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Design of experiments for bivariate binary responses modelled by Copula functions

Denman, Nick, McGree, James, Eccleston, John, & Duffull, Stephen (2011) Design of experiments for bivariate binary responses modelled by Copula functions. Computational Statistics and Data Analysis, 55(4), pp. 1509-1520.

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Abstract

Optimal design for generalized linear models has primarily focused on univariate data. Often experiments are performed that have multiple dependent responses described by regression type models, and it is of interest and of value to design the experiment for all these responses. This requires a multivariate distribution underlying a pre-chosen model for the data. Here, we consider the design of experiments for bivariate binary data which are dependent. We explore Copula functions which provide a rich and flexible class of structures to derive joint distributions for bivariate binary data. We present methods for deriving optimal experimental designs for dependent bivariate binary data using Copulas, and demonstrate that, by including the dependence between responses in the design process, more efficient parameter estimates are obtained than by the usual practice of simply designing for a single variable only. Further, we investigate the robustness of designs with respect to initial parameter estimates and Copula function, and also show the performance of compound criteria within this bivariate binary setting.

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ID Code: 42929
Item Type: Journal Article
Keywords: Bivariate binary response, Copulas, Dependence, D-optimality, Multiple responses, Multivariate distributions, Optimal design, P-optimality
DOI: 10.1016/j.csda.2010.07.025
ISSN: 0167-9473
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000) > COMPUTATION THEORY AND MATHEMATICS (080200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 13 Jul 2011 23:08
Last Modified: 03 Dec 2012 16:42

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