation of direct and interference effects of treatments and two such series of designs have been constructed. Furthermore, considering direct treatment × block non additivity with interference effects, the optimality is studied and the optimal designs are obtained.

Keywords:

• Interference
• Neighboring units
• Non additive
• Left circular
• Balanced, universal optimality

Mathematics Subject Classification:

• 62K99