IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v65y2024i5d10.1007_s00362-023-01514-0.html
   My bibliography  Save this article

Locally optimal designs for comparing curves in generalized linear models

Author

Listed:
  • Chang-Yu Liu

    (Shanghai Normal University)

  • Xin Liu

    (Donghua University)

  • Rong-Xian Yue

    (Shanghai Normal University)

Abstract

This article is concerned with the optimal design problem of efficient statistical inference for comparing regression mean curves in two generalized linear models (GLMs) estimated from two samples of independent measurements. The main objective is to find the locally $$\mu _p$$ μ p -optimal designs for given values of the model parameters that minimize an $$L_p$$ L p -norm of the asymptotic variance of the difference between the two estimated regression curves. Two equivalence theorems are given to verify the locally $$\mu _p$$ μ p -optimality of the designs in the set of all approximate designs for the comparison of regression curves in two GLMs. Several numerical examples are presented to illustrate the superiorities of the locally $$\mu _p$$ μ p -optimal designs ( $$p=1,\infty $$ p = 1 , ∞ ) by comparing them with equidistant designs and individual D-optimal designs for the comparison of regression curves in different scenarios.

Suggested Citation

  • Chang-Yu Liu & Xin Liu & Rong-Xian Yue, 2024. "Locally optimal designs for comparing curves in generalized linear models," Statistical Papers, Springer, vol. 65(5), pages 3181-3201, July.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01514-0
    DOI: 10.1007/s00362-023-01514-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-023-01514-0
    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/s00362-023-01514-0?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. Liu W. & Jamshidian M. & Zhang Y., 2004. "Multiple Comparison of Several Linear Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 395-403, January.
    2. Dette, Holger & Schorning, Kirsten & Konstantinou, Maria, 2017. "Optimal designs for comparing regression models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 273-286.
    3. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    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. Sanyu Zhou, 2018. "An exact method for the multiple comparison of several polynomial regression models with applications in dose-response study," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 413-429, July.
    2. Liu, Xin & Ye, Min & Yue, Rong-Xian, 2021. "Optimal designs for comparing population curves in hierarchical models," Statistics & Probability Letters, Elsevier, vol. 178(C).
    3. Sanyu Zhou & Defa Wang & Jingjing Zhu, 2020. "Construction of simultaneous confidence bands for a percentile hyper-plane with predictor variables constrained in an ellipsoidal region," Statistical Papers, Springer, vol. 61(3), pages 1335-1346, June.
    4. Kato, Naohiro & Kuriki, Satoshi, 2013. "Likelihood ratio tests for positivity in polynomial regressions," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 334-346.
    5. Kathrin Möllenhoff & Achim Tresch, 2023. "Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(3), pages 483-507, July.
    6. Su, Haiyan & Liang, Hua, 2010. "An empirical likelihood-based method for comparison of treatment effects--Test of equality of coefficients in linear models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1079-1088, April.
    7. Sanyu Zhou, 2017. "One-sided hyperbolic simultaneous confidence bands for multiple and polynomial regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 187-200, February.
    8. Dette, Holger & Schorning, Kirsten & Konstantinou, Maria, 2017. "Optimal designs for comparing regression models with correlated observations," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 273-286.
    9. Lu, Xiaolei & Kuriki, Satoshi, 2017. "Simultaneous confidence bands for contrasts between several nonlinear regression curves," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 83-104.
    10. Jamshidian, Mortaza & Jennrich, Robert I. & Liu, Wei, 2007. "A study of partial F tests for multiple linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6269-6284, August.
    11. Frank Schaarschmidt, 2017. "Multiple treatment comparisons in analysis of covariance with interaction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(4), pages 609-628, November.
    12. Christopher Withers & Saralees Nadarajah, 2012. "Maximum modulus confidence bands," Statistical Papers, Springer, vol. 53(4), pages 811-819, November.
    13. Sophia Rosen & Ori Davidov, 2017. "Ordered Regressions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(4), pages 817-842, December.
    14. Jamshidian, Mortaza & Liu, Wei & Zhang, Ying & Jamishidian, Farid, 2005. "Simreg: a Software Including Some New Developments in Multiple Comparison and Simultaneous Confidence Bands for Linear Regression Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 12(i02).
    15. Liu, W. & Hayter, A.J. & Piegorsch, W.W. & Ah-Kine, P., 2009. "Comparison of hyperbolic and constant width simultaneous confidence bands in multiple linear regression under MVCS criterion," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1432-1439, August.
    16. W. Liu & F. Bretz & A. J. Hayter & H. P. Wynn, 2009. "Assessing Nonsuperiority, Noninferiority, or Equivalence When Comparing Two Regression Models Over a Restricted Covariate Region," Biometrics, The International Biometric Society, vol. 65(4), pages 1279-1287, December.
    17. Jamshidian, Mortaza & Liu, Wei & Bretz, Frank, 2010. "Simultaneous confidence bands for all contrasts of three or more simple linear regression models over an interval," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1475-1483, June.
    18. Soichiro Yamauchi, 2020. "Difference-in-Differences for Ordinal Outcomes: Application to the Effect of Mass Shootings on Attitudes toward Gun Control," Papers 2009.13404, arXiv.org.

    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:stpapr:v:65:y:2024:i:5:d:10.1007_s00362-023-01514-0. 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.