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A three-parameter logistic regression model

Xiaoli Yu ,

School of Mathematics and Statistics, University of British Columbia, Vancouver, Canada

Shaoting Li ,

School of Mathematics and Statistics, Dongbei University of Finance and Economics, Dalian, People’s Republic of China

Jiahua Chen

aSchool of Mathematics and Statistics, University of British Columbia, Vancouver, Canada;School of Mathematics and Statistics, Yunnan University, Kunming, People’s Republic of China

Pages 265-274 | Received 11 Feb. 2020, Accepted 18 Jun. 2020, Published online: 24 Jul. 2020,
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Dose–response experiments and data analyses are often carried out according to an optimal design under a model assumption. A two-parameter logistic model is often used because of its nice mathematical properties and plausible stochastic response mechanisms. There is an extensive literature on its optimal designs and data analysis strategies. However, a model is at best a good approximation in a real-world application, and researchers must be aware of the risk of model mis-specification. In this paper, we investigate the effectiveness of the sequential EDdesign, the D-optimal design, and the up-and-down design under the three-parameter logistic regression model, and we develop a numerical method for the parameter estimation. Simulations show that the combination of the proposed model and the data analysis strategy performs well. When the logistic model is correct, this more complex model has hardly any efficiency loss. The three-parameter logistic model works better than the two-parameter logistic model in the presence of model mis-specification.

To cite this article: Xiaoli Yu, Shaoting Li & Jiahua Chen (2021) A three-parameter logistic regression model, Statistical Theory and Related Fields, 5:3, 265-274, DOI: 10.1080/24754269.2020.1796098

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