IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v86y2023i6d10.1007_s00184-022-00890-1.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-022-00890-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s00184-022-00890-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Xin & Yue, Rong-Xian & Chatterjee, Kashinath, 2014. "R-optimal designs in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 88(C), pages 127-132.
    2. He, Lei & He, Daojiang, 2020. "R-optimal designs for individual prediction in random coefficient regression models," Statistics & Probability Letters, Elsevier, vol. 159(C).
    3. Dennis Schmidt & Rainer Schwabe, 2015. "On optimal designs for censored data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 237-257, April.
    4. Lenka Filová & Mária Trnovská & Radoslav Harman, 2012. "Computing maximin efficient experimental designs using the methods of semidefinite programming," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(5), pages 709-719, July.
    5. Sanjoy Sinha, 2013. "Robust designs for multivariate logistic regression," METRON, Springer;Sapienza Università di Roma, vol. 71(2), pages 157-173, September.
    6. Dette, Holger & O'Brien, Timothy E., 2003. "Efficient experimental design for the Behrens-Fisher problem with application to bioassay," Technical Reports 2003,21, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    7. Harman, Radoslav & Jurík, Tomás, 2008. "Computing c-optimal experimental designs using the simplex method of linear programming," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 247-254, December.
    8. Dette, Holger & Melas, Viatcheslav B. & Pepelyshev, Andrey, 2006. "Optimal designs for free knot least squares splines," Technical Reports 2006,34, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    9. Geraint Johnes & Robert McNabb, 2004. "Never Give up on the Good Times: Student Attrition in the UK," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 66(1), pages 23-47, February.
    10. Li, Guanghui & Zhang, Chongqi, 2017. "The pseudo component transformation design for experiment with mixture," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 19-24.
    11. Dette, Holger & Pepelyshev, Andrey & Wong, Weng Kee, 2008. "Optimal designs for dose finding experiments in toxicity studies," Technical Reports 2008,09, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    12. Kumbhakar, Subal C. & Tsionas, Efthymios G., 2005. "Measuring technical and allocative inefficiency in the translog cost system: a Bayesian approach," Journal of Econometrics, Elsevier, vol. 126(2), pages 355-384, June.
    13. Dette, Holger & Pepelyshev, Andrey & Zhigljavsky, Anatoly, 2014. "‘Nearly’ universally optimal designs for models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 1103-1112.
    14. Tekle, Fetene B. & Tan, Frans E.S. & Berger, Martijn P.F., 2008. "Maximin D-optimal designs for binary longitudinal responses," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5253-5262, August.
    15. Tutz, Gerhard & Kauermann, Goran, 2003. "Generalized linear random effects models with varying coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 43(1), pages 13-28, May.
    16. Giorgio Calzolari & F. Mealli & C. Rampichini, 2001. "Alternative Simulation-Based Estimators of Logit Models with Random Effects," Econometrics Working Papers Archive quaderno48, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
    17. Dette, Holger & Biedermann, Stefanie & Pepelyshev, Andrey, 2004. "Some robust design strategies for percentile estimation in binary response models," Technical Reports 2004,19, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    18. Dette, Holger & Biedermann, Stefanie & Zhu, Wei, 2005. "Geometric construction of optimal designs for dose-responsemodels with two parameters," Technical Reports 2005,08, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    19. Holger Dette & Laura Hoyden & Sonja Kuhnt & Kirsten Schorning, 2017. "Optimal designs for thermal spraying," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 66(1), pages 53-72, January.
    20. Kocher, Martin G. & Pogrebna, Ganna & Sutter, Matthias, 2013. "Other-regarding preferences and management styles," Journal of Economic Behavior & Organization, Elsevier, vol. 88(C), pages 109-132.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:86:y:2023:i:6:d:10.1007_s00184-022-00890-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.