A multidimensional item response model: Constrained latent class analysis using the Gibbs sampler and posterior predictive checks

Psychometrika

Volumn 62, Issue 2, 1997, Pages 171-189

  Hoijtink, Herbert ^a   Molenaar, Ivo W ^b  

^a NONE   (Netherlands)

^b NONE

Author keywords

Conditional association; Gibbs sampler; Local homogeneity; Manifest monotonicity; Multidimensional; Nonparametric item response theory; Posterior predictive checks

Indexed keywords

EID: 0040655766     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02295273     Document Type: Article

References (42)

1. Albert, J. H. (1992). Bayesian estimation of normal ogive item response curves using Gibbs sampling. Journal of Educational Statistics, 17, 251-269.
2. Casella, G., & George, E. (1992). Explaining the Gibbs sampler. American Statistician, 46, 167-174.
3. Croon, M. A. (1990). Latent class analysis with ordered latent classes. British Journal of Mathematical and Statistical Psychology, 43, 171-192.
4. Croon, M. A. (1991). Investigating Mokken scalability of dichotomous items by means of ordinal latent class analysis. British Journal of Mathematical and Statistical Psychology, 44, 315-331.
5. Ellis, J. L., & van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model. Psychometrika, 58, 417-429.
6. Gelfand, A. E., Hills, S. E., Racine-Poon, A., & Smith, A. F. M. (1990). Illustration of Bayesian inference in normal data models using Gibbs sampling. Journal of the American Statistical Association, 85, 972-985.
7. Gelfand, A. E., & Smith, A. F. M. (1990). Sampling-based approaches to calculating marginal densities. Journal of the American Statistical Association, 85, 398-409.
8. Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (1995). Bayesian Data Analysis. London: Chapman and Hall.
9. Gelman, A., Meng, X., & Stern, H. S. (in press). Posterior predictive assessment of model fitness via realized discrepancies (with discussion). Statistica Sinica. to appear.
10. Gelman, A., & Rubin, D. B. (1992). Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457-511.
11. Grayson, D. A. (1988). Two-group classification in latent trait theory: scores with monotone likelihood ratio. Psychometrika, 53, 383-392.
12. Holland, P. W. (1981). When are item response models consistent with observed data. Psychometrika, 46, 79-92.
13. Holland, P. W., & Rosenbaum, P. R. (1986). Conditional association and unidimensionality in monotone latent variable models. The Annals of Statistics, 14, 1523-1543.
14. Holm, S. (1979). A simple sequentially rejective multiple test procedure. Scandinavian Journal of Statistics, 6, 65-70.
15. Junker, B. W. (1991). Essential independence and likelihood-based ability estimation for polytomous items. Psychometrika, 56, 255-278.
16. Junker, B. W. (1993). Conditional association, essential independence and monotone unidimensional item response models. The Annals of Statistics, 3, 1359-1378.
17. Lindsay, B., Clogg, C. C., & Grego, J (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86, 96-107.
18. Lord, F. M., & Novick, M. R. (1968). Statistical theory of mental test scores. London: Addison-Wesley.
19. MacEachern, S. N., & Berliner, L. M. (1994). Subsampling the Gibbs sampler. The American Statistician, 48, 188-190.
20. Meng, X. L. (1994). Posterior Predictive p-Values. The Annals of Statistics, 22, 1142-1160.
21. Mokken, R. J. (1971). A theory and procedure of scale analysis. The Hague/Berlin: Mouton/DeGruyler.
22. Mokken, R. J., and, Lewis, C. (1982). A nonparametric approach to the analysis of dichotomous item responses. Applied Psychological Measurement, 6, 417-430.
23. Molenaar, I. W. (1996). Nonparametric models for polytomous responses. In W. J. van der Linden, & R. K. Hambleton (Eds.), Handbook of Modern Item Response Theory (pp. 361-372). New York: Springer.
24. Molenaar, I. W., Debets, P., Sijtsma, K., & Hemker, B. T. (1994). User's Manual MSP. Groningen: IecProgamma.
25. NAG (1992). Foundation library. Oxford: The Numerical Algorithms Group.
26. Narayanan, A. (1990). Computer generation of Dirichlet random vectors. Journal of Statistical Computations and Simulations, 36, 19-30.
27. Ripley, B. D. (1987). Stochastic Simulation. New York: Wiley.
28. Rosenbaum, P. R. (1984). Testing the conditional independence and monotonicity assumptions of item response theory. Psychometrika, 49, 425-435
29. Rubin, D. B. (1984). Bayesian justifiable and relevant frequency calculations for the applied statistician. The Annals of Statistics, 12, 1151-1172.
30. Rubin, D. B., & Stern, H. L. (1993). Testing in latent class models using a posterior predictive check distribution. In A. von Eye & C. Clogg (Eds.), Latent variables Analysis. Applications for Developmental Research. London: SAGE.
31. Sanders, K, & Hoijtink, H. (1992). Androgynie bestaat (Persons who are both psychologically masculine and feminine exist). Nederlands Tijdschrift voor de Psychologie, 47, 123-133.
32. Shaffer, J. P. (1994). Multiple hypothesis testing: A review. (Tech. Rep. No. 23). Research Triangle Park, NC: National Institute of Statistical Sciences.
33. Shealy, R., & Stout, W. (1993). A model based standardization approach that separates true bias/DIF from group ability differences and detects test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159-194.
34. Sijtsma, K., & Molenaar, I. W. (1987). Reliability of test scores in nonparametric item response theory. Psychometrika, 52, 79-97.
35. 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, Series B, 55, 2-23.
36. Stout, W. (1987). A nonparametric approach for assessing the latent trait dimensionality. Psychometrika, 52, 589-618.
37. Stout, W. F. (1990). A new item response theory modelling approach with applications to unidimensionality assessment and ability estimation. Psychometrika, 55, 293-326.
38. Tanner, M. A. (1993). Tools for statistical inference, methods for the explorations of posterior distributions and likelihood functions. New York: Springer.
39. Tierney, L. (1994). Markov chains for exploring posterior distributions (with discussion). Annals of Statistics, 22, 1701-1762.
40. Thissen, D., Steinberg, L., & Wainer, H. (1988). Use of item response theory in the study of group differences in trace lines. In H. Wainer, & H. I. Braun (Eds.). Test validity (pp. 147-169). Hillsdale, NJ: Erlbaum.
41. Zeger, S. L., and Karim, M. R. (1991). Generalized linear models with random effect; a Gibbs sampling approach. Journal of the American statistical association, 86, 79-86.
42. Zellner, A., & Min, C. (1995). Gibbs sampler convergence criteria. Journal of the American Statistical Association, 90, 921-927.