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

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  • 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
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    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.
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