Simulations of Computerized Adaptive Tests

  • David Magis
  • Duanli Yan
  • Alina A. von Davier
Part of the Use R! book series (USE R)


In this chapter, we describe the R package catR that contains most CAT options and routines currently developed. Its general architecture is presented and most important R functions are explained and illustrated. Focus is put on detailing the input arguments and output values of the main functions, as well as the relationships between them and their accurate use in adaptive and non-adaptive contexts.


  1. Barrada, J. R., Abad, F. J., & Veldkamp, B. P. (2009). Comparison of methods for controlling maximum exposure rates in computerized adaptive testing. Psicothema, 21, 313–320.Google Scholar
  2. Barrada, J. R., Olea, J., Ponsoda, V., & Abad, F. J. (2008). Incorporating randomness to the fisher information for improving item exposure control in cats. British Journal of Mathematical and Statistical Psychology, 61, 493–513. MathSciNetCrossRefGoogle Scholar
  3. Barrada, J. R., Olea, J., Ponsoda, V., & Abad, F. J. (2010). A method for the comparison of item selection rules in computerized adaptive testing. Applied Psychological Measurement, 34, 438–452. CrossRefGoogle Scholar
  4. Bradlow, E. T. (1996). Negative information and the three-parameter logistic model. Journal of Educational and Behavioral Statistics, 21, 179–185. Google Scholar
  5. Dodd, B. G., De Ayala, R. J., & Koch, W. R. (1995). Computerized adaptive testing with polytomous items. Applied Psychological Measurement, 19, 5–22. CrossRefGoogle Scholar
  6. Jeffreys, H. (1939). Theory of probability. Oxford, UK: Oxford University Press.zbMATHGoogle Scholar
  7. Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 186, 453–461.Google Scholar
  8. Kingsbury, G. G., & Zara, A. R. (1989). Procedures for selecting items for computerized adaptive tests. Applied Measurement in Education, 2, 359–375.\_6 CrossRefGoogle Scholar
  9. Magis, D. (2013). A note on the item information function of the four-parameter logistic model. Applied Psychological Measurement, 37, 304–315. CrossRefGoogle Scholar
  10. Magis, D., & Barrada, J. R. (2017). Computerized adaptive testing with R: Recent updates of the package catR. Journal of Statistical Software, Code Snippets, 76(1), 1–19. Google Scholar
  11. Magis, D., & Raîche, G. (2012). Random generation of response patterns under computerized adaptive testing with the R package catR. Journal of Statistical Software, 48(8), 1–31. CrossRefGoogle Scholar
  12. Revuelta, J., & Ponsoda, V. (1998). A comparison of item exposure control methods in computerized adaptive testing. Journal of Educational Measurement, 35, 311–327. CrossRefGoogle Scholar
  13. Thompson, N. A. (2009). Item selection in computerized classification testing. Educational and Psychological Measurement, 69, 778–793. MathSciNetCrossRefGoogle Scholar
  14. van der Linden, W. J., & Veldkamp, B. P. (2004). Constraining item exposure in computerized adaptive testing with shadow tests. Journal of Educational and Behavioral Statistics, 29, 273–291. CrossRefGoogle Scholar
  15. Warm, T. (1989). Weighted likelihood estimation of ability in item response models. Psychometrika, 54, 427–450. MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • David Magis
    • 1
  • Duanli Yan
    • 2
  • Alina A. von Davier
    • 3
  1. 1.Department of EducationUniversity of LiegeLiegeBelgium
  2. 2.Educational Testing ServicePrincetonUSA
  3. 3.ACTNext by ACTIowa CityUSA

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