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What Do You Mean by a Difficult Item? On the Interpretation of the Difficulty Parameter in a Rasch Model

  • Ernesto San MartínEmail author
  • Paul De Boeck
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 89)

Abstract

Three versions of the Rasch model are considered: the fixed-effects model, the random-effects model with normal distribution, and the random-effects model with unspecified distribution. For each of the three, we discuss the meaning of the difficulty parameter starting each time from the corresponding likelihood and the resulting identified parameters. Because the likelihood and the identified parameters are different depending on the model, the identification of the parameter of interest is also different, with consequences for the meaning of the item difficulty. Finally, for all the three models, the item difficulties are monotonically related to the marginal probabilities of a correct response.

Keywords

Likelihood Function Marginal Probability Item Difficulty Item Parameter Difficulty Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This research was partially funded by the ANILLO Project SOC1107 Statistics for Public Policy in Education from the Chilean Government.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Mathematics and Faculty of EducationPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Center for Operations Research and Econometrics CORELouvain-la-NeuveBelgium
  3. 3.Department of PsychologyThe Ohio State UniversityColumbusUSA

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