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Item Response Modeling of Multivariate Count Data With Zero Inflation, Maximum Inflation, and Heaping

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  • Brooke E. Magnus

    (Marquette University)

  • David Thissen

    (University of North Carolina)

Abstract

Questionnaires that include items eliciting count responses are becoming increasingly common in psychology. This study proposes methodological techniques to overcome some of the challenges associated with analyzing multivariate item response data that exhibit zero inflation, maximum inflation, and heaping at preferred digits. The modeling framework combines approaches from three literatures: item response theory (IRT) models for multivariate count data, latent variable models for heaping and extreme responding, and mixture IRT models. Data from the Behavioral Risk Factor Surveillance System are used as a motivating example. Practical implications are discussed, and recommendations are provided for researchers who may wish to use count items on questionnaires.

Suggested Citation

  • Brooke E. Magnus & David Thissen, 2017. "Item Response Modeling of Multivariate Count Data With Zero Inflation, Maximum Inflation, and Heaping," Journal of Educational and Behavioral Statistics, , vol. 42(5), pages 531-558, October.
    • Handle: RePEc:sae:jedbes:v:42:y:2017:i:5:p:531-558
    DOI: 10.3102/1076998617694878
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    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. De Boeck, Paul & Partchev, Ivailo, 2012. "IRTrees: Tree-Based Item Response Models of the GLMM Family," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(c01).
    3. R. Darrell Bock, 1972. "Estimating item parameters and latent ability when responses are scored in two or more nominal categories," Psychometrika, Springer;The Psychometric Society, vol. 37(1), pages 29-51, March.
    4. Deb, Partha & Trivedi, Pravin K, 1997. "Demand for Medical Care by the Elderly: A Finite Mixture Approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(3), pages 313-336, May-June.
    5. repec:ehl:lserod:61889 is not listed on IDEAS
    6. Wedel, Michel & Böckenholt, Ulf & Kamakura, Wagner A., 2003. "Factor models for multivariate count data," Journal of Multivariate Analysis, Elsevier, vol. 87(2), pages 356-369, November.
    Full references (including those not matched with items on IDEAS)

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