A Gibbs Sampler for the (Extended) Marginal Rasch Model

Psychometrika

Volumn 80, Issue 4, 2015, Pages 859-879

  Maris, Gunter ^a   Bechger, Timo ^b   Martin, Ernesto San ^c  

^a ACADEMIC MEDICAL CENTER   (Netherlands)

^b Cito group   (Netherlands)

^c PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

Author keywords

extended Rasch model; Gibbs sampler; item response theory; marginal Rasch model

Indexed keywords

ALGORITHM; BAYES THEOREM; MARKOV CHAIN; PSYCHOMETRY; STATISTICAL MODEL; STATISTICS AND NUMERICAL DATA;

ALGORITHMS; BAYES THEOREM; LIKELIHOOD FUNCTIONS; MARKOV CHAINS; PSYCHOMETRICS;

EID: 84947128486     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-015-9479-4     Document Type: Article

References (23)

1. Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17(3), 251–269.
2. Albert, J. H., & Chib, S. (1993). Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association, 88(422), 669–679.
3. Andersen, E. B. (1973). Conditional inference and models for measuring. Unpublished doctoral dissertation, Mentalhygiejnisk Forskningsinstitut.
4. Anderson, C., Li, Z., & Vermunt, J. (2007). Estimation of models in the rasch family for polytomous items and multiple latent variables. Journal of Statistical Software, 20(6), 1–36.
5. Béguin, A. A., & Glas, C. A. W. (2001). MCMC estimation and some model-fit analysis of multidimensional IRT models. Psychometrika, 66(4), 541–562.
6. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51.
7. Casella, G., & George, E. I. (1992). Explaining the gibbs sampler. The American Statistician, 46(3), 167–174.
8. Cressie, N., & Holland, P. (1983). Characterizing the manifest probabilities of latent trait models. Psychometrika, 48, 129–141.
9. Fox, J. P., & Glas, C. A. W. (2001). Bayesian estimation of a multilevel IRT model using Gibbs sampling. Psychometrika, 66, 269–286.
10. Gelfand, A. E., & Smith, A. F. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85(410), 398–409.
11. 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.
12. Gilks, W. R., & Wild, P. (1992). Adaptive rejection sampling for gibbs sampling. Journal of the Royal Statistical Society Series C (Applied Statistics), 41, 337–348.
13. Hessen, D. J. (2011). Loglinear representations of multivariate bernoulli rasch models. British Journal of Mathematical and Statistical Psychology, 64, 337–354.
14. Hessen, D. J. (2012). Fitting and testing conditional multinormal partial credit models. Psychometrika, 77(4), 693–709.
15. Holland, P. W. (1990). The dutch identity: A new tool for the study of item response models. Psychometrika, 55, 5–18.
16. Johnson, M. S., & Junker, B. W. (2003). Using data augmentation and Markov Chain Monte Carlo for the estimation of unfolding response models. Journal of Educational and Behavioral Statistics, 28, 195–230.
17. Maris, G., & Maris, E. (2002). A MCMC-method for models with continuous latent responses. Psychometrika, 67, 335–350.
18. Masters, G. N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149–174.
19. R Development Core Team. (2011). R: A language and environment for statistical computing [Computer software manual]. Vienna, Austria. Retrieved from http://www.R-project.org/ (ISBN 3-900051-07-0).
20. Shohat, J. H., & Tamarkin, J. D. (1943). The problem of moments. New York: American Mathematics Society.
21. Tjur, T. (1982). A connection between Rasch’s item analysis model and a multiplicative poisson model. Scandinavian Journal of Statistics, 9(1), 23–30.
22. Verhelst, N. D., & Glas, C. A. W. (1995). The one parameter logistic model: OPLM. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, recent developments and applications (pp. 215–238). New York: Springer.
23. Verhelst, N. D., Glas, C. A. W., & van der Sluis, A. (1984). Estimation problems in the Rasch model: The basic symmetric functions. Computational Statistics Quarterly, 1(3), 245–262.