Copula‐based robust optimal block designs

• Published in: Applied stochastic models in business and industry Vol. 36; no. 1; pp. 210 - 219
• Main Authors: Rappold, A., Müller, W.G., Woods, D.C.
• Format: Journal Article
• Language: English
• Published: England Wiley Subscription Services, Inc 01.01.2020; John Wiley and Sons Inc
• Subjects: Binary response; Blocking; Design; equivalence theorem; Experiments; generalized linear model; marginal model; Materials testing; Population statistics; pseudo‐Bayesian D‐optimality; Special Issue on Energy Networks and Stochastic Optimization; Special Issue Paper; generalized linear model; Binary response; pseudo‐Bayesian D‐optimality; equivalence theorem; marginal model
• ISSN: 1524-1904; 1526-4025
• DOI: 10.1002/asmb.2469

Blocking is often used to reduce known variability in designed experiments by collecting together homogeneous experimental units. A common modeling assumption for such experiments is that responses from units within a block are dependent. Accounting for such dependencies in both the design of the experiment and the modeling of the resulting data when the response is not normally distributed can be challenging, particularly in terms of the computation required to find an optimal design. The application of copulas and marginal modeling provides a computationally efficient approach for estimating population‐average treatment effects. Motivated by an experiment from materials testing, we develop and demonstrate designs with blocks of size two using copula models. Such designs are also important in applications ranging from microarray experiments to experiments on human eyes or limbs with naturally occurring blocks of size two. We present a methodology for design selection, make comparisons to existing approaches in the literature, and assess the robustness of the designs to modeling assumptions.