IDEAS home Printed from https://ideas.repec.org/a/spr/psycho/v79y2014i3p377-402.html
   My bibliography  Save this article

An Analysis of Item Response Theory and Rasch Models Based on the Most Probable Distribution Method

Author

Listed:
  • Stefano Noventa
  • Luca Stefanutti
  • Giulio Vidotto

Abstract

The most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system. The item response theory logistic models, with a particular focus on the one-parameter logistic model, or Rasch model, and their properties and assumptions, are discussed for both infinite and finite populations. Copyright The Psychometric Society 2014

Suggested Citation

  • Stefano Noventa & Luca Stefanutti & Giulio Vidotto, 2014. "An Analysis of Item Response Theory and Rasch Models Based on the Most Probable Distribution Method," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 377-402, July.
    • Handle: RePEc:spr:psycho:v:79:y:2014:i:3:p:377-402
    DOI: 10.1007/s11336-013-9348-y
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11336-013-9348-y
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11336-013-9348-y?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Fishburn, Peter C., 1981. "Uniqueness properties in finite-continuous additive measurement," Mathematical Social Sciences, Elsevier, vol. 1(2), pages 145-153, January.
    2. Geoff Masters, 1982. "A rasch model for partial credit scoring," Psychometrika, Springer;The Psychometric Society, vol. 47(2), pages 149-174, June.
    3. Gerhard Fischer, 1995. "Some neglected problems in IRT," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 459-487, December.
    4. Jan Toporowski & Jo Michell, 2012. "Introduction," Chapters, in: Jan Toporowski & Jo Michell (ed.), Handbook of Critical Issues in Finance, pages i-ii, Edward Elgar Publishing.
    5. David Andrich, 1982. "An extension of the rasch model for ratings providing both location and dispersion parameters," Psychometrika, Springer;The Psychometric Society, vol. 47(1), pages 105-113, March.
    6. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    7. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    8. Hartman Scheiblechner, 1999. "Additive conjoint isotonic probabilistic models (ADISOP)," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 295-316, September.
    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. 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.

    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. Henk Kelderman & Carl Rijkes, 1994. "Loglinear multidimensional IRT models for polytomously scored items," Psychometrika, Springer;The Psychometric Society, vol. 59(2), pages 149-176, June.
    2. Anders Skrondal & Sophia Rabe-Hesketh, 2022. "The Role of Conditional Likelihoods in Latent Variable Modeling," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 799-834, September.
    3. Singh, Jagdip, 2004. "Tackling measurement problems with Item Response Theory: Principles, characteristics, and assessment, with an illustrative example," Journal of Business Research, Elsevier, vol. 57(2), pages 184-208, February.
    4. Silvana Bortolotti & Rafael Tezza & Dalton Andrade & Antonio Bornia & Afonso Sousa Júnior, 2013. "Relevance and advantages of using the item response theory," Quality & Quantity: International Journal of Methodology, Springer, vol. 47(4), pages 2341-2360, June.
    5. Chang, Hsin-Li & Yang, Cheng-Hua, 2008. "Explore airlines’ brand niches through measuring passengers’ repurchase motivation—an application of Rasch measurement," Journal of Air Transport Management, Elsevier, vol. 14(3), pages 105-112.
    6. Ivana Bassi & Matteo Carzedda & Enrico Gori & Luca Iseppi, 2022. "Rasch analysis of consumer attitudes towards the mountain product label," Agricultural and Food Economics, Springer;Italian Society of Agricultural Economics (SIDEA), vol. 10(1), pages 1-25, December.
    7. Hua-Hua Chang, 1996. "The asymptotic posterior normality of the latent trait for polytomous IRT models," Psychometrika, Springer;The Psychometric Society, vol. 61(3), pages 445-463, September.
    8. Curt Hagquist & Raili Välimaa & Nina Simonsen & Sakari Suominen, 2017. "Differential Item Functioning in Trend Analyses of Adolescent Mental Health – Illustrative Examples Using HBSC-Data from Finland," Child Indicators Research, Springer;The International Society of Child Indicators (ISCI), vol. 10(3), pages 673-691, September.
    9. Chang, Hsin-Li & Wu, Shun-Cheng, 2008. "Exploring the vehicle dependence behind mode choice: Evidence of motorcycle dependence in Taipei," Transportation Research Part A: Policy and Practice, Elsevier, vol. 42(2), pages 307-320, February.
    10. Jesper Tijmstra & Maria Bolsinova, 2019. "Bayes Factors for Evaluating Latent Monotonicity in Polytomous Item Response Theory Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 846-869, September.
    11. Salzberger, Thomas & Koller, Monika, 2013. "Towards a new paradigm of measurement in marketing," Journal of Business Research, Elsevier, vol. 66(9), pages 1307-1317.
    12. Richard N McNeely & Salissou Moutari & Samuel Arba-Mosquera & Shwetabh Verma & Jonathan E Moore, 2018. "An alternative application of Rasch analysis to assess data from ophthalmic patient-reported outcome instruments," PLOS ONE, Public Library of Science, vol. 13(6), pages 1-32, June.
    13. Francesca DE BATTISTI & Giovanna NICOLINI & Silvia SALINI, 2008. "Methodological overview of Rasch model and application in customer satisfaction survey data," Departmental Working Papers 2008-04, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    14. 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.
    15. van der Ark, L. Andries, 2012. "New Developments in Mokken Scale Analysis in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i05).
    16. Piotr Tarka, 2013. "Model of latent profile factor analysis for ordered categorical data," Statistics in Transition new series, Główny Urząd Statystyczny (Polska), vol. 14(1), pages 171-182, March.
    17. Xiaohui Zheng & Sophia Rabe-Hesketh, 2007. "Estimating parameters of dichotomous and ordinal item response models with gllamm," Stata Journal, StataCorp LP, vol. 7(3), pages 313-333, September.
    18. Ghady El Khoury & Olivier Barbier & Xavier Libouton & Jean-Louis Thonnard & Philippe Lefèvre & Massimo Penta, 2020. "Manual ability in hand surgery patients: Validation of the ABILHAND scale in four diagnostic groups," PLOS ONE, Public Library of Science, vol. 15(12), pages 1-17, December.
    19. 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.
    20. Georg Gittler & Gerhard Fischer, 2011. "IRT-Based Measurement of Short-Term Changes of Ability, With an Application to Assessing the “Mozart Effectâ€," Journal of Educational and Behavioral Statistics, , vol. 36(1), pages 33-75, February.

    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:spr:psycho:v:79:y:2014:i:3:p:377-402. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.