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V-optimality of designs in random effects Poisson regression models

Author

Listed:
  • Mehrdad Niaparast

    (Razi University)

  • Sahar MehrMansour

    (Razi University)

  • Rainer Schwabe

    (Otto-von-Guericke University)

Abstract

The knowledge of the Fisher information is a fundamental tool to judge the quality of an experiment. Unlike in linear and generalized linear models without random effects, there is no closed form for the Fisher information in the situation of generalized linear mixed models, in general. To circumvent this problem, we make use of the quasi-information in this paper as an approximation to the Fisher information. We derive optimal designs based on the V-criterion, which aims to minimize the average variance of prediction of the mean response. For this criterion, we obtain locally optimal designs in two specific cases of a Poisson straight line regression model with either random intercepts or random slopes.

Suggested Citation

  • Mehrdad Niaparast & Sahar MehrMansour & Rainer Schwabe, 2023. "V-optimality of designs in random effects Poisson regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(8), pages 879-897, November.
    • Handle: RePEc:spr:metrik:v:86:y:2023:i:8:d:10.1007_s00184-023-00896-3
    DOI: 10.1007/s00184-023-00896-3
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    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. Niaparast, Mehrdad, 2009. "On optimal design for a Poisson regression model with random intercept," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 741-747, March.
    3. 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.
    Full references (including those not matched with items on IDEAS)

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