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ISRN Computational Mathematics
Volume 2012 (2012), Article ID 264040, 9 pages
http://dx.doi.org/10.5402/2012/264040
Research Article

High Performance Gibbs Sampling for IRT Models Using Row-Wise Decomposition

1Educational Measurement and Statistics, Department of Educational Psychology & Special Education, Southern Illinois University Carbondale, Carbondale, IL 62901-4618, USA
2Department of Computer Science, Southern Illinois University Carbondale, Carbondale, IL 62901, USA

Received 15 October 2012; Accepted 4 November 2012

Academic Editors: L. S. Heath, R. Tuzun, and P. B. Vasconcelos

Copyright © 2012 Yanyan Sheng and Mona Rahimi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. R. D. Bock and M. Aitkin, “Marginal maximum likelihood estimation of item parameters: application of an EM algorithm,” Psychometrika, vol. 46, no. 4, pp. 443–459, 1981. View at Publisher · View at Google Scholar · View at Scopus
  2. R. J. Mislevy, “Estimation of latent group effects,” Journal of the American Statistical Association, vol. 80, no. 392, pp. 993–997, 1985.
  3. R. J. Patz and B. W. Junker, “A straightforward approach to markov Chain Monte Carlo Methods for item response models,” Journal of Educational and Behavioral Statistics, vol. 24, no. 2, pp. 146–178, 1999. View at Scopus
  4. R. K. Tsutakawa and H. Y. Lin, “Bayesian estimation of item response curves,” Psychometrika, vol. 51, no. 2, pp. 251–267, 1986. View at Publisher · View at Google Scholar · View at Scopus
  5. J. Bafumi, A. Gelman, D. K. Park, and N. Kaplan, “Practical issues in implementing and understanding Bayesian ideal point estimation,” Political Analysis, vol. 13, no. 2, pp. 171–187, 2005. View at Publisher · View at Google Scholar · View at Scopus
  6. C. S. Martin, T. Chung, L. Kirisci, and J. W. Langenbucher, “Item response theory analysis of diagnostic criteria for alcohol and cannabis use disorders in adolescents: implications for DSM-V,” Journal of Abnormal Psychology, vol. 115, no. 4, pp. 807–814, 2006. View at Publisher · View at Google Scholar · View at Scopus
  7. U. Feske, L. Kirisci, R. E. Tarter, and P. A. Pilkonis, “An application of item response theory to the DSM-III-R criteria for borderline personality disorder,” Journal of Personality Disorders, vol. 21, no. 4, pp. 418–433, 2007. View at Publisher · View at Google Scholar · View at Scopus
  8. C. L. Beseler, L. A. Taylor, and R. F. Leeman, “An item-response theory analysis of DSM-IV Alcohol-Use disorder criteria and “binge” drinking in undergraduates,” Journal of Studies on Alcohol and Drugs, vol. 71, no. 3, pp. 418–423, 2010. View at Scopus
  9. D. A. Gilder, I. R. Gizer, and C. L. Ehlers, “Item response theory analysis of binge drinking and its relationship to lifetime alcohol use disorder symptom severity in an American Indian Community sample,” Alcoholism: Clinical and Experimental Research, vol. 35, no. 5, pp. 984–995, 2011. View at Publisher · View at Google Scholar · View at Scopus
  10. A. T. Panter and B. B. Reeve, “Assessing tobacco beliefs among youth using item response theory models,” Drug and Alcohol Dependence, vol. 68, no. 1, pp. S21–S39, 2002. View at Scopus
  11. D. Courvoisier and J. F. Etter, “Using item response theory to study the convergent and discriminant validity of three questionnaires measuring cigarette dependence,” Psychology of Addictive Behaviors, vol. 22, no. 3, pp. 391–401, 2008. View at Publisher · View at Google Scholar · View at Scopus
  12. J. S. Rose and L. C. Dierker, “An item response theory analysis of nicotine dependence symptoms in recent onset adolescent smokers,” Drug and Alcohol Dependence, vol. 110, no. 1-2, pp. 70–79, 2010. View at Publisher · View at Google Scholar · View at Scopus
  13. S. E. Fienberg, M. S. Johnson, and B. W. Junker, “Classical multilevel and Bayesian approaches to population size estimation using multiple lists,” Journal of the Royal Statistical Society A, vol. 162, no. 3, pp. 383–405, 1999. View at Scopus
  14. M. Reiser, “An application of the item-response model to psychiatric epidemiology,” Sociological Methods and Research, vol. 18, no. 1, pp. 66–103, 1989.
  15. M. Orlando, C. D. Sherbourne, and D. Thissen, “Summed-score linking using item response theory: application to depression measurement,” Psychological Assessment, vol. 12, no. 3, pp. 354–359, 2000. View at Publisher · View at Google Scholar · View at Scopus
  16. A. Tsutsumi, N. Iwata, N. Watanabe, et al., “Application of item response theory to achieve cross-cultural comparability of occupational stress measurement,” International Journal of Methods in Psychiatric Research, vol. 18, no. 1, pp. 58–67, 2009. View at Publisher · View at Google Scholar · View at Scopus
  17. A. Birnbaum, “Statistical theory for logistic mental test models with a prior distribution of ability,” Journal of Mathematical Psychology, vol. 6, no. 2, pp. 258–276, 1969. View at Scopus
  18. F. B. Baker and S. H. Kim, Item Response Theory: Parameter Estimation Techniques, Dekker, New York, NY, USA, 2nd edition, 2004.
  19. I. W. Molenaar, “Estimation of item parameters,” in Rasch Models: Foundations, Recent Developments, and Applications, G. H. Fischer and I. W. Molenaar, Eds., pp. 39–51, Springer, New York, NY, USA, 1995.
  20. A. F. M. Smith and G. O. Roberts, “Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods (with discussion),” Journal of the Royal Statistical Society B, vol. 55, no. 1, pp. 3–23, 1993.
  21. L. Tierney, “Markov chains for exploring posterior distributions,” The Annals of Statistics, vol. 22, no. 4, pp. 1701–1728, 1994.
  22. K. Patsias, M. Rahimi, Y. Sheng, and S. Rahimi, “Parallel computing with a Bayesian item response model,” American Journal of Computational Mathematics, vol. 2, no. 2, pp. 65–71, 2012.
  23. S. Geman and D. Geman, “Stochastic relaxation, Gibbs distributions, and the Bayeisan restoration of images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 6, no. 6, pp. 721–741, 1984. View at Scopus
  24. F. M. Lord and M. R. Novick, Statistical Theories of Mental Test Scores, Addison-Wesley, Boston, Mass, USA, 1968.
  25. J. H. Albert, “Bayesian estimation of normal ogive item response curves using Gibbs sampling,” Journal of Educational Statistics, vol. 17, no. 3, pp. 251–269, 1992.
  26. Y. Sheng and T. C. Headrick, “An algorithm for implementing Gibbs sampling for 2PNO IRT models,” Journal of Modern Applied Statistical Methods, vol. 6, no. 1, pp. 341–349, 2007. View at Scopus
  27. G. Casella and E. I. George, “Explaining the Gibbs sampler,” The American Statistician, vol. 46, no. 3, pp. 167–174, 1992.
  28. M. Galassi, J. Davies, J. Theiler et al., GNU Scientific Library Reference Manual, Network Theory, Bristol, UK, 3rd edition, 2009.
  29. I. Foster, Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering, Addison-Wesley, Boston, Mass, USA, 1995.