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D-Optimal Design for a Five-Parameter Logistic Model

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mODa 9 – Advances in Model-Oriented Design and Analysis

Part of the book series: Contributions to Statistics ((CONTRIB.STAT.))

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Abstract

We explore the D-optimal design for a five-parameter logistic model, which includes a shape parameter to handle asymmetries, and two threshold parameters to account for situations where the asymptotes are not at 0 and 1. The optimal design is five points, including points at -∞ and ∞ representing the thresholds. We compare the efficiencies of the optimal designs arising from the two- and five- parameter models. We find a significant loss of efficiency when the two-parameter model is used on data generated from the five-parameter model.

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Acknowledgements

The authors thank two excellent referees for their detailed comments. One of the referees found a major mistake, and the authors are deeply appreciative.

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Authors and Affiliations

  1. The EMMES Corporation, 401 N. Washington St, Rockville, MD, 20850, USA

    Zorayr Manukyan

  2. Department of Statistics, George Mason University, 4400 University Dr., MS 4A7, Fairfax, VA, 22030-4444, USA

    William F. Rosenberger

Authors
  1. Zorayr Manukyan
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  2. William F. Rosenberger
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Corresponding author

Correspondence to Zorayr Manukyan .

Editor information

Editors and Affiliations

  1. Dipt. di Scienze Statistiche, University of Bologna, Via Belle Arti 41, Bologna, 40126, Italy

    Alessandra Giovagnoli

  2. and Political Science, Department of Statistics, London School Economics, Houghton Street, London, WC2A 2AE, United Kingdom

    Anthony C. Atkinson

  3. Department of Statistics, University of Glasgow, University Gardens 15, Glasgow, G12 8QW, United Kingdom

    Bernard Torsney

  4. , SEMEQ, Università del Piemonte Orientale, via Perrone 18, Novara, 28100, Italy

    Caterina May

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Manukyan, Z., Rosenberger, W.F. (2010). D-Optimal Design for a Five-Parameter Logistic Model. In: Giovagnoli, A., Atkinson, A., Torsney, B., May, C. (eds) mODa 9 – Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2410-0_15

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