Robustness of Circular Neighbor-Balanced Designs with Correlated Data and Missing Observations

This paper examines the robustness of circular neighbor-balanced designs (CNBDs), a significant issue in experimental design when observations are missing and errors are correlated. Treatments may affect not only the designated unit but also its adjacent units, hence complicating the estimation of treatment effects in assessments utilizing adjoining plots. This paper proposes to measure the robustness of CNBDs by analyzing two models, one with and one without block effects, under four correlation structures: MA(1), NN, AR(1), and ARMA(1,1). It considers the robustness of these designs in terms of A- and D-efficiencies for direct and neighboring effects. We observed that designs with lower correlations between observations also yield smaller efficiency losses when data is missing, resulting in more robust designs. Some neighbor designs offer strong performance with missing observations and correlated errors, minimizing efficiency losses. This study contributes to experimental design for CNBDs under challenging conditions for missing observations and correlated data—that is significant.