IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v78y2016i1d10.1007_s13571-015-0109-z.html
   My bibliography  Save this article

Goodness of Fit of Product Multinomial Regression Models to Sparse Data

Author

Listed:
  • Dianliang Deng

    (University of Regina)

  • Sudhir R. Paul

    (University of Windsor)

Abstract

Tests of goodness of fit of sparse multinomial models with non-canonical links is proposed by using approximations to the first three moments of the conditional distribution of a modified Pearson Chi-square statistic. The modified Pearson statistic is obtained using a supplementary estimating equation approach. Approximations to the first three conditional moments of the modified Pearson statistic are derived. A simulation study is conducted to compare, in terms of empirical size and power, the usual Pearson Chi-square statistic, the standardized modified Pearson Chi-square statistic using the first two conditional moments, a method using Edgeworth approximation of the p-values based on the first three conditional moments and a score test statistic. There does not seems to be any qualitative difference in size of the four methods. However, the standardized modified Pearson Chi-square statistic and the Edgeworth approximation method of obtaining p-values using the first three conditional moments show power advantages compared to the usual Pearson Chi-square statistic, and the score test statistic. In some situations, for example, for small nominal level, the standardized modified Pearson Chi-square statistic shows some power advantage over the method using Edgeworth approximation of the p-values using the first three conditional moments. Also, the former is easier to use and so is preferable. Two data sets are analyzed and a discussion is given.

Suggested Citation

  • Dianliang Deng & Sudhir R. Paul, 2016. "Goodness of Fit of Product Multinomial Regression Models to Sparse Data," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 78-95, May.
    • Handle: RePEc:spr:sankhb:v:78:y:2016:i:1:d:10.1007_s13571-015-0109-z
    DOI: 10.1007/s13571-015-0109-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-015-0109-z
    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/s13571-015-0109-z?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. Kim, Sung-Ho & Choi, Hyemi & Lee, Sangjin, 2009. "Estimate-based goodness-of-fit test for large sparse multinomial distributions," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1122-1131, February.
    2. S. R. Paul & D. Deng, 2000. "Goodness of fit of generalized linear models to sparse data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 323-333.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Farzana Afroz & Matt Parry & David Fletcher, 2020. "Estimating overdispersion in sparse multinomial data," Biometrics, The International Biometric Society, vol. 76(3), pages 834-842, September.

    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. Farzana Afroz & Matt Parry & David Fletcher, 2020. "Estimating overdispersion in sparse multinomial data," Biometrics, The International Biometric Society, vol. 76(3), pages 834-842, September.
    2. Jiménez-Gamero, M.D. & Pino-Mejías, R. & Alba-Fernández, V. & Moreno-Rebollo, J.L., 2011. "Minimum [phi]-divergence estimation in misspecified multinomial models," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3365-3378, December.

    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:78:y:2016:i:1:d:10.1007_s13571-015-0109-z. 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.