IDEAS home Printed from https://ideas.repec.org/a/spr/stmapp/v28y2019i1d10.1007_s10260-018-0429-z.html
   My bibliography  Save this article

Mantel–Haenszel estimators of a common odds ratio for multiple response data

Author

Listed:
  • Thomas Suesse

    (University of Wollongong)

  • Ivy Liu

    (Victoria University of Wellington)

Abstract

For a two-way contingency table, odds ratios are commonly used to describe the relationships between the row and column variables. In the ordinary case cells are mutually exclusive, that is each subject must fit into one and only one cell. However, in many surveys respondents may select more than one outcome category, commonly referred to as multiple responses. We discuss model-based and Mantel–Haenszel estimators of an assumed common odds ratio for several $$2\times c$$ 2 × c tables, where the two rows refer to independent groups and the c columns to multiple responses, treating the multiple responses as an extension of the multinomial sampling model. We derive new dually consistent (co)variance estimators for the Mantel–Haenszel odds ratio estimators and show their performance in a simulation study and illustrate the estimators on a linguistic data set.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:1:d:10.1007_s10260-018-0429-z
    DOI: 10.1007/s10260-018-0429-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10260-018-0429-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/s10260-018-0429-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. Y. J. Decady & D. R. Thomas, 2000. "A Simple Test of Association for Contingency Tables with Multiple Column Responses," Biometrics, The International Biometric Society, vol. 56(3), pages 893-896, September.
    2. 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.
    3. Christopher R. Bilder & Thomas M. Loughin, 2004. "Testing for Marginal Independence between Two Categorical Variables with Multiple Responses," Biometrics, The International Biometric Society, vol. 60(1), pages 241-248, March.
    4. 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.
    5. Christopher R. Bilder & Thomas M. Loughin, 2002. "Testing for Conditional Multiple Marginal Independence," Biometrics, The International Biometric Society, vol. 58(1), pages 200-208, March.
    6. 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.
    7. Christopher R. Bilder & Thomas M. Loughin, 2001. "On the First-Order Rao—Scott Correction of the Umesh—Loughin—Scherer Statistic," Biometrics, The International Biometric Society, vol. 57(4), pages 1253-1255, 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. 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. Christopher R. Bilder & Thomas M. Loughin, 2002. "Testing for Conditional Multiple Marginal Independence," Biometrics, The International Biometric Society, vol. 58(1), pages 200-208, March.
    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. Stahl, Florian & Schomm, Fabian & Vomfell, Lara & Vossen, Gottfried, 2015. "Marketplaces for digital data: Quo vadis?," ERCIS Working Papers 24, University of Münster, European Research Center for Information Systems (ERCIS).
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    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. Dongjuan Xu & Greg Arling, 2023. "Are Frail Older People from Racial/Ethnic Minorities at Double Jeopardy of Putting off Healthcare during the Pandemic?," IJERPH, MDPI, vol. 20(2), pages 1-12, January.
    11. 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.
    12. Christopher R. Bilder & Thomas M. Loughin, 2001. "On the First-Order Rao—Scott Correction of the Umesh—Loughin—Scherer Statistic," Biometrics, The International Biometric Society, vol. 57(4), pages 1253-1255, December.
    13. 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.
    14. 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.
    15. Thomas W. McDaniel & Carissa L. Wonkka & Morgan L. Treadwell & Urs P. Kreuter, 2021. "Factors Influencing County Commissioners’ Decisions about Burn Bans in the Southern Plains, USA," Land, MDPI, vol. 10(7), pages 1-13, June.

    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:stmapp:v:28:y:2019:i:1:d:10.1007_s10260-018-0429-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.