Bayesian estimation of the multidimensional graded response model with nonignorable missing data

Journal of Statistical Computation and Simulation

Volumn 80, Issue 11, 2010, Pages 1237-1252

  Fu, Zhi Hui ^a,b   Tao, Jian ^c   Shi, Ning Zhong ^c  

^a JILIN UNIVERSITY   (China)

^b SHENYANG NORMAL UNIVERSITY   (China)

^c NORTHEAST NORMAL UNIVERSITY   (China)

Author keywords

Bayesian estimation; Data augmentation; Gibbs sampling; Item response theory; Nonignorable missing data

Indexed keywords

EID: 77958489694     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949650903029276     Document Type: Article

References (22)

1. D.B. Rubin, Inference and missing data, Biometrika 63 (1976), pp. 581-592.
2. I. Moustaki and C. O'Muircheartaigh, A one dimensional latent trait model to infer attitude from nonresponse fornominal data, Statistica 60(2) (2000), pp. 259-276.
3. I. Moustaki and M. Knott, Weighting for item non-response in attitude scales by using latent variable models withcovariates, J. R. Statist. Soc. Ser. A 163 (2000), pp. 445-459.
4. C.A. Bernaards and K. Sijtsma, Factor analysis of multidimensional polytomous item response data suffering fromignorable item nonresponse, Multivariate Behav. Res. 34(3) (1999), pp. 277-313.
5. C.A. Bernaards and K. Sijtsma, Influence of imputation and EM methods on factor analysis when item nonresponsein questionnaire data is nonignorable, Multivariate Behav. Res. 35(3) (2000), pp. 321-364.
6. R. Holman and C.A.W. Glas, Modelling non-ignorable missing-data mechanism with item response theory models, British J. Math. Statist. Psych. 58 (2005), pp. 1-18.
7. P.J. Diggle, P. Heagerty, K.Y. Liang, and S.L. Zeger, Analysis of Longitudinal Data, Oxford, Clarendon, 2002.
8. J.H. Albert, Bayesian estimation of normal ogive item response functions using Gibbs sampling, J. Educ. Statist. 17 (1992), pp. 251-269.
9. M. Ghosh, A. Ghosh, M.H. Chen, and A. Agresti, Noninformative priors for one-parameter item response models, J. Statist. Plann. Inference 88 (2000), pp. 99-115.
10. R.J. Patz and B.W. Junker, Applications and extensions of MCMC in IRT: Multiple item types, missing data, andrated responses, J. Educ. Behav. Stat. 24 (1999), pp. 146-178.
11. S.K. Sahu, Bayesian estimation and model choice in item response models, J. Stat. Comput. Simul. 72 (2002), pp. 217-232.
12. F. Samejima, Estimation of latent ability using a response pattern of graded scores, Psychometrika Monogr. Suppl. 34(4) (1969), pp. 100-114.
13. M.D. Reckase,A linear logistic multidimensional model for dichotomous item response data, inHandbook of ModernItem Response Theory, W.J. van der Linden and R.K. Hambleton, eds., Springer, NewYork, 1997, pp. 271-286.
14. T.A. Ackerman, Developments in multidimensional item response theory, Appl. Psychol. Meas. 20 (1996), pp. 309-310.
15. N.D. Verhelst and C.A.W. Glas, The one-parameter logistic model, in Rasch Models: Foundations, RecentDevelopments, and Applications, G.H. Fischer and I.W. Molenaar, eds., Springer-Verlag, New York, 1995, pp. 215-237.
16. A.A. Béguin and C.A.W. Glas, MCMC estimation and some model-fit analysis of multidimensional IRT models, Psychometrika 66 (2001), pp. 541-562.
17. A.E. Gelfand and A.F.M. Smith, Sampling based approaches to calculating marginal densities. J. Amer. Statist.Assoc. 85 (1990), pp. 398-409.
18. A. Gelman and D.B. Rubin, Inference from iterative simulation using multiple sequences (with discussion), Statist.Sci. 7 (1992), pp. 457-511.
19. A. Gelman, Inference and monitoring convergence, in Markov Chain Monte Carlo in Practice, W.R. Gilks, S. Richardson and D.T. Spiegelhalter, eds., Chapman and Hall, London, 1996, pp. 131-143.
20. A.P. Dempster, N.M. Laird, and D.B. Rubin, Maximum likelihood from incomplete data via the EM algorithm (withdiscussion), J. R. Statist. Soc. Ser. B 39 (1977), pp. 1-38.
21. X.L. Meng and D. van Dyk, The EM algorithm-an old folk-song sung to a fast new tune, J. R. Statist. Soc. Ser. B59 (1997), pp. 511-540.
22. R.P. Gupta, Multivariate Statistical Analysis. North-Holland, NewYork, 1980.