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Publication: The analytic construction of D-optimal designs for the two-variable binary logistic regression model without interaction
Kabera, Gaëtan M. Haines, Linda M. Ndlovu, Principal
Kabera, Gaëtan M.
Haines, Linda M.
Ndlovu, Principal
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Abstract
Candidate locally D-optimal designs for the binary two-variable logistic model with no interaction, which comprise 3 and 4 support points lying in the first quadrant of the two-dimensional Euclidean space, were introduced by Haines et al. (D-optimal designs for logistic regression in two variables. In: Lopez-Fidalgo J, Rodrigez-Diaz JM, Torsney B, editors. MODA8 – advances in model-oriented designs and analysis. Heidelberg: Physica-Verlag; 2007. p. 91–98). The authors proved algebraically the global D-optimality of the 3-point design for the special case in which the intercept parameter is equal to−1.5434. However for other selected values of the intercept parameter, the global D-optimality of the proposed 3- and 4-point designs was only demonstrated numerically. In this paper, we provide analytical proofs of the D-optimality of these 3- and 4-point designs for all negative and zero intercept parameters of the binary two-variable logistic model with no interaction. The results are extended to the construction of D-optimal designs on a rectangular design space and illustrated by means of two examples of which one is a real example taken from the literature.
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2015-09-03
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Keywords
trapezium design,D-optimality,binary two-variable logistic model,no interaction,stand-ardized variance function
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The analytic construction of D-optimal designs for the two-variable binary logistic regression model without interaction 2014, 49 (5):1169 Statistics