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D-optimal designs for Poisson regression with synergetic interaction effect

Author

Listed:
  • Fritjof Freise

    (University of Veterinary Medicine Hannover)

  • Ulrike Graßhoff

    (Humboldt-University Berlin)

  • Frank Röttger

    (University of Geneva)

  • Rainer Schwabe

    (Otto-von-Guericke-University Magdeburg)

Abstract

We characterize D-optimal designs in the two-dimensional Poisson regression model with synergetic interaction and provide an explicit proof. The proof is based on the idea of reparameterization of the design region in terms of contours of constant intensity. This approach leads to a substantial reduction in complexity as properties of the sensitivity can be treated along and across the contours separately. Furthermore, some extensions of this result to higher dimensions are presented.

Suggested Citation

  • Fritjof Freise & Ulrike Graßhoff & Frank Röttger & Rainer Schwabe, 2021. "D-optimal designs for Poisson regression with synergetic interaction effect," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1004-1025, December.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:4:d:10.1007_s11749-020-00752-w
    DOI: 10.1007/s11749-020-00752-w
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    References listed on IDEAS

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    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, September.
    2. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
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