IDEAS home Printed from https://ideas.repec.org/a/sae/jedbes/v42y2017i5p531-558.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.3102/1076998617694878
    Download Restriction: no
    File URL: https://libkey.io/10.3102/1076998617694878?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
    ---><---

    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, September.
    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)

    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. Christian Kleiber & Achim Zeileis, 2016. "Visualizing Count Data Regressions Using Rootograms," The American Statistician, Taylor & Francis Journals, vol. 70(3), pages 296-303, July.
    2. Moritz Berger & Gerhard Tutz, 2021. "Transition models for count data: a flexible alternative to fixed distribution models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(4), pages 1259-1283, October.
    3. Yingbin Zhang & Zhaoxi Yang & Yehui Wang, 2022. "The Impact of Extreme Response Style on the Mean Comparison of Two Independent Samples," SAGE Open, , vol. 12(2), pages 21582440221, June.
    4. Besstremyannaya, Galina, 2017. "Measuring income equity in the demand for healthcare with finite mixture models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 46, pages 5-29.
    5. Anne Thissen-Roe & David Thissen, 2013. "A Two-Decision Model for Responses to Likert-Type Items," Journal of Educational and Behavioral Statistics, , vol. 38(5), pages 522-547, October.
    6. Bach, Philipp & Farbmacher, Helmut & Spindler, Martin, 2018. "Semiparametric count data modeling with an application to health service demand," Econometrics and Statistics, Elsevier, vol. 8(C), pages 125-140.
    7. Gerhard Tutz & Moritz Berger, 2016. "Response Styles in Rating Scales," Journal of Educational and Behavioral Statistics, , vol. 41(3), pages 239-268, June.
    8. Galina Besstremyannaya, 2014. "Heterogeneous effect of coinsurance rate on healthcare costs: generalized finite mixtures and matching estimators," Discussion Papers 14-014, Stanford Institute for Economic Policy Research.
    9. Prince, Diogo de, 2018. "Are price hazard functions really decreasing functions in Brazil?," Journal of Macroeconomics, Elsevier, vol. 57(C), pages 266-276.
    10. Luiz Paulo Fávero & Joseph F. Hair & Rafael de Freitas Souza & Matheus Albergaria & Talles V. Brugni, 2021. "Zero-Inflated Generalized Linear Mixed Models: A Better Way to Understand Data Relationships," Mathematics, MDPI, vol. 9(10), pages 1-28, May.
    11. Gan, Li & Huang, Feng & Mayer, Adalbert, 2015. "A simple test for private information in insurance markets with heterogeneous insurance demand," Economics Letters, Elsevier, vol. 136(C), pages 197-200.
    12. Brown, Sarah & Greene, William H. & Harris, Mark N. & Taylor, Karl, 2015. "An inverse hyperbolic sine heteroskedastic latent class panel tobit model: An application to modelling charitable donations," Economic Modelling, Elsevier, vol. 50(C), pages 228-236.
    13. Riccardo (Jack) Lucchetti & Luca Pedini, 2020. "ParMA: Parallelised Bayesian Model Averaging for Generalised Linear Models," Working Papers 2020:28, Department of Economics, University of Venice "Ca' Foscari".
    14. Landry, Craig E. & Shonkwiler, J. Scott & Whitehead, John C., 2020. "Economic Values of Coastal Erosion Management: Joint Estimation of Use and Existence Values with recreation demand and contingent valuation data," Journal of Environmental Economics and Management, Elsevier, vol. 103(C).
    15. Mónica Moreno-Gutiérrez & Víctor Hernández-Trejo & Ramón Valdivia-Alcalá & Judith Juárez-Mancilla & Plácido Roberto Cruz-Chávez & Ulianov Jakes-Cota, 2024. "Linking Tourist Willingness to Pay and Beach Management: A Travel Cost Analysis for Balandra Marine Park, Mexico," Tourism and Hospitality, MDPI, vol. 5(4), pages 1-20, October.
    16. Ghosh, Prasenjit & Rong, Jian & Khanna, Madhu & Wang, Weiwei & Miao, Ruiqing, 2017. "Have They Gone with the Wind? Indirect Effects of Wind Turbines on Bird Abundance," 2017 Annual Meeting, July 30-August 1, Chicago, Illinois 258100, Agricultural and Applied Economics Association.
    17. Mullahy, John, 2024. "Analyzing health outcomes measured as bounded counts," Journal of Health Economics, Elsevier, vol. 95(C).
    18. Michel Beine & Ilan Noy & Christopher Parsons, 2021. "Climate change, migration and voice," Climatic Change, Springer, vol. 167(1), pages 1-27, July.
    19. Andrés López-Sepulcre & Sebastiano De Bona & Janne K. Valkonen & Kate D.L. Umbers & Johanna Mappes, 2015. "Item Response Trees: a recommended method for analyzing categorical data in behavioral studies," Behavioral Ecology, International Society for Behavioral Ecology, vol. 26(5), pages 1268-1273.
    20. D M Zimmer, 2023. "The effect of food stamps on fibre intake," Economic Issues Journal Articles, Economic Issues, vol. 28(2), pages 71-86, September.

    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:sae:jedbes:v:42:y:2017:i:5:p:531-558. 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: SAGE Publications (email available below). General contact details of provider: .

    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.