Optimal Designs under Proportional Interference Models when the sign of proportionality constants is known

Fakhari-Esferizi, Akram; Khodsiani, Razieh

doi:10.22055/jamm.2026.50934.2430

Optimal Designs under Proportional Interference Models when the sign of proportionality constants is known

Articles in Press

Document Type : Review Paper

Authors

Akram Fakhari-Esferizi ¹

Razieh Khodsiani ²

¹ Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, 84156-83111, Iran

² Department of Computer Science and Statistics, Faculty of Mathematics, K. N. Toosi University of Technology, 16315-1618, Tehran, Iran

10.22055/jamm.2026.50934.2430

Abstract

The interference model is widely used in block experiments, where a

treatment applied to one plot also affects its neighbors. This paper examines two

proportional interference models, where the neighbor effects are proportional to the

direct treatment effect. These models have the advantage of requiring fewer parameters

to estimate but face challenges due to the nonlinearity of the estimates. Although

conceptually simple, their technical implementation is somewhat more complex.

In this paper, we examine two-sided and one-sided proportional interference models

and transform their nonlinear nature into a more manageable form by assuming that

the proportionality constants are known. Our findings provide a closed-form analytical

solution for optimal designs under proportional interference models.

Keywords

Proportional interference model

Circular block designs

Universally optimal design

Neighbor balanced designs

Subjects