Optimal Designs for Proportional Interference Models with Different Guarding Strategies

Interference models are commonly used in agriculture, industry, and other related fields. Optimal designs for these models are important topics in block designs. In this work, we consider both direct and total effects under both guarded and unguarded proportional interference models. Some general equivalence theorems are established to characterize such efficient designs. For guarded models, we generate optimal noncircular designs for estimating both direct and total effects, respectively. Particularly, we remove the traditional circular assumption for guarded models and introduce noncircular designs which have less restriction and, more importantly, perform higher efficiency than existing circular designs. For unguarded models, we also give the construction of some optimal designs under the proportional interference model.