Copula-based robust optimal block designs
Copula-based robust optimal block designs
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.
Binary response, equivalence theorem, generalized linear model, marginal model, pseudo-Bayesian D-optimality
Rappold, A.
9b1d3839-e1fc-4c8c-b65b-7c4f8057c5ba
Müller, W. G.
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Woods, D. C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Rappold, A.
9b1d3839-e1fc-4c8c-b65b-7c4f8057c5ba
Müller, W. G.
4392a0df-327c-404b-98fe-09f708350b80
Woods, D. C.
ae21f7e2-29d9-4f55-98a2-639c5e44c79c
Rappold, A., Müller, W. G. and Woods, D. C.
(2019)
Copula-based robust optimal block designs.
Applied Stochastic Models in Business and Industry.
(doi:10.1002/asmb.2469).
Abstract
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.
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Rappold_et_al-2019-Applied_Stochastic_Models_in_Business_and_Industry
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Accepted/In Press date: 15 May 2019
e-pub ahead of print date: 30 May 2019
Keywords:
Binary response, equivalence theorem, generalized linear model, marginal model, pseudo-Bayesian D-optimality
Identifiers
Local EPrints ID: 431796
URI: http://eprints.soton.ac.uk/id/eprint/431796
ISSN: 1524-1904
PURE UUID: 7cd51072-16ff-4b9d-ace2-de2aeb1a0505
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Date deposited: 17 Jun 2019 16:30
Last modified: 16 Mar 2024 03:15
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Author:
A. Rappold
Author:
W. G. Müller
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