IDEAS home Printed from https://ideas.repec.org/a/bla/istatr/v89y2021i1p18-35.html
   My bibliography  Save this article

Hierarchical Models for the Analysis of Likert Scales in Regression and Item Response Analysis

Author

Listed:
  • Gerhard Tutz

Abstract

Appropriate modelling of Likert‐type items should account for the scale level and the specific role of the neutral middle category, which is present in most Likert‐type items that are in common use. Powerful hierarchical models that account for both aspects are proposed. To avoid biased estimates, the models separate the neutral category when modelling the effects of explanatory variables on the outcome. The main model that is propagated uses binary response models as building blocks in a hierarchical way. It has the advantage that it can be easily extended to include response style effects and non‐linear smooth effects of explanatory variables. By simple transformation of the data, available software for binary response variables can be used to fit the model. The proposed hierarchical model can be used to investigate the effects of covariates on single Likert‐type items and also for the analysis of a combination of items. For both cases, estimation tools are provided. The usefulness of the approach is illustrated by applying the methodology to a large data set.

Suggested Citation

  • Gerhard Tutz, 2021. "Hierarchical Models for the Analysis of Likert Scales in Regression and Item Response Analysis," International Statistical Review, International Statistical Institute, vol. 89(1), pages 18-35, April.
    • Handle: RePEc:bla:istatr:v:89:y:2021:i:1:p:18-35
    DOI: 10.1111/insr.12396
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/insr.12396
    Download Restriction: no
    File URL: https://libkey.io/10.1111/insr.12396?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. David Andrich, 2010. "Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 292-308, June.
    2. Fumiko Samejima, 1995. "Acceleration model in the heterogeneous case of the general graded response model," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 549-572, December.
    3. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    4. Marx, Brian D. & Eilers, Paul H. C., 1998. "Direct generalized additive modeling with penalized likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 28(2), pages 193-209, August.
    5. Timothy Johnson, 2003. "On the use of heterogeneous thresholds ordinal regression models to account for individual differences in response style," Psychometrika, Springer;The Psychometric Society, vol. 68(4), pages 563-583, December.
    6. 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).
    7. Rainer Göb & Christopher McCollin & Maria Ramalhoto, 2007. "Ordinal Methodology in the Analysis of Likert Scales," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(5), pages 601-626, October.
    8. Geofferey Masters & Benjamin Wright, 1984. "The essential process in a family of measurement models," Psychometrika, Springer;The Psychometric Society, vol. 49(4), pages 529-544, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Katarina Repkova Stofkova & Dominik Laitkep & Zuzana Stofkova, 2022. "Shopping Behavior in the Context of the Digital Economy," JRFM, MDPI, vol. 15(2), pages 1-13, January.
    2. Kamal, Mustafa & Blacklow, Paul, 2021. "Attitudes to gender and personality in the Australian gender wage gap," Working Papers 2021-07, University of Tasmania, Tasmanian School of Business and Economics.

    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. Gerhard Tutz & Moritz Berger, 2016. "Response Styles in Rating Scales," Journal of Educational and Behavioral Statistics, , vol. 41(3), pages 239-268, June.
    2. Fumiko Samejima, 1997. "Departure from normal assumptions: A promise for future psychometrics with substantive mathematical modeling," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 471-493, December.
    3. Geofferey Masters, 1985. "A comparison of latent trait and latent class analyses of Likert-type data," Psychometrika, Springer;The Psychometric Society, vol. 50(1), pages 69-82, March.
    4. Wenjia Wang & Mickaël Guedj & Viviane Bertrand & Julie Foucquier & Elisabeth Jouve & Daniel Commenges & Cécile Proust-Lima & Niall P Murphy & Olivier Blin & Laurent Magy & Daniel Cohen & Shahram Attar, 2017. "A Rasch Analysis of the Charcot-Marie-Tooth Neuropathy Score (CMTNS) in a Cohort of Charcot-Marie-Tooth Type 1A Patients," PLOS ONE, Public Library of Science, vol. 12(1), pages 1-14, January.
    5. Kuan-Yu Jin & Yi-Jhen Wu & Hui-Fang Chen, 2022. "A New Multiprocess IRT Model With Ideal Points for Likert-Type Items," Journal of Educational and Behavioral Statistics, , vol. 47(3), pages 297-321, June.
    6. Ligtvoet, R., 2015. "A test for using the sum score to obtain a stochastic ordering of subjects," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 136-139.
    7. Dirk Lubbe & Christof Schuster, 2020. "A Scaled Threshold Model for Measuring Extreme Response Style," Journal of Educational and Behavioral Statistics, , vol. 45(1), pages 86-107, February.
    8. 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.
    9. Yang Ann Shawing, 2015. "Measuring Self-Service Technology Latent Difficulties: Insurance Decisions on Utilitarian and Hedonic Influences," Asia-Pacific Journal of Risk and Insurance, De Gruyter, vol. 9(1), pages 1-33, January.
    10. David Andrich, 2010. "Sufficiency and Conditional Estimation of Person Parameters in the Polytomous Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 75(2), pages 292-308, June.
    11. Timothy R. Johnson & Daniel M. Bolt, 2010. "On the Use of Factor-Analytic Multinomial Logit Item Response Models to Account for Individual Differences in Response Style," Journal of Educational and Behavioral Statistics, , vol. 35(1), pages 92-114, February.
    12. Bas Hemker & L. Andries van der Ark & Klaas Sijtsma, 2001. "On measurement properties of continuation ratio models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 487-506, December.
    13. Gerhard Tutz, 2022. "Ordinal Trees and Random Forests: Score-Free Recursive Partitioning and Improved Ensembles," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 241-263, July.
    14. van der Ark, L.A., 1999. "A reference card for the relationships between IRT models for ordered polytomous items and some relevant properties," WORC Paper 99.10.02, Tilburg University, Work and Organization Research Centre.
    15. Weicong Lyu & Daniel M. Bolt & Samuel Westby, 2023. "Exploring the Effects of Item-Specific Factors in Sequential and IRTree Models," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 745-775, September.
    16. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 635-659, September.
    17. Bacci, Silvia & Fabbricatore, Rosa & Iannario, Maria, 2023. "Multilevel IRT models for the analysis of satisfaction for distance learning during the Covid-19 pandemic," Socio-Economic Planning Sciences, Elsevier, vol. 86(C).
    18. Sen-Chi Yu & Berlin Wu, 2009. "Fuzzy item response model: a new approach to generate membership function to score psychological measurement," Quality & Quantity: International Journal of Methodology, Springer, vol. 43(3), pages 381-390, May.
    19. Stefano Noventa & Andrea Spoto & Jürgen Heller & Augustin Kelava, 2019. "On a Generalization of Local Independence in Item Response Theory Based on Knowledge Space Theory," Psychometrika, Springer;The Psychometric Society, vol. 84(2), pages 395-421, June.
    20. Gerhard Tutz, 2022. "Item Response Thresholds Models: A General Class of Models for Varying Types of Items," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1238-1269, December.

    More about this item

    Statistics

    Access and download statistics

    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:bla:istatr:v:89:y:2021:i:1:p:18-35. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/isiiinl.html .

    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.