A MATLAB package for Markov chain Monte Carlo with a multi-unidimensional IRT model

Journal of Statistical Software

Volumn 28, Issue 10, 2008, Pages 1-20

  Sheng, Yanyan ^a  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

Bayesian DIC; Gelman Rubin R; Gibbs sampling; MATLAB; MCMC; Multi unidimensional IRT; Posterior predictive model checks; Two parameter normal ogive models

Indexed keywords

EID: 56549087864     PISSN: 15487660     EISSN: 15487660     Source Type: Journal    
DOI: 10.18637/jss.v028.i10     Document Type: Article

References (45)

1. Adams RJ, Wilson M, Wang WC (1997). "The Multidimensional Random Coefficients Multinomial Logit Model." Applied Psychological Measurement, 21, 1-23.
2. Albert JH (1992). "Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling." Journal of Educational Statistics, 17, 251-269.
3. Bafumi J, Gelman A, Park DK, Kaplan N (2005). "Practical Issues in Implementing and Understanding Bayesian Ideal Point Estimation." Political Analysis Advance Access, 13, 171-187.
4. Bezruckzo N (ed.) (2005). Rasch Measurement in Health Sciences. JAM Press, Maple Grove, MN.
5. Birnbaum A (1968). "The Logistic Test Model." In FM Lord, MR Novick (eds.), "Statistical Theories of Mental Test Scores," pp. 397-423. Addison-Wesley.
6. Birnbaum A (1969). "Statistical Theory for Logistic Mental Test Models with a Prior Distribution of Ability." Journal of Mathematical Psychology, 6, 258-276.
7. Bock RD, Aitkin M (1981). "Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm." Psychometrika, 46, 443-459.
8. Brooks SP, Gelman A (1998). "General Methods for Monitoring Convergence of Iterative Simulations." Journal of Computational and Graphical Statistics, 7, 434-455.
9. Carlin BP, Louis TA (2000). Bayes and Empirical Bayes Methods for Data Analysis. 2nd edition. Chapman & Hall, London.
10. Casella G, George EI (1992). "Explaining the Gibbs Sampler." The American Statistician, 46, 167-174.
11. Chang CH, Reeve BB (2005). "Item Response Theory and Its Applications to Patient-Reported Outcomes Measurement." Evaluation & the Health Professions, 28, 264-282.
12. Chib S, Greenberg E (1995). "Understanding the Metropolis-Hastings Algorithm." The American Statistician, 49, 327-335.
13. Embretson SE, Reise SP (2000). Item Response Theory for Psychologists. Lawrence Erlbaum Associates, New Jersey.
14. Feske U, Kirisci L, Tarter RE, Plkonis PA (2007). "An Application of Item Response Theory to the DSM-III-R Criteria for Borderline Personality Disorder." Journal of Personality Disorders, 21, 418-433.
15. Gelfand AE, Smith AFM (1990). "Sampling-Based Approaches to Calculating Marginal Densities." Journal of the American Statistical Association, 85, 398-409.
16. Gelman A, Carlin JB, Stern HS, Rubin DB (2004). Bayesian Data Analysis. Chapman & Hall/CRC, Boca Raton.
17. Gelman A, Meng XL, Stern HS (1996). "Posterior Predictive Assessment of Model Fitness via Realized Discrepancies." Statistica Sinica, 6, 733-807.
18. Gelman A, Rubin DB (1992). "Inference from Iterative Simulation Using Multiple Sequences." Statistical Science, 7, 457-511.
19. 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.
20. Geyer GJ (1992). "Practical Markov Chain Monte Carlo." Statistical Science, 7, 473-483.
21. Imbens GW (2000). "The Role of the Propensity Score in Estimating Dose-Response Functions." Biometrika, 87, 706-710.
22. Johnson VE, Albert JH (1999). Ordinal Data Modeling. Springer-Verlag, New York.
23. Kass RE, Raftery AE (1995). "Bayes Factors." Journal of the American Statistical Association, 90, 773-795.
24. Kolen MJ, Brennan RL (eds.) (1995). Test Equating: Methods and Practices. Springer-Velag, New York.
25. Lee H (1995). Markov Chain Monte Carlo Methods for Estimating Multidimensional Ability in Item Response Analysis. Ph.D. thesis, University of Missouri, Columbia, MO.
26. Li YH, Schafer WD (2005). "Trait Parameter Recovery Using Multidimensional Computerized Adaptive Testing in Reading and Mathematics." Applied Psychological Measurement, 29, 3-25.
27. Lord FM (1980). Applications of Item Response Theory to Practical Testing Problems. Lawrence Erlbaum Associates, Hillsdale, New Jersey.
28. McDonald RP (1999). Test Theory: A Unified Approach. Lawrence Erlbaum, Mahwah, NJ.
29. Molenaar IW (1995). "Estimation of Item Parameters." In GH Fischer, IW Molenaar (eds.), "Rasch Models: Foundations, Recent Developments, and Applications," pp. 39-51. Springer-Verlag, New York.
30. Osterlind SJ (1997). "A National Review of Scholastic Achievement in General Education: How Are We Doing and Why Should We Care?" ASHE-ERIC Higher Education Report Volume 25, No. 8, George Washington University Graduate School of Education and Human Development, Washington, DC.
31. Patz RJ, Junker BW (1999a). "Applications and Extensions of MCMC in IRT: Multiple Item Types, Missing Data, and Rated Responses." Journal of Educational and Behavioral Statistics, 24, 342-366.
32. Patz RJ, Junker BW (1999b). "A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models." Journal of Educational and Behavioral Statistics, 24, 146-178.
33. Reckase MD (1997). "The Past and Future of Multidimensional Item Response Theory." Applied Psychological Measurement, 21, 25-36.
34. Ripley BD (1987). Stochastic Simulation. John Wiley & Sons, New York.
35. Rubin DB (1984). "Bayesianly Justifiable and Relevant Frequency Calculations for the Applied Statistician." Annals of Statistics, 12, 1151-1172.
36. Sheng Y (2008). "Markov Chain Monte Carlo Estimation of Normal Ogive IRT Models in MATLAB." Journal of Statistical Software, 25, 1-15. URL http://www.jstatsoft.org/v25/i08/.
37. Sheng Y, Wikle CK (2007). "Comparing Multiunidimensional and Unidimensional IRT Models." Educational & Psychological Measurement, 67, 899-919.
38. Sinharay S, Johnson MS, Stern HS (2006). "Posterior Predictive Assessment of Item Response Theory Models." Applied Psychological Measurement, 30, 298-321.
39. Sinharay S, Stern HS (2002). "On the Sensitivity of Bayes Factors to the Prior Distribution." The American Statistician, 56, 196-201.
40. Sinharay S, Stern HS (2003). "Posterior Predictive Model Checking in Hierarchical Models." Journal of Statistical Planning and Inference, 111, 209-221.
41. Spiegelhalter D, Best N, Carlin B (1998). "Bayesian Deviance, the Effective Number of Parameters, and the Comparison of Arbitrarily Complex Models." Technical Report 98-009, Division of Biostatistics, University of Minnesota.
42. Tanner MA, Wong WH (1987). "The Calculation of Posterior Distribution by Data Augmentation." Journal of the American Statistical Association, 82, 528-550.
43. The MathWorks, Inc (2007). MATLAB - The Language of Technical Computing, Version 7.5. The MathWorks, Inc., Natick, Massachusetts. URL http://www.mathworks.com/products/matlab/.
44. Verdinelli I, Wasserman L (1995). "Computing Bayes Factors Using a Generalization of the Savage-Dickey Density Ratio." Journal of the American Statistical Association, 90, 614-618.
45. Wainer H, Dorans N, Eignor D, Flaugher R, Green B, Mislevy R, Steinberg L, Thissen D (eds.) (2000). Computerized Adaptive Testing: A Primer. Lawrence Erlbaum Associates, Hillsdale, NJ.