IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v56y2012i9p2705-2717.html
   My bibliography  Save this article

Mantel–Haenszel estimators of odds ratios for stratified dependent binomial data

Author

Listed:
  • Suesse, Thomas
  • Liu, Ivy

Abstract

A standard approach to analyzing n binary matched pairs usually represented in n 2×2 tables is to apply a subject-specific model; for the simplest situation it is the so-called Rasch model. An alternative population-averaged approach is to apply a marginal model to the single 2×2 table formed by n subjects. For the situation of having an additional stratification variable with K levels forming K 2×2 tables, standard fitting approaches, such as generalized estimating equations and maximum likelihood, or, alternatively, the standard Mantel–Haenszel (MH) estimator, can be applied. However, while all these standard approaches are consistent under a large-stratum limiting model, they are not consistent under a sparse-data limiting model. In this paper, we propose a new MH estimator and a variance estimator that are both dually consistent: consistent under both large-stratum and sparse-data limiting situations. In a simulation study, the properties of the proposed estimators are confirmed, and the estimator is compared with standard marginal methods. The simulation study also considers the case when the homogeneity assumption of the odds ratios does not hold, and the asymptotic limit of the proposed MH estimator under this situation is derived. The results show that the proposed MH estimator is generally better than the standard estimator, and the same can be said about the associated Wald-type confidence intervals.

Suggested Citation

  • Suesse, Thomas & Liu, Ivy, 2012. "Mantel–Haenszel estimators of odds ratios for stratified dependent binomial data," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2705-2717.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2705-2717
    DOI: 10.1016/j.csda.2012.02.015
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000977
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2012.02.015?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. Haber, Michael, 1985. "Maximum likelihood methods for linear and log-linear models in categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 3(1), pages 1-10, May.
    2. Alan Agresti & I-Ming Liu, 1999. "Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices," Biometrics, The International Biometric Society, vol. 55(3), pages 936-943, September.
    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. Thomas Suesse & Ivy Liu, 2013. "Modelling Strategies for Repeated Multiple Response Data," International Statistical Review, International Statistical Institute, vol. 81(2), pages 230-248, August.
    2. Thomas Suesse & Ivy Liu, 2019. "Mantel–Haenszel estimators of a common odds ratio for multiple response data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 57-76, March.

    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. Alan Agresti & Ivy Liu, 2001. "Strategies for Modeling a Categorical Variable Allowing Multiple Category Choices," Sociological Methods & Research, , vol. 29(4), pages 403-434, May.
    2. Inés M. Varas & Jorge González & Fernando A. Quintana, 2020. "A Bayesian Nonparametric Latent Approach for Score Distributions in Test Equating," Journal of Educational and Behavioral Statistics, , vol. 45(6), pages 639-666, December.
    3. Pelenur, Marcos J. & Cruickshank, Heather J., 2012. "Closing the Energy Efficiency Gap: A study linking demographics with barriers to adopting energy efficiency measures in the home," Energy, Elsevier, vol. 47(1), pages 348-357.
    4. Högberg, Hans & Svensson, Elisabeth, 2008. "An Overview of Methods in the Analysis of Dependent ordered catagorical Data: Assumptions and Implications," Working Papers 2008:7, Örebro University, School of Business.
    5. Jokinen, Jukka, 2006. "Fast estimation algorithm for likelihood-based analysis of repeated categorical responses," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 1509-1522, December.
    6. Nettleton, Dan & Banerjee, T., 2001. "Testing the equality of distributions of random vectors with categorical components," Computational Statistics & Data Analysis, Elsevier, vol. 37(2), pages 195-208, August.
    7. Alan Agresti & I-Ming Liu, 1999. "Modeling a Categorical Variable Allowing Arbitrarily Many Category Choices," Biometrics, The International Biometric Society, vol. 55(3), pages 936-943, September.
    8. Menendez, M. L. & Pardo, J. A. & Pardo, L. & Zografos, K., 2003. "On tests of homogeneity based on minimum [phi]-divergence estimator with constraints," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 215-234, June.
    9. Paulino, Carlos Daniel M. & Silva, Giovani Loiola, 1999. "On the maximum-likelihood analysis of the general linear model in categorical data," Computational Statistics & Data Analysis, Elsevier, vol. 30(2), pages 197-204, April.
    10. Thomas Suesse & Ivy Liu, 2019. "Mantel–Haenszel estimators of a common odds ratio for multiple response data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(1), pages 57-76, March.

    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:eee:csdana:v:56:y:2012:i:9:p:2705-2717. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.