Parallel Computing with a Bayesian Item Response Model

DOI: 10.4236/ajcm.2012.22009   PDF   HTML   XML   4,566 Downloads   8,351 Views   Citations


Item response theory (IRT) is a modern test theory that has been used in various aspects of educational and psychological measurement. The fully Bayesian approach shows promise for estimating IRT models. Given that it is computation- ally expensive, the procedure is limited in practical applications. It is hence important to seek ways to reduce the execution time. A suitable solution is the use of high performance computing. This study focuses on the fully Bayesian algorithm for a conventional IRT model so that it can be implemented on a high performance parallel machine. Empirical results suggest that this parallel version of the algorithm achieves a considerable speedup and thus reduces the execution time considerably.

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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, 2012, pp. 65-71. doi: 10.4236/ajcm.2012.22009.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] R. Hambleton, H. Swaminathan and H. J. Rogers, “Fundamentals of Item Response Theory,” SAGE Publications, Thou-sand Oaks, 1991.
[2] M. J. Kolen and R. L. Brennan, “Test Equating: Methods and Practices,” Springer-Verlag, New York, 1995.
[3] S. E. Embretson and S. P. Reise, “Item Response Theory for Psychologist,” Lawrence Erlbaum Associates Inc., Mahwah, 2000.
[4] H. Wainer, N. Dorans, D. Eignor, R. Flaugher, B. Green, R. Mislevy, L. Steinberg and D. Thissen, “Computerized Adaptive Testing: A Primer,” Lawrence Erlbaum Associates Inc., Mahwah, 2000.
[5] J. Bafumi, A. Gelman, D. K. Park and N. Kaplan, “Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation,” Political Analysis Advance Access, Vol. 13, No. 2, 2005, pp. 171-187. doi:10.1093/pan/mpi010
[6] N. Bezruckzo, “Rasch Measurement in Health Sciences,” JAM Press, Maple Grove, 2005.
[7] C. H. Chang and B. B. Reeve, “Item Response Theory and Its Applications to Patient-Reported Outcomes Measurement,” Evaluation & the Health Professions, Vol. 28, No. 3, 2005, pp. 264-282. doi:10.1177/0163278705278275
[8] U. Feske, L. Kirisci, R. E. Tarter and P. A. Plkonis, “An Application of Item Response Theory to the DSM-III-R Criteria for Borderline Personality Disorder,” Journal of Personality Disorders, Vol. 21, No. 4, 2007, pp. 418-433. doi:10.1521/pedi.2007.21.4.418
[9] G. W. Imbens, “The Role of the Propensity Score in Estimating Dose-Response Functions,” Biometrika, Vol. 87, No. 3, 2000, pp. 706-710. doi:10.1093/biomet/87.3.706
[10] S. Sinharay and H. S. Stern, “On the Sensitivity of Bayes Factors to the Prior Distribution.” The American Statistician, Vol. 56, No. 3, 2002, pp. 196-201. doi:10.1198/000313002137
[11] Birnbaum, “Statistical Theory for Logistic Mental Test Models with a Prior Distribution of Ability,” Journal of Mathematical Psychology, Vol. 6, No. 2, 1969, pp. 258- 276. doi:10.1016/0022-2496(69)90005-4
[12] F. B. Baker and S. H. Kim, “Item Response Theory: Pa- rameter Estimation Techniques,” 2nd Edition, Dekker, New York, 2004.
[13] R. D. Bock and M. Aitkin, “Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm,” Psychometrika, Vol. 46, No. 4, 1981, pp. 443-459. doi:10.1007/BF02293801
[14] W. Molenaar, “Estimation of Item Parameters,” In: G. H. Fischer and I. W. Molenaar, Eds., Rasch Models: Foundations, Recent Developments, and Applications, Springer-Verlag, New York, 1995, pp. 39-51.
[15] R. K. Tsutakawa and J. C. Johnson, “The Effect of Un- certainty of Item Parameter Estimation on Ability Estimates,” Psychometrika, Vol. 55, No. 2, 1990, pp. 371-390. doi:10.1007/BF02295293
[16] R. K. Tsutakawa and M. J. Soltys, “Approximation for Bayesian Ability Estimation,” Journal of Educational Statistics, Vol. 13, No. 2, 1988, pp. 117-130. doi:10.2307/1164749
[17] J. H. Albert, “Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling,” Journal of Educational Statistics, Vol. 17, No. 3, 1992, pp. 251-269. doi:10.2307/1165149
[18] S. Geman and D. Geman, “Stochastic Relaxation, Gibbs Distributions, and the Bayesian Restoration of Images,” IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 6, No. 6, 1984, pp. 721-741. doi:10.1109/TPAMI.1984.4767596
[19] F. M. Smith and G. O. Roberts, “Bayesian Computation via the Gibbs Sampler and Related Markov Chain Monte Carlo Methods,” Journal of the Royal Statistical Society, Series B, Vol. 55, No. 1, 1993, pp. 3-24.
[20] L. Tierney, “Markov Chains for Exploring Posterior Distributions (with discussion),” Annals of Statistics, Vol. 22, No. 4, 1994, 1701-1762. doi:10.1214/aos/1176325750
[21] F. M. Lord and M. R. Novick, “Statistical Theories of Mental Test Scores,” Addison-Wesley, Boston, 1968.
[22] 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, 2007, pp. 341-349.
[23] R. Noronha and K. P. Dhabaleswar, “Performance Evaluation of MM5 on Clusters with Modern Interconnects: Scalability and Impact,” Euro-Par 2005 Parallel Processing, 2005, Vol. 3648, pp. 134-145. doi:10.1007/11549468_18
[24] Foster, “Designing and Building Parallel Programs: Concepts and Tools for Parallel Software Engineering,” Addison-Wesley, Boston, 1995.
[25] M. Galassi, J. Davies, J. Theiler, B. Gough, G. Jungman M. Booth, et al., “GNU Scientific Library Reference Manual,” 2009.

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