A comparison of estimation methods for a multi-unidimensional graded response IRT model

Frontiers in Psychology

Volumn 7, Issue JUN, 2016, Pages

  Kuo, Tzu Chun ^a   Sheng, Yanyan ^a  

^a SOUTHERN ILLINOIS UNIVERSITY   (United States)

Author keywords

BMIRT; Fully Bayesian; Graded response model; IRTPRO; Item response theory; Markov chain Monte Carlo; MML; Multi unidimensional model

Indexed keywords

EID: 84979983635     PISSN: None     EISSN: 16641078     Source Type: Journal    
DOI: 10.3389/fpsyg.2016.00880     Document Type: Article

References (40)

1. Akaike, H. (1987). Factor analysis and AIC. Psychometrika 62, 317-332. doi: 10.1007/BF02294359
2. Albert, J. H., and Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. J. Am. Statist. Assoc. 88, 669-679. doi: 10.1080/01621459.1993.10476321
3. Andrich, D. (1978). A rating formulation for ordered response categories. Psychometrika 43, 561-573. doi: 10.1007/BF02293814
4. Baker, F. B. (1998). An investigation of item parameter recovery characteristics of a Gibbs sampling procedure. Appl. Psychol. Meas. 22, 153-169. doi: 10.1177/01466216980222005
5. Baker, F. B., and Kim, S. H. (2004). Item Response Theory: Parameter Estimation Techniques. Statistics: A Series of Textbooks and Monographs. New York, NY: Taylor & Francis.
6. Bock, R. D., and Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: applications of an EM algorithm. Psychometrika 46, 443-459. doi: 10.1007/BF02293801
7. Buchanan, R. D. (1994). The development of the Minnesota multiphasic personality inventory. J. Hist. Behav. Sci. 30, 148-161.
8. Cai, L. (2010a). High-dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins-Monro algorithm. Psychometrika 75, 33-57. doi: 10.1007/s11336-009-9136-x
9. Cai, L. (2010b). Metropolis-Hastings Robbins-Monro algorithm for confirmatory item factor analysis. J. Educ. Behav. Stat. 35, 307-335. doi: 10.3102/1076998609353115
10. Cai, L., Thissen, D., and du Toit, S. H. C. (2011). IRTPRO for Windows [Computer Software]. Lincolnwood, IL: Scientific Software International.
11. Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. J. Stat. Softw. 46, 1-29. doi: 10.18637/jss.v048.i06
12. Cowels, M. K. (1996). Accelerating Monte Carlo Markov chain convergence for cumulative-link generalized linear models. Stat. Comput. 6, 101-111. doi: 10.1007/BF00162520
13. Ferero, C. G., and Maydeu-Olivares, A. (2009). Estimation of IRT graded response models: limited versus full information methods. Psychol. Methods 14, 275-299. doi: 10.1037/a0015825
14. Fu, Z. H., Tao, J., and Shi, N. Z. (2010). Bayesian estimation of the multidimensional graded response model with nonignorable missing data. J. Stat. Comput. Simul. 80, 1237-1252. doi: 10.1080/00949650903029276
15. Geman, S., and Geman, D. (1984). Stochastic relaxation, Gibbs distribution and the Bayesian restoration of images. IEEE Trans. Pattern Anal. Mach. Intell. 6, 721-741. doi: 10.1109/TPAMI.1984.4767596
16. Han, K. T., and Paek, I. (2014). A review of commercial software packages for multidimensional IRT modeling. Appl. Psychol. Meas. 38, 486-498. doi: 10.1177/0146621614536770
17. Harwell, M., Stone, C. A., Hsu, T.-C., and Kirisci, L. (1996). Monte carlo studies in item response theory. Appl. Psychol. Meas. 20, 101-125. doi: 10.1177/014662169602000201
18. Hastings, W. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika 57, 97-109. doi: 10.1093/biomet/57.1.97
19. Kuo, T. C., and Sheng, Y. (2015). Bayesian estimation of a multi-unidimensional graded response IRT model. Behaviormetrika 42, 79-94. doi: 10.2333/bhmk.42.79
20. Li, T., Gubes, N. O., and Paek, I. (2014). "A comparison between BMIRT and IRTPRO-A simulation study using a between-item multidimensional 2PL model". in Paper presented at 59th Annual Meeting of the Florida Educational Research Association (FERA), (Cocoa Beach, FA).
21. Likert, R. (1932). A technique for the measurement of attitudes. Arch. Psychol. 22, 5-55.
22. Lord, F. M. (1980). Applications of Item Response Theory to Practical Testing Problems. Hillsdale, NJ: Lawrnce Erlbaum Associates.
23. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika 47, 147-174. doi: 10.1007/BF02296272
24. McDonald, R. P. (1999). Test Theory: A Unified Approach. Mahwah, NJ: Lawrence Erlbaum.
25. Metropolis, N., and Ulam, S. (1949). The Monte Carlo method. J. Am. Stat. Assoc. 44, 335-341. doi: 10.1080/01621459.1949.10483310
26. Patz, R. J., and Junker, B. W. (1999a). Application and extensions of MCMC in IRT: Multiple item types missing data, and related responses. J. Educ. Behav. Stat. 24, 342-366.
27. Patz, R. J., and Junker, B. W. (1999b). A straightforward approach to Markov chain Monte Carlo methods for item response models. J. Educ. Behav. Stat. 24, 146-178.
28. Reckase, M. (1997). The past and future of multidimensional item response theory. Appl. Psychol. Meas. 21, 25-36. doi: 10.1177/0146621697211002
29. Reckase, M. (2009). Multidimensional Item Response Theory. New York, NY: Springer-Verlag.
30. Robbins, H., and Monro, S. (1951). A stochastic approximation method. Ann. Math. Stat. 22, 400-407. doi: 10.1214/aoms/1177729586
31. Rubio, V. J., Aguado, D., Hontangas, P. M., and Hernandez, J. M. (2007). Psychometric properties of an emotional adjustment measure. Eur. J. Psychol. Asses. 23, 39-46. doi: 10.1027/1015-5759.23.1.39
32. Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika 35, 139-139. doi: 10.1007/BF02290599
33. Schilling, S., and Bock, R. D. (2005). High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature. Psychometrika 70, 533-555. doi: 10.1007/s11336-003-1141-x
34. Sheng, Y., and Headrick, T. C. (2012). A Gibbs sampler for the multidimensional item response model. ISRN Appl. Math. 2012:269385. doi: 10.5402/2012/269385
35. Sheng, Y., and Wikle, C. K. (2007). Comparing multiunidimensional and unidimensional item response theroy models. Educ. Psychol. Meas. 67, 899-919. doi: 10.1177/0013164406296977
36. Sheng, Y., and Wikle, C. K. (2008). Bayesian multidimensional IRT models with a hierarchical structure. Educ. Psychol. Meas. 68, 413-430. doi: 10.1177/0013164407308512
37. Wollack, J. A., Bolt, D. M., Cohen, A. S., and Lee, Y. S. (2002). Recovery of item parameters in the nominal response model: a comparison of marginal maximum likelihood estimation and Markov chain Monte Carlo estimation. Appl. Psychol. Meas. 26, 339-352. doi: 10.1177/0146621602026003007
38. Yao, L. (2003). BMIRT: Bayesian Multivariate Item Response Theory. Monterey, CA: CTB/McGraw-Hill.
39. Yao, L., and Boughton, K. A. (2007). A multidimensional item response modeling approach for improving subscale proficiency estimation and classification. Appl. Psychol. Meas. 31, 83-105. doi: 10.1177/0146621606291559
40. Yao, L., and Schwarz, R. (2006). A multidimensional partial credit model with associated item and test statistics: an application to mixed-format tests. Appl. Psychol. Meas. 30, 469-492. doi: 10.1177/0146621605284537