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Interpreting Error Measurement: A Case Study Based on Rasch Tree Approach

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Statistical Models for Data Analysis

Abstract

This paper describes the appropriateness of Differential Item Functioning (DIF) analysis performed via mixed-effects Rasch models. Groups of subjects with homogeneous Rasch item parameters are found automatically by a model-based partitioning (Rasch tree model). The unifying framework offers the advantage of including the terminal nodes of Rasch tree in the multilevel formulation of Rasch models. In such a way we are able to handle different measurement issues. The approach is illustrated with a cross-national survey on attitude towards female stereotypes. Evidence of groups DIF was detected and presented as well as the estimates of model parameters.

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References

  • Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrika, 38, 123–140.

    Article  MathSciNet  MATH  Google Scholar 

  • Baayen, R. H., Davidson D. J., & Bates, D. M. (2008). Mixed-effects modeling with crossed random effects for subject and items. Journal of Memory and Language, 59, 390–412.

    Article  Google Scholar 

  • Bernabei, D., Di Zio, S., Fontanella, L., & Maretti, M. (2010). Attitude towards women stereotypes: the partial credit model for questionnaire validation. In Proceedings of MTISD 2010, Methods, Models and Information Technologies for Decision Support Systems.

    Google Scholar 

  • De Boeck, P. (2008). Random item IRT models. Psychometrika, 73(4), 533–559.

    Article  MathSciNet  MATH  Google Scholar 

  • De Boeck, P., Bakker, M., Zwitser, R., Nivard, M., Hofman, A., Tuerlinckx, F., & Partchev, I. (2011). The estimation of item response models with the lmer function from the lme4 package in R, 73(4). Journal of Statistical Software, 39(12), 1–28.

    Google Scholar 

  • Doran, H., Bates, D., Bliese, P., & Dowling M. (2007). Estimating the multilevel rasch model: with the lme4 package. Journal of Statistical Software, 20(2), 1–18.

    Google Scholar 

  • Strobl, C., Kopf, J., & Zeiles, A. (2010). A new method for detecting differential item functioning in the rasch model. Technical Report 92, Department of Statistics, Ludwig-Maximilians Universitt Mnchen. http://epub.ub.uni-muenchen.de/1195/.

  • Zeiles, A., & Hornik, K. (2007). Generalised M-fluctuation tests for parameters instability. Statistica Neerlandica, 61(4), 488–508.

    Article  MathSciNet  Google Scholar 

  • Zeiles, A., Hothor, T., & Hornik, K. (2008). Model-based recursive partitioning. Journal of Computational and Graphical Statistics, 17(2), 492–514.

    Article  MathSciNet  Google Scholar 

  • Zeiles, A., Strobl, C., Wickelmaier, F., & Kopf, J. (2010). Psychotree: recursive partitioning based on psycometric models. R package version 0.11-1 htpp://CRAN.R-project.org/package=psychotree.

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Correspondence to Annalina Sarra .

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Sarra, A., Fontanella, L., Di Battista, T., Di Nisio, R. (2013). Interpreting Error Measurement: A Case Study Based on Rasch Tree Approach. In: Giudici, P., Ingrassia, S., Vichi, M. (eds) Statistical Models for Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00032-9_37

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