IDEAS home Printed from https://ideas.repec.org/a/jss/jstsof/v020i09.html
   My bibliography  Save this article

Extended Rasch Modeling: The eRm Package for the Application of IRT Models in R

Author

Listed:
  • Mair, Patrick
  • Hatzinger, Reinhold

Abstract

Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided.

Suggested Citation

  • 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).
    • Handle: RePEc:jss:jstsof:v:020:i09
    DOI: http://hdl.handle.net/10.18637/jss.v020.i09
    as

    Download full text from publisher

    File URL: https://www.jstatsoft.org/index.php/jss/article/view/v020i09/v20i09.pdf
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v020i09/eRm_0.9.0.tar.gz
    Download Restriction: no
    File URL: https://www.jstatsoft.org/index.php/jss/article/downloadSuppFile/v020i09/v20i09.R.zip
    Download Restriction: no
    File URL: https://libkey.io/http://hdl.handle.net/10.18637/jss.v020.i09?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. C. Glas & N. Verhelst, 1989. "Extensions of the partial credit model," Psychometrika, Springer;The Psychometric Society, vol. 54(4), pages 635-659, September.
    2. Anderson, Carolyn J. & Li, Zhushan & Vermunt, Jeroen K., 2007. "Estimation of Models in a Rasch Family for Polytomous Items and Multiple Latent Variables," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 20(i06).
    3. David Andrich, 1978. "A rating formulation for ordered response categories," Psychometrika, Springer;The Psychometric Society, vol. 43(4), pages 561-573, December.
    4. Denny Borsboom, 2006. "The attack of the psychometricians," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 425-440, September.
    5. Erling Andersen, 1973. "A goodness of fit test for the rasch model," Psychometrika, Springer;The Psychometric Society, vol. 38(1), pages 123-140, March.
    6. G. Fischer & P. Parzer, 1991. "An extension of the rating scale model with an application to the measurement of change," Psychometrika, Springer;The Psychometric Society, vol. 56(4), pages 637-651, December.
    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. repec:jss:jstsof:20:i09 is not listed on IDEAS
    2. Clemens Draxler, 2010. "Sample Size Determination for Rasch Model Tests," Psychometrika, Springer;The Psychometric Society, vol. 75(4), pages 708-724, December.
    3. Erling Andersen, 1995. "Residualanalysis in the polytomous rasch model," Psychometrika, Springer;The Psychometric Society, vol. 60(3), pages 375-393, September.
    4. Clemens Draxler & Rainer Alexandrowicz, 2015. "Sample Size Determination Within the Scope of Conditional Maximum Likelihood Estimation with Special Focus on Testing the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 897-919, December.
    5. Alberto Maydeu-Olivares & Rosa Montaño, 2013. "How Should We Assess the Fit of Rasch-Type Models? Approximating the Power of Goodness-of-Fit Statistics in Categorical Data Analysis," Psychometrika, Springer;The Psychometric Society, vol. 78(1), pages 116-133, January.
    6. Clemens Draxler, 2018. "Bayesian conditional inference for Rasch models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 245-262, April.
    7. 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.
    8. 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.
    9. David J. Hessen, 2010. "Likelihood Ratio Tests for Special Rasch Models," Journal of Educational and Behavioral Statistics, , vol. 35(6), pages 611-628, December.
    10. Gerhard Fischer, 1995. "Some neglected problems in IRT," Psychometrika, Springer;The Psychometric Society, vol. 60(4), pages 459-487, December.
    11. 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.
    12. Mark Wilson & Raymond Adams, 1995. "Rasch models for item bundles," Psychometrika, Springer;The Psychometric Society, vol. 60(2), pages 181-198, June.
    13. Cheng-Hua, Yang & Hsin-Li, Chang, 2012. "Exploring the perceived competence of airport ground staff in dealing with unruly passenger behaviors," Tourism Management, Elsevier, vol. 33(3), pages 611-621.
    14. Karl Christensen & Jakob Bjorner & Svend Kreiner & Jørgen Petersen, 2002. "Testing unidimensionality in polytomous Rasch models," Psychometrika, Springer;The Psychometric Society, vol. 67(4), pages 563-574, December.
    15. Steven Andrew Culpepper & Herman Aguinis & Justin L. Kern & Roger Millsap, 2019. "High-Stakes Testing Case Study: A Latent Variable Approach for Assessing Measurement and Prediction Invariance," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 285-309, March.
    16. Eun-Young Park & Soojung Chae, 2020. "Rasch Analysis of the Korean Parenting Stress Index Short Form (K-PSI-SF) in Mothers of Children with Cerebral Palsy," IJERPH, MDPI, vol. 17(19), pages 1-11, September.
    17. P. A. Ferrari & S. Salini, 2008. "Measuring Service Quality: The Opinion of Europeans about Utilities," Working Papers 2008.36, Fondazione Eni Enrico Mattei.
    18. 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.
    19. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    20. Lionel WILNER, 2019. "The Dynamics of Individual Happiness," Working Papers 2019-18, Center for Research in Economics and Statistics.
    21. 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.

    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:jss:jstsof:v:020:i09. 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: Christopher F. Baum (email available below). General contact details of provider: http://www.jstatsoft.org/ .

    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.