A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models

Journal of Educational and Behavioral Statistics

Volumn 24, Issue 2, 1999, Pages 146-178

  Patz, Richard J ^a   Junker, Brian W ^b  

^a CTB MCGRAW HILL   (United States)

^b NONE

Author keywords

Item response theory; Markov chain Monte Carlo; National Assessment of Educational Progress (NAEP)

Indexed keywords

EID: 0033411905     PISSN: 10769986     EISSN: None     Source Type: Journal    
DOI: 10.3102/10769986024002146     Document Type: Article

References (64)

1. Adams, R. J., Wilson, M., & Wu, M. (1997). Multilevel item response models: An approach to errors in variables regression. Journal of Educational and Behavioral Statistics, 22, 47-76.
2. Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251-269.
3. Algina, J. (1992). Special issue: The National Assessment of Educational Progress (Editor's Note). Journal of Educational Measurement, 29, 93-94.
4. Baker, F. B. (1992). Item response theory: Parameter estimation techniques. New York: Marcel Dekker.
5. Bartholomew, D. J. (1987). Latent variable models and factor analysis. New York: Oxford University Press.
6. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord and M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 395-479). Reading, MA: Addison-Wesley.
7. Bock R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
8. Bradlow, E. T. (1994). Analysis of Ordinal Survey Data with "No Answer" Responses. Ph.D. dissertation, Harvard Statistics Department.
9. Bradlow, E. T., Wainer, H., & Wang, X. (in press). A Bayesian random effects model for testlets. Psychometrika.
10. Carlin B. P., Kass R. E., Lerch, F. J., & Huguenard, B. R. (1992). Predicting working memory failure: A subjective Bayesian approach to model selection. Journal of the American Statistical Association, 87, 319-327.
11. Chib, S., & Greenberg, E. (1995). Understanding the Metropolis-Hastings Algorithm. The American Statistician, 49, 327-335.
12. Cowles, K., & Carlin, B. (1995). Markov chain Monte Carlo convergence diagnostics: A comparative review. University of Minnesota Technical Report.
13. DiBello, L., Stout, W. F., & Roussos, L. (1995). Unified cognitive/psychometric diagnostic assessment likelihood-based classification techniques. In P. Nichols, S. Chipman, and R. Brennen (Eds.), Cognitively diagnostic assessment (pp. 361-389). Hillsdale, NJ: Erlbaum.
14. Douglas, J. (1997). Joint consistency of nonparametric item characteristic curve and ability estimation. Psychometrika, 62, 7-28.
15. Douglas, J., & Qui, P. (1997). Generalized linear factor analysis with Markov chain Monte Carlo. Unpublished manuscript.
16. Engelhard, G., Jr. (1994). Examining rater errors in the assessment of written composition with many-faceted Rasch models. Journal of Educational Measurement, 31, 93-112.
17. Engelhard, G., Jr. (1996). Evaluating rater accuracy in performance assessments. Journal of Educational Measurement, 33, 56-70.
18. Fischer, G. H., & Molenaar, I. W. (1995). Rasch models: Foundations, recent developments, and applications. New York: Springer-Verlag.
19. Fischer, G. H., & Ponocny, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177-192.
20. Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
21. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian data analysis. New York: Chapman and Hall.
22. Gelman A., Roberts, G. O., & Gilks, W. R. (1996). Efficient Metropolis jumping rules. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian Statistics 5: Proceedings of the Fifth Valencia International Meeting, pp. 599-608. New York: Oxford.
23. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-472.
24. Geman, S., & Geman, D. (1984). Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721-741.
25. Geyer, C. J. (1992). Practical Markov chain Monte Carlo. Statistical Science, 7, 473-483.
26. Ghosh, M., Ghosh, A., Chen, M.-H., & Agresti, A. Bayesian estimation for item response models. Unpublished manuscript.
27. Gilks, W. (1992). Derivative-free adaptive rejection sampling for Gibbs sampling. In J. M. Bernardo, J. O. Berger, A. P. Dawid, & A. F. M. Smith (Eds.), Bayesian Statistics 4. Oxford: Clarendon Press.
28. Haberman, S. J. (1977). Maximum likelihood estimates in exponential response models. Annals of Statistics, 5, 815-841.
29. Hastings, W. K. (1970). Monte Carlo simulation methods using Markov chains and their applications. Biometrika, 57, 97-109.
30. Hoijtink, H. & Molenaar, I. W. (1997). A multidimensional item response model: constrained latent class analysis using the Gibbs sampler and posterior predictive checks. Psychometrika, 67, 171-189.
31. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577-601.
32. Holland, P. W., & Rubin, D. B. (Eds.) (1982). Test equating. New York: Academic Press.
33. Holland, P. W., & Wainer, H. (1993). Differential item functioning. Hillsdale, NJ: Erlbaum.
34. Huguenard, B. R., Lerch, F. J., Junker, B. W., Patz, R. J., & Kass, R. E. (1997). Working memory failure in phone-based interaction. ACM Transactions on Computer-Human Interaction, 4(2), 67-102.
35. Johnson, E. G., Mazzeo, J., & Kline, D. L. (1994). Technical Report of the NAEP 1992 Trial State Assessment Program in Reading. Washington, DC: Office of Educational Research and Improvement, U.S. Department of Education.
36. Johnson, E. G., Mislevy, R. J., & Thomas, N. (1994). Theoretical background and philosophy of NAEP scaling procedures. In E. G. Johnson, J. Mazzeo, & D. L. Kline. (Eds.), Technical Report of the NAEP 1992 Trial State Assessment Program in Reading, (pp. 133-146). Washington, DC: Office of Educational Research and Improvement, U.S. Department of Education.
37. Johnson, V. E. (1996). On Bayesian analysis of multirater ordinal data: An application to automated essay grading. Journal of the American Statistical Association, 91, 42-51.
38. Johnson, V. E. (1997). Alternatives to GPA-based evaluation of student performance (with discussion). Statistical Science, 12, 247-277.
39. Kelderman, H. & Rijkes, C. P. M. (1994). Loglinear multidimensional IRT models for polytomously scored items. Psychometrika, 59, 149-176.
40. Lee, H., & Tsutakawa, R. K. (1997). Bayesian method for estimating multidimensional ability in item response analysis. Unpublished manuscript.
41. Legler, J. M., & Ryan, L. M. (1997). Latent variable models for teratogenesis using multiple binary outcomes. Journal of the American Statistical Association, 92, 13-20.
42. Levine, M., & Drasgow, F. (1988). Optimal appropriateness measurement. Psychometrika, 53, 161-176.
43. Linn, Robert L. (Ed.) (1989). Educational measurement (Third edition). New York: Macmillan.
44. Liu, J. S., Wong, W. H. & Kong, A. (1994). Covariance structure of the Gibbs sampler with applications to the comparisons of estimators and augmentation schemes. Biometrika, 81, 27-40.
45. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, New Jersey: Erlbaum.
46. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
47. Meng, X.-L., & Rubin, D. B. (1993). Maximum likelihood estimation via the ECM algorithm: a general framework. Biometrika, 80, 267-278.
48. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., & Teller, E. (1953). Equations of state space calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1091.
49. Mislevy, R. J. (1985). Estimation of latent group effects. Journal of the American Statistical Association, 80, 993-997.
50. Mislevy, R. J., & Bock, R. D. (1985). BILOG (Computer program). Scientific Software.
51. Mislevy, R. J., & Sheehan, K. M. (1989). The role of collateral information about examinees in item parameter estimation. Psychometrika, 54, 661-679.
52. Molenaar, I. W., & Hoijtink, H. (1990). The many null distributions of person fit indices. Psychometrika, 55, 75-106.
53. Patz, R. J. (1996). Markov Chain Monte Carlo Methods for item response theory models with applications for the National Assessment of Educational Progress. Doctoral dissertation, Carnegie Mellon University.
54. Patz, R. J., & Junker, B. W. (in press). Applications and extensions of MCMC in IRT: multiple item types, missing data, and rated responses. Journal of Educational and Behavioral Statistics.
55. Ripley (1987). Stochastic Simulation. New York: Wiley.
56. Rubin, D. B. (1991). EM and beyond. Psychometrika, 56, 241-254.
57. Seltzer, M. H., Wong, W. H., & Bryk, A. S. (1996). Bayesian analysis in applications of hierarchical models: Issues and methods. Journal of Educational and Behavioral Statistics, 21, 131-167.
58. Smith, A. F. M., & Roberts, G. O. (1993). Bayesian computation via the Gibbs sampler and related Markov chain Monte Carlo methods. Journal of the Royal Statistical Society, Ser. B, 55, 3-24.
59. Spiegelhalter D., Thomas, A., Best, N., & Gilks, W. (1996). BUGS 0.5: Bayesian inference using Gibbs Sampling, Version ii. Technical report of the MRC Biostatistics Unit, Institute of Public Health, Cambridge UK.
60. Tanner M. A., & Wong, W. H. (1987). The calculation of posterior distributions by data augmentation (with discussion). Journal of the American Statistical Association, 82, 528-550.
61. Tierney, L. (1994). Exploring posterior distributions with Markov Chains. Annals of Statistics, 22, 1701-1762.
62. Tsutakawa, R. K., & Soltys, M. J. (1988), Approximation for Bayesian ability estimation. Journal of Educational Statistics, 13, 117-130.
63. van der Linden, W. J., & Hambleton, R. K. (Eds.) (1997). Handbook of modern item response theory. New York: Springer-Verlag.
64. Zwick, R. (1992). Special issue on the National Assessment of Educational Progress. Journal of Educational Measurement, 17, 93-94.