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D-optimal Designs For Logistic Regression In Two Variables

L. Haines, Gaëtan Kabera, P. Ndlovu, T. E. O’Brien
Published 2007 · Mathematics

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In this paper locally D-optimal designs for the logistic regression model with two explanatory variables, both constrained to be greater than or equal to zero, and no interaction term are considered. The setting relates to dose-response experiments with doses, and not log doses, of two drugs. It is shown that there are two patterns of D-optimal design, one based on 3 and the other on 4 points of support, and that these depend on whether or not the intercept parameter β 0 is greater than or equal to a cut-off value of −1.5434. The global optimality of the designs over a range of β 0 values is demonstrated numerically and proved algebraically for the special case of the cut-off value of β 0.
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