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Strategies for Modeling a Categorical Variable Allowing Multiple Category Choices

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  • ALAN AGRESTI

    (University of Florida)

  • IVY LIU

    (Victoria University of Wellington)

Abstract

This article discusses strategies for modeling a categorical variable when subjects can select any subset of the categories. With c outcome categories, the models relate to a c- dimensional binary response, with each component indicating whether a particular category is chosen. The strategies are the following: (1) Using logit models directly for the marginal distribution of each component; this accounts for dependence among the component responses but does not treat the dependence as an integral part of the model. (2) Using logit models containing subject random effects to generate the dependence among the components; this approach is limited by implying nonnegative associations having a certain exchangeability. (3) Using loglinear modeling; quasi-symmetric ones are useful but are limited to estimation of within-subject effects. Marginal logit models less fully describe the dependence patterns for the data but require fewer assumptions and focus more directly on the effects of greatest substantive interest.

Suggested Citation

  • 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.
    • Handle: RePEc:sae:somere:v:29:y:2001:i:4:p:403-434
    DOI: 10.1177/0049124101029004001
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    References listed on IDEAS

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    1. Brent A. Coull & Alan Agresti, 2000. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution," Biometrics, The International Biometric Society, vol. 56(1), pages 73-80, 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. 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.
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    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.
    3. 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.

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