IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v81y2019i2d10.1007_s13571-018-0171-4.html
   My bibliography  Save this article

Liu-Type Multinomial Logistic Estimator

Author

Listed:
  • Mohamed R. Abonazel

    (Cairo University)

  • Rasha A. Farghali

    (Helwan University)

Abstract

Multicollinearity in multinomial logistic regression affects negatively on the variance of the maximum likelihood estimator. That leads to inflated confidence intervals and theoretically important variables become insignificant in testing hypotheses. In this paper, Liu-type estimator is proposed that has smaller total mean squared error than the maximum likelihood estimator. The proposed estimator is a general estimator which includes other biased estimators such as Liu estimator and ridge estimator as special cases. Simulation studies and an application are given to evaluate the performance of our estimator. The results indicate that the proposed estimator is more efficient and reliable than the conventional estimators.

Suggested Citation

  • Mohamed R. Abonazel & Rasha A. Farghali, 2019. "Liu-Type Multinomial Logistic Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(2), pages 203-225, December.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0171-4
    DOI: 10.1007/s13571-018-0171-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-018-0171-4
    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/s13571-018-0171-4?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. Månsson, Kristofer & Kibria, B.M. Golam & Shukur, Ghazi, 2012. "On Liu estimators for the logit regression model," Economic Modelling, Elsevier, vol. 29(4), pages 1483-1488.
    2. Faisal Zahid & Gerhard Tutz, 2013. "Ridge estimation for multinomial logit models with symmetric side constraints," Computational Statistics, Springer, vol. 28(3), pages 1017-1034, June.
    3. Fatma Kurnaz & Kadri Akay, 2015. "A new Liu-type estimator," Statistical Papers, Springer, vol. 56(2), pages 495-517, May.
    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. Adewale F. Lukman & B. M. Golam Kibria & Cosmas K. Nziku & Muhammad Amin & Emmanuel T. Adewuyi & Rasha Farghali, 2023. "K-L Estimator: Dealing with Multicollinearity in the Logistic Regression Model," Mathematics, MDPI, vol. 11(2), pages 1-14, January.
    2. R. Salmerón & J. García & C. B. García & M. M. López Martín, 2017. "A note about the corrected VIF," Statistical Papers, Springer, vol. 58(3), pages 929-945, September.
    3. Faisal Zahid & Gerhard Tutz, 2013. "Multinomial logit models with implicit variable selection," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(4), pages 393-416, December.
    4. M. Revan Özkale & Atif Abbasi, 2022. "Iterative restricted OK estimator in generalized linear models and the selection of tuning parameters via MSE and genetic algorithm," Statistical Papers, Springer, vol. 63(6), pages 1979-2040, December.
    5. Iqra Babar & Hamdi Ayed & Sohail Chand & Muhammad Suhail & Yousaf Ali Khan & Riadh Marzouki, 2021. "Modified Liu estimators in the linear regression model: An application to Tobacco data," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-13, November.
    6. N. H. Jadhav, 2020. "On linearized ridge logistic estimator in the presence of multicollinearity," Computational Statistics, Springer, vol. 35(2), pages 667-687, June.
    7. Ghazi Shukur & Kristofer Månsson & Pär Sjölander, 2015. "Developing Interaction Shrinkage Parameters for the Liu Estimator — with an Application to the Electricity Retail Market," Computational Economics, Springer;Society for Computational Economics, vol. 46(4), pages 539-550, December.
    8. M. Arashi & T. Valizadeh, 2015. "Performance of Kibria’s methods in partial linear ridge regression model," Statistical Papers, Springer, vol. 56(1), pages 231-246, February.
    9. Arashi, M. & Kibria, B.M. Golam & Norouzirad, M. & Nadarajah, S., 2014. "Improved preliminary test and Stein-rule Liu estimators for the ill-conditioned elliptical linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 53-74.
    10. M. Revan Özkale, 2016. "Iterative algorithms of biased estimation methods in binary logistic regression," Statistical Papers, Springer, vol. 57(4), pages 991-1016, December.
    11. Özkale, M. Revan & Arıcan, Engin, 2015. "First-order r−d class estimator in binary logistic regression model," Statistics & Probability Letters, Elsevier, vol. 106(C), pages 19-29.

    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:sankhb:v:81:y:2019:i:2:d:10.1007_s13571-018-0171-4. 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.