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Detection of Mutually Dependent Test Items Using the LCI Test

  • Takamitsu Hashimoto
  • Maomi Ueno
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6797)

Abstract

Item response theory (IRT) is widely used for test analyses. Most models of IRT assume local independence, meaning that when the ability variables influencing the test performance are held constant, an examinee’s responses to any pair of items are statistically independent. However, many factors might cause local dependence among items. Consequently, conditional independence (CI) tests are needed among items given a latent ability variable. Hashimoto and Ueno (2011) proposed the latent conditional independence (LCI) test. While other CI tests are sensitive to dependencies of items aside from the targets, the LCI test is robust to such dependencies. However, when the two target items affect the same items, the LCI test might fail to detect local independency between the targets. The previous work of Hashimoto and Ueno (2011) is improved on to obtain a more accurate detection method.

Keywords

latent variable conditional independence test Bayesian network IRT 

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References

  1. 1.
    Lord, F.M., Novick, M.R.: Statistical Theories of Mental Test Scores. Addison-Wesley, Reading (1968)zbMATHGoogle Scholar
  2. 2.
    Rasch, G.: An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology 19, 49–57 (1966)CrossRefGoogle Scholar
  3. 3.
    Birnbaum, A.: Efficient design and use of tests of a mental ability for various decision-making problems (Series Report 58-16, no.7755-23). USAF School of Aviation Medicine, Randolph Air Force Base, Texas (1957)Google Scholar
  4. 4.
    Birnbaum, A.: Some latent trait models. In: Load, F.M., Novick, M.R. (eds.) Statistical Theories of Mental Test Scores, pp. 397–424. Addison-Wesley, Reading (1968)Google Scholar
  5. 5.
    Samejima, F.: Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph (17) (1969)Google Scholar
  6. 6.
    Samejima, F.: A general model for free-response data. Psychometrika Monograph (18) (1972)Google Scholar
  7. 7.
    Masters, G.N.: A Rasch model for partial credit scoring. Psychometrika 35, 43–50 (1982)zbMATHGoogle Scholar
  8. 8.
    Bock, R.D.: Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika 37, 29–51 (1972)CrossRefzbMATHGoogle Scholar
  9. 9.
    Yen, W.M.: Effects of local item dependence on the fit and equating performance of the three-parameter logistic model. Applied Psychological Measurement 8, 125–145 (1984)CrossRefGoogle Scholar
  10. 10.
    Chen, W.H., Thissen, D.: Local dependence indexes for item pairs using item response theory. Journal of Educational and Behavioral Statistics 22, 265–289 (1997)CrossRefGoogle Scholar
  11. 11.
    Reese, L.M.: The impact of local dependencies on some LSAT outcomes. Law School Admission Council Statistical Report 95(02) (1995)Google Scholar
  12. 12.
    Sano, M.: Detecting overestimation of discrimination parameter applying mutual information. Japanese Journal for Research on Testing 5, 3–21 (2009)Google Scholar
  13. 13.
    Sireci, S.G., Thissen, D., Wainer, H.: On the reliability of testlet-based tests. Journal of Educational Measurement 28, 237–247 (1991)CrossRefGoogle Scholar
  14. 14.
    Hashimoto, T., Ueno, M.: Latent conditional independence test using Bayesian network item response theory. IEICE Transactions E94-D(4), 743–753 (2011)CrossRefGoogle Scholar
  15. 15.
    Ueno, M.: An extension of the IRT to a network model. Behaviormetrika 29, 59–79 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Wilks, S.S.: Mathematical Statistics, 2nd edn., pp. 355–356. Wiley, Chichester (1962)zbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Takamitsu Hashimoto
    • 1
    • 2
  • Maomi Ueno
    • 1
  1. 1.University of Electro-CommunicationsChofu-shiJapan
  2. 2.National Center for University Entrance ExaminationsMeguro-kuJapan

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