IDEAS home Printed from https://ideas.repec.org/a/bla/stanee/v72y2018i3p224-245.html
   My bibliography  Save this article

Modelling uncertainty and response styles in ordinal data

Author

Listed:
  • Rosaria Simone
  • Gerhard Tutz

Abstract

Mixture models for ordinal responses in the tradition of cub models use the uniform distribution to account for uncertainty of respondents. A model is proposed that uses more flexible distributions in the uncertainty component: the discretized Beta distribution allows to account for response styles, in particular the preference for middle or extreme categories. The proposal is compared with traditional cub models in simulation studies and its use is illustrated by two applications.

Suggested Citation

  • Rosaria Simone & Gerhard Tutz, 2018. "Modelling uncertainty and response styles in ordinal data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 72(3), pages 224-245, August.
    • Handle: RePEc:bla:stanee:v:72:y:2018:i:3:p:224-245
    DOI: 10.1111/stan.12129
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/stan.12129
    Download Restriction: no
    File URL: https://libkey.io/10.1111/stan.12129?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. Gerhard Tutz & Micha Schneider & Maria Iannario & Domenico Piccolo, 2017. "Mixture models for ordinal responses to account for uncertainty of choice," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(2), pages 281-305, June.
    2. 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.
    3. Anna Gottard & Maria Iannario & Domenico Piccolo, 2016. "Varying uncertainty in CUB models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 10(2), pages 225-244, June.
    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. Janette Larney & Gerrit Lodewicus Grobler & James Samuel Allison, 2022. "Introducing Two Parsimonious Standard Power Mixture Models for Bimodal Proportional Data with Application to Loss Given Default," Mathematics, MDPI, vol. 10(23), pages 1-19, November.
    2. Manisera, Marica & Zuccolotto, Paola, 2022. "A mixture model for ordinal variables measured on semantic differential scales," Econometrics and Statistics, Elsevier, vol. 22(C), pages 98-123.
    3. Simone, Rosaria & Tutz, Gerhard & Iannario, Maria, 2020. "Subjective heterogeneity in response attitude for multivariate ordinal outcomes," Econometrics and Statistics, Elsevier, vol. 14(C), pages 145-158.
    4. Rosaria Simone, 2021. "An accelerated EM algorithm for mixture models with uncertainty for rating data," Computational Statistics, Springer, vol. 36(1), pages 691-714, March.
    5. Rosaria Simone, 2023. "Uncertainty Diagnostics of Binomial Regression Trees for Ordered Rating Data," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 79-105, April.
    6. Roberto Colombi & Sabrina Giordano & Gerhard Tutz, 2021. "A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 682-716, December.
    7. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    8. E. Nardo & R. Simone, 2019. "A model-based fuzzy analysis of questionnaires," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 187-215, June.
    9. Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
    10. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    11. Capecchi, Stefania & Amato, Mario & Sodano, Valeria & Verneau, Fabio, 2019. "Understanding beliefs and concerns towards palm oil: Empirical evidence and policy implications," Food Policy, Elsevier, vol. 89(C).

    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. Domenico Piccolo & Rosaria Simone, 2019. "The class of cub models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 389-435, September.
    2. Roberto Colombi & Sabrina Giordano, 2019. "Likelihood-based tests for a class of misspecified finite mixture models for ordinal categorical data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(4), pages 1175-1202, December.
    3. Simone, Rosaria & Tutz, Gerhard & Iannario, Maria, 2020. "Subjective heterogeneity in response attitude for multivariate ordinal outcomes," Econometrics and Statistics, Elsevier, vol. 14(C), pages 145-158.
    4. E. Nardo & R. Simone, 2019. "A model-based fuzzy analysis of questionnaires," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 187-215, June.
    5. Roberto Colombi & Sabrina Giordano & Gerhard Tutz, 2021. "A Rating Scale Mixture Model to Account for the Tendency to Middle and Extreme Categories," Journal of Educational and Behavioral Statistics, , vol. 46(6), pages 682-716, December.
    6. Stefania Capecchi & Maria Iannario & Rosaria Simone, 2018. "Well-Being and Relational Goods: A Model-Based Approach to Detect Significant Relationships," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 135(2), pages 729-750, January.
    7. Kim, Jung Seek & Ratchford, Brian T., 2013. "A Bayesian multivariate probit for ordinal data with semiparametric random-effects," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 192-208.
    8. Maria Iannario & Domenico Piccolo, 2016. "A comprehensive framework of regression models for ordinal data," METRON, Springer;Sapienza Università di Roma, vol. 74(2), pages 233-252, August.
    9. Jay Verkuilen & Michael Smithson, 2012. "Mixed and Mixture Regression Models for Continuous Bounded Responses Using the Beta Distribution," Journal of Educational and Behavioral Statistics, , vol. 37(1), pages 82-113, February.
    10. Gerhard Tutz, 2020. "Modelling heterogeneity: on the problem of group comparisons with logistic regression and the potential of the heterogeneous choice model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(3), pages 517-542, September.
    11. Pieter Schoonees & Michel Velden & Patrick Groenen, 2015. "Constrained Dual Scaling for Detecting Response Styles in Categorical Data," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 968-994, December.
    12. Gerhard Tutz & Moritz Berger, 2016. "Response Styles in Rating Scales," Journal of Educational and Behavioral Statistics, , vol. 41(3), pages 239-268, June.
    13. Lynd Bacon & Peter Lenk, 2012. "Augmenting discrete-choice data to identify common preference scales for inter-subject analyses," Quantitative Marketing and Economics (QME), Springer, vol. 10(4), pages 453-474, December.
    14. Bettina Grün & Sara Dolnicar, 2016. "Response style corrected market segmentation for ordinal data," Marketing Letters, Springer, vol. 27(4), pages 729-741, December.
    15. de Jong, M.G., 2006. "Response bias in international marketing research," Other publications TiSEM 5d4031be-97b5-4db3-962b-2, Tilburg University, School of Economics and Management.
    16. 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.
    17. Omori, Yasuhiro & Miyawaki, Koji, 2010. "Tobit model with covariate dependent thresholds," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2736-2752, November.
    18. Manisera, Marica & Zuccolotto, Paola, 2022. "A mixture model for ordinal variables measured on semantic differential scales," Econometrics and Statistics, Elsevier, vol. 22(C), pages 98-123.
    19. Alan Agresti & Maria Kateri, 2019. "The class of CUB models: statistical foundations, inferential issues and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 445-449, September.
    20. Timothy Johnson, 2007. "Discrete Choice Models for Ordinal Response Variables: A Generalization of the Stereotype Model," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 489-504, 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:stanee:v:72:y:2018:i:3:p:224-245. 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: http://www.blackwellpublishing.com/journal.asp?ref=0039-0402 .

    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.