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Standardized maximin D- and c-optimal designs for the Poisson–Gamma model

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  • Marius Schmidt

    (Otto-von-Guericke-University Magdeburg)

Abstract

The Poisson–Gamma model is obtained as a generalization of the Poisson model, when Gamma distributed block effects are assumed for Poisson count data. We show that optimal designs for estimating linear combinations of the model parameters coincide for the case of known and unknown parameters of the Gamma distribution. To obtain robust designs regarding parameter misspecification we determine standardized maximin D-optimal designs for a binary and a continuous design region. For standardized maximin c-optimality we show that the optimal designs for the Poisson–Gamma and Poisson model are equal and derive optimal designs for both models.

Suggested Citation

  • Marius Schmidt, 2023. "Standardized maximin D- and c-optimal designs for the Poisson–Gamma model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(6), pages 697-721, August.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:6:d:10.1007_s00184-022-00890-1
    DOI: 10.1007/s00184-022-00890-1
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    References listed on IDEAS

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    1. Thomas Schmelter, 2007. "The Optimality of Single-group Designs for Certain Mixed Models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 65(2), pages 183-193, February.
    2. Longford, N. T., 1994. "Logistic regression with random coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 17(1), pages 1-15, January.
    3. 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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