The use of predicted values for item parameters in item response theory models: an application in intelligence tests

Journal of Applied Statistics

Volumn 39, Issue 12, 2012, Pages 2665-2683

  Matteucci, Mariagiulia ^a   Mignani, Stefania ^a   Veldkamp, Bernard P ^b  

^a UNIVERSITY OF BOLOGNA   (Italy)

^b UNIVERSITY OF TWENTE   (Netherlands)

Author keywords

adaptive testing; Bayesian estimation; intelligence tests; item calibration; item response theory models; multivariate regression trees

Indexed keywords

EID: 84867871202     PISSN: 02664763     EISSN: 13600532     Source Type: Journal    
DOI: 10.1080/02664763.2012.725034     Document Type: Article

References (42)

1. Albert, J. H. 1992. Bayesian estimation of normal ogive item response curves using Gibbs sampling. J. Educ. Stat., 17: 251-269. (doi:10.2307/1165149)
2. Ariel, A., Veldkamp, B. P. and Breithaupt, K. 2006. Optimal testlet pool assembly for multi-stage testing designs. Appl. Psych. Meas., 30: 204-215. (doi:10.1177/0146621605284350)
3. Béguin, A. A. and Glas, C. A.W. 2001. MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika, 66: 541-562. (doi:10.1007/BF02296195)
4. Birnbaum, A. 1968. "Some latent trait models and their use in inferring an examinee's ability". In Statistical Theories of Mental Test Scores, Edited by: Lord, F. M. and Novick, M. R. 397-479. Addison-Wesley, Reading.
5. Bock, R. D. and Aitkin, M. 1981. Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46: 443-459. (doi:10.1007/BF02293801)
6. Bolt, D. M. and Lall, V. F. 2003. Estimation of compensatory and noncompensatory multidimensional item response models using Markov chain Monte Carlo. Appl. Psych. Meas., 27: 395-414. (doi:10.1177/0146621603258350)
7. Bousquet, N. 2008. Diagnostics of prior-data agreement in applied Bayesian analysis. J. Appl. Stat., 35: 1011-1029. (doi:10.1080/02664760802192981)
8. Breiman, L., Friedman, J. H., Olshen, R. A. and Stone, C. J. 1984. Classification and Regression Trees, Belmont: Wadsworth International.
9. Cowles, M. K. and Carlin, B. P. 1996. Markov chain Monte Carlo convergence diagnostics: A comparative review. J. Amer. Statist. Assoc., 91: 883-904. (doi:10.1080/01621459.1996.10476956)
10. De'ath, G. 2002. Multivariate regression trees: A new technique for modeling species-environment relationships. Ecology, 83: 1105-1117.
11. De Ayala, R. J. 2009. The Theory and Practice of Item Response Theory, New York: The Guilford Press.
12. De Gruijter, D. N.M. and van der Kamp, L. J.T. 2008. Statistical Test Theory for the Behavioral Sciences, Boca Raton, FL: Chapman & Hall/CRC.
13. Enright, M. K. and Sheehan, K. M. 2002. "Modeling the difficulty of quantitative reasoning items: Implication for item generation". In Item Generation for Test Development, Edited by: Irvine, S. H. and Kyllonen, P. C. 129-158. Mahwah, NJ: Lawrence Erlbaum Associates.
14. Fox, J. P. and Glas, C. A.W. 2001. Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66: 271-288. (doi:10.1007/BF02294839)
15. Gelman, A. 2002. "Prior distribution". In Encyclopedia of Environmetrics, Edited by: El-Shaarawi, A. H. and Piegorsch, W. W. 1634-1637. Chichester: John Wiley & Sons.
16. Geman, S. and Geman, D. 1984. Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell., 6: 721-741. (doi:10.1109/TPAMI.1984.4767596)
17. Geweke, J. 1992. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments". In Bayesian Statistics 4, Edited by: Bernardo, J. M., Berger, J., Dawid, A. P. and Smith, A. F.M. 169-193. Oxford: Oxford University Press.
18. Haley, D. C. 1952. Estimation of the dosage mortality relationship when the dose is subject to error, Stanford: Stanford University, Applied Mathematics and Statistics Laboratory. Tech. Rep. N. 15
19. Hambleton, R. K. and Swaminathan, H. 1985. Item Response Theory: Principles And Applications, Boston, MA: Kluwer Nijhoff Publishing.
20. Larsen, D. R. and Speckman, P. L. 2004. Multivariate regression trees for analysis of abundance data. Biometrics, 60: 543-549. (doi:10.1111/j.0006-341X.2004.00202.x)
21. van der Kleij, F. M., Eggen, T. J.H.M., Timmers, C. F. and Veldkamp, B. P. 2012. Effects of feedback in a computer-based assessment for learning. Comput. Educ., 58: 263-272. (doi:10.1016/j.compedu.2011.07.020)
22. van der Linden, W. J. 1999. Empirical initialization of the trait estimation in adaptive testing. Appl. Psych. Meas., 23: 21-29. (doi:10.1177/01466219922031149)
23. van der Linden, W. J. and Glas, C. A.W. 2010. Elements of Adaptive Testing, New York: Springer-Verlag.
24. van der Linden, W. J. and Hambleton, R. K. 1997. Handbook of Modern Item Response Theory, New York: Springer-Verlag.
25. van der Linden, W. J. and Pashley, P. J. 2010. "Item selection and ability estimation in adaptive testing". In Elements of Adaptive Testing, Edited by: van der Linden, W. J. and Glas, C. A.W. 3-30. New York: Springer.
26. Lord, F. M. 1952. A theory of test scores. Psychometric Monogr., 7: 1-84.
27. Lord, F. M. and Novick, M. R. 1968. Statistical Theories of Mental Test Scores, Reading, MA: Addison-Wesley.
28. Maij-de Meij, A. M., Schakel, L., Smid, N., Verstappen, N. and Jaganjac, A. 2008. Connector Ability, Professional Manual, Utrecht: Pi Company B.V.
29. Makransky, G. and Glas, C. A.W. 2010. An automatic online calibration design in adaptive testing. J. Appl. Test. Technol., 11: 1-29.
30. Matteucci, M. and Veldkamp, B. P. 2011. "Including empirical prior information in test administration". In Classification and Multivariate Analysis for Complex Data Structures, Edited by: Fichet, B., Piccolo, D., Verde, R. and Vichi, M. 173-181. Berlin, Heidelberg: Springer-Verlag.
31. Matteucci, M., Mignani, S. and Veldkamp, B. P. 2009. "Issues on item response theory modeling". In Statistical Methods for the Evaluation of Educational Services and Quality of Products, Edited by: Bini, M., Monari, P., Piccolo, D. and Salmaso, L. 29-45. Berlin, Heidelberg: Springer-Verlag.
32. Matteucci, M., Mignani, S. and Veldkamp, B. P. 2012. Prior distributions for item parameters in IRT models. Commun. Stat. Theory Methods., 41: 2944-2958. (doi:10.1080/03610926.2011.639973)
33. OECD. 2010. PISA 2009 Results: Overcoming Social Background-Equity in Learning, Opportunities and Outcomes (Volume II) Available at http://dx.doi.org/10.1787/9789264091504-en.
34. Patz, R. J. and Junker, B. W. 1999. A straightforward approach to Markov chain Monte Carlo methods for item response models. J. Educ. Behav. Stat., 24: 146-178.
35. Segal, M. R. 1992. Tree-structured methods for longitudinal data. J. Amer. Statist. Assoc., 87: 407-418. (doi:10.1080/01621459.1992.10475220)
36. Smith, B. J. 2007. Boa: An R package for MCMC output convergence assessment and posterior inference. J. Stat. Softw., 21: 1-37.
37. The MathWorks Inc. 2005. MATLAB 7.1 Natick, MA
38. Tsutakawa, R. K. 1992. Prior distribution for item response curves. Br. J. Math. Stat. Psych., 45: 51-74. (doi:10.1111/j.2044-8317.1992.tb00977.x)
39. Veldkamp, B. P. 2012. "Ensuring the future of CAT". In Psychometrics in Practice at RCEC Edited by: Eggen, T. J.H.M. and Veldkamp, B. P. 35-46. Available at: http://dx.doi.org/10.3990/3.9789036533744.ch4.
40. Veldkamp, B. P., Matteucci, M. and de Jong, M. 2012. "Uncertainties in the item parameter estimates and robust automated test assembly". submitted for publication. Available at http://amsacta.unibo.it/3240/.
41. Wright, D. 2002. "Scoring tests when items have been generated". In Item Generation for Test Development, Edited by: Irvine, S. H. and Kyllonen, P. C. 277-286. Mahwah, NJ: Lawrence Erlbaum Associates.
42. Zwinderman, A. H. 1997. "Response models with manifest predictors". In Handbook of Modern Item Response Theory, Edited by: van der Linden, W. J. and Hambleton, R. K. 245-256. New York: Springer-Verlag.