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

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  • 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
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Frick, Hannah & Strobl, Carolin & Leisch, Friedrich & Zeileis, Achim, 2012. "Flexible Rasch Mixture Models with Package psychomix," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 48(i07).
    2. Tomislav Ridzak, 2012. "Are some Banks More Lenient in the Implementation of Placement Classification Rules?," Working Papers 32, The Croatian National Bank, Croatia.
    3. Krammer, Georg, 2019. "The Andersen likelihood ratio test with a random split criterion lacks power," OSF Preprints gu8sq, Center for Open Science.
    4. Cervantes, VĂ­ctor 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. 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).
    6. 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).
    7. Gerhard Tutz & Gunther Schauberger, 2015. "A Penalty Approach to Differential Item Functioning in Rasch Models," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 21-43, March.
    8. 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).
    9. Carolin Strobl & Julia Kopf & Achim Zeileis, 2015. "Rasch Trees: A New Method for Detecting Differential Item Functioning in the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 80(2), pages 289-316, June.

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