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Flexible Rasch Mixture Models with Package psychomix

Author

Listed:
  • Hannah Frick

    ()

  • Carolin Strobl

    ()

  • Friedrich Leisch

    ()

  • Achim Zeileis

    ()

Abstract

Measurement invariance is an important assumption in the Rasch model and mixture models constitute a flexible way of checking for a violation of this assumption by detecting unobserved heterogeneity in item response data. Here, a general class of Rasch mixture models is established and implemented in R, using conditional maximum likelihood estimation of the item parameters (given the raw scores) along with flexible specification of two model building blocks: (1) Mixture weights for the unobserved classes can be treated as model parameters or based on covariates in a concomitant variable model. (2) The distribution of raw score probabilities can be parametrized in two possible ways, either using a saturated model or a specification through mean and variance. The function raschmix() in the R package "psychomix" provides these models, leveraging the general infrastructure for fitting mixture models in the "flexmix" package. Usage of the function and its associated methods is illustrated on artificial data as well as empirical data from a study of verbally aggressive behavior.

Suggested Citation

  • Hannah Frick & Carolin Strobl & Friedrich Leisch & Achim Zeileis, 2011. "Flexible Rasch Mixture Models with Package psychomix," Working Papers 2011-21, Faculty of Economics and Statistics, University of Innsbruck.
  • Handle: RePEc:inn:wpaper:2011-21
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    References listed on IDEAS

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    1. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    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. GrĂ¼n, Bettina & Leisch, Friedrich, 2008. "FlexMix Version 2: Finite Mixtures with Concomitant Variables and Varying and Constant Parameters," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 28(i04).
    4. Rizopoulos, Dimitris, 2006. "ltm: An R Package for Latent Variable Modeling and Item Response Analysis," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 17(i05).
    5. Carolin Strobl & Julia Kopf & Achim Zeileis, 2011. "A new method for detecting differential item functioning in the Rasch model," Working Papers 2011-01, Faculty of Economics and Statistics, University of Innsbruck.
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    Cited by:

    1. Hannah Frick & Carolin Strobl & Achim Zeileis, 2013. "Rasch Mixture Models for DIF Detection: A Comparison of Old and New Score Specifications," Working Papers 2013-36, Faculty of Economics and Statistics, University of Innsbruck.

    More about this item

    Keywords

    mixed Rasch model; Rost model; mixture model; flexmix; R;

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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