IDEAS home Printed from https://ideas.repec.org/a/vrs/eaiada/v22y2018i1p11-25n1.html
   My bibliography  Save this article

Item Response Theory Models in the Measurement Theory with the Use of ltm Package in R

Author

Listed:
  • Brzezińska Justyna

    (University of Economics in Katowice, Katowice, Poland)

Abstract

Item Response Theory (IRT) is an extension of the Classical Test Theory (CCT) and focuses on how specific test items function in assessing a construct. They are widely known in psychology, medicine, and marketing, as well as in social sciences. An item response model specifies a relationship between the observable examinee test performance and the unobservable traits or abilities assumed to underlie performance on the test. Within the broad framework of item response theory, many models can be operationalized because of the large number of choices available for the mathematical form of the item characteristic curves. In this paper we introduce several types of IRT models such as: the Rasch, and the Birnbaum model. We present the main assumptions for IRT analysis, estimation method, properties, and model selection methods. In this paper we present the application of IRT analysis for binary data with the use of the ltm package in R.

Suggested Citation

  • Brzezińska Justyna, 2018. "Item Response Theory Models in the Measurement Theory with the Use of ltm Package in R," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 22(1), pages 11-25, March.
  • Handle: RePEc:vrs:eaiada:v:22:y:2018:i:1:p:11-25:n:1
    DOI: 10.15611/eada.2018.1.01
    as

    Download full text from publisher

    File URL: https://doi.org/10.15611/eada.2018.1.01
    Download Restriction: no

    File URL: https://libkey.io/10.15611/eada.2018.1.01?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. Frederic Lord, 1974. "Estimation of latent ability and item parameters when there are omitted responses," Psychometrika, Springer;The Psychometric Society, vol. 39(2), pages 247-264, June.
    2. Mair, Patrick & Hatzinger, Reinhold, 2007. "Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i09).
    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. Weeks, Jonathan P., 2010. "plink: An R Package for Linking Mixed-Format Tests Using IRT-Based Methods," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 35(i12).
    5. Frederic Lord, 1974. "The relative efficiency of two tests as a function of ability level," Psychometrika, Springer;The Psychometric Society, vol. 39(3), pages 351-358, September.
    6. Doran, Harold & Bates, Douglas & Bliese, Paul & Dowling, Maritza, 2007. "Estimating the Multilevel Rasch Model: With the lme4 Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i02).
    7. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    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. Rikkert M. van der Lans & Ridwan Maulana & Michelle Helms-Lorenz & Carmen-María Fernández-García & Seyeoung Chun & Thelma de Jager & Yulia Irnidayanti & Mercedes Inda-Caro & Okhwa Lee & Thys Coetze, 2021. "Student Perceptions of Teaching Quality in Five Countries: A Partial Credit Model Approach to Assess Measurement Invariance," SAGE Open, , vol. 11(3), pages 21582440211, August.
    2. Björn Andersson & Tao Xin, 2021. "Estimation of Latent Regression Item Response Theory Models Using a Second-Order Laplace Approximation," Journal of Educational and Behavioral Statistics, , vol. 46(2), pages 244-265, April.
    3. Yang Liu & Jan Hannig & Abhishek Pal Majumder, 2019. "Second-Order Probability Matching Priors for the Person Parameter in Unidimensional IRT Models," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 701-718, September.
    4. Cervantes, Víctor H., 2017. "DFIT: An R Package for Raju's Differential Functioning of Items and Tests Framework," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 76(i05).
    5. Jouni Kuha & Myrsini Katsikatsou & Irini Moustaki, 2018. "Latent variable modelling with non‐ignorable item non‐response: multigroup response propensity models for cross‐national analysis," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 181(4), pages 1169-1192, October.
    6. repec:jss:jstsof:20:i01 is not listed on IDEAS
    7. repec:jss:jstsof:39:i12 is not listed on IDEAS
    8. Jochen Ranger & Kay Brauer, 2022. "On the Generalized S − X 2 –Test of Item Fit: Some Variants, Residuals, and a Graphical Visualization," Journal of Educational and Behavioral Statistics, , vol. 47(2), pages 202-230, April.
    9. de Leeuw, Jan & Mair, Patrick, 2007. "An Introduction to the Special Volume on "Psychometrics in R"," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i01).
    10. repec:jss:jstsof:36:c01 is not listed on IDEAS
    11. Alexander Robitzsch, 2021. "A Comprehensive Simulation Study of Estimation Methods for the Rasch Model," Stats, MDPI, vol. 4(4), pages 1-23, October.
    12. Harold Doran, 2023. "A Collection of Numerical Recipes Useful for Building Scalable Psychometric Applications," Journal of Educational and Behavioral Statistics, , vol. 48(1), pages 37-69, February.
    13. Yang Liu & Jan Hannig, 2017. "Generalized Fiducial Inference for Logistic Graded Response Models," Psychometrika, Springer;The Psychometric Society, vol. 82(4), pages 1097-1125, December.
    14. 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.
    15. repec:jss:jstsof:35:i12 is not listed on IDEAS
    16. Carmen Köhler & Alexander Robitzsch & Johannes Hartig, 2020. "A Bias-Corrected RMSD Item Fit Statistic: An Evaluation and Comparison to Alternatives," Journal of Educational and Behavioral Statistics, , vol. 45(3), pages 251-273, June.
    17. 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).
    18. Daphna Harel & Russell J. Steele, 2018. "An Information Matrix Test for the Collapsing of Categories Under the Partial Credit Model," Journal of Educational and Behavioral Statistics, , vol. 43(6), pages 721-750, December.
    19. Chalmers, R. Philip, 2012. "mirt: A Multidimensional Item Response Theory Package for the R Environment," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i06).
    20. Wickelmaier, Florian & Strobl, Carolin & Zeileis, Achim, 2012. "Psychoco: Psychometric Computing in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i01).
    21. Myszkowski, Nils & Storme, Martin, 2018. "A snapshot of g? Binary and polytomous item-response theory investigations of the last series of the Standard Progressive Matrices (SPM-LS)," Intelligence, Elsevier, vol. 68(C), pages 109-116.
    22. Tendeiro, Jorge N. & Meijer, Rob R. & Niessen, A. Susan M., 2016. "PerFit: An R Package for Person-Fit Analysis in IRT," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 74(i05).
    23. Ting Wang & Benjamin Graves & Yves Rosseel & Edgar C. Merkle, 2022. "Computation and application of generalized linear mixed model derivatives using lme4," Psychometrika, Springer;The Psychometric Society, vol. 87(3), pages 1173-1193, September.
    24. Sandip Sinharay, 2018. "Detecting Fraudulent Erasures at an Aggregate Level," Journal of Educational and Behavioral Statistics, , vol. 43(3), pages 286-315, June.

    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:vrs:eaiada:v:22:y:2018:i:1:p:11-25:n:1. 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: Peter Golla (email available below). General contact details of provider: https://www.sciendo.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.