Mixture rasch models with joint maximum likelihood estimation

Educational and Psychological Measurement

Volumn 71, Issue 1, 2011, Pages 5-19

  Willse, John T ^a  

^a UNIVERSITY OF NORTH CAROLINA AT GREENSBORO   (United States)

Author keywords

item response theory; joint maximum likelihood estimation; latent class analysis; mixture models; R; Rasch models

Indexed keywords

EID: 79951711573     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164410387335     Document Type: Article

References (26)

1. Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317-332.
2. Andrich, D.A. (1978). A rating formulation for ordered categories. Psychometrika, 43, 561-573.
3. Baker, F.B., & Harwell, M.R. (1996). Computing elementary symmetric functions and their derivatives: A didactic. Applied Psychological Measurement, 20, 169-192.
4. Bond, T.G., & Fox, C.M. (2007). Applying the Rasch model. Mahwah, NJ: Lawrence Erlbaum.
5. Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345-370.
6. Cohen, A.S. & Bolt, D.M. (2005). A mixture model analysis of differential item functioning. Journal of Educational Measurement, 42, 133-148.
7. Dempster, A.P., Laird, N.M., & Rubin, D.B. (1977). Maximum likelihood estimation from incomplete data via the EM-algorithm. Journal of the Royal Statistical Society, Series B, 39, 1-22.
8. Goodman, L.A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215-231.
9. Hancock, G. R., & Samuelsen, K. M. (Eds.). (2007). Advances in latent variable mixture models. Charlotte, NC: Information Age.
10. Hong, S., & Min, S.-Y. (2007). Mixed Rasch modeling of the Self-Rating Depression Scale. Educational and Psychological Measurement, 67, 280-299.
11. Lazarsfeld, P.F., & Henry, N.W. (1968). Latent structure analysis. Boston, MA: Houghton Mifflin.
12. Linacre, J.M. (2003). A user's guide to Winsteps: Rasch-model computer program [Computer program and manual]. Chicago, IL: Winsteps.com.
13. Masters, G.N. (1982). A Rasch model for partial credit scoring. Psychometrika, 47, 149-174.
14. R Development Core Team. (2008). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing. ISBN 3-900051-07-0. Retrieved from http://www.R-project.org.
15. Raftery, A.E. (1986). A note on Bayes factors for log-linear contingency table models with vague prior information. Journal of the Royal Statistical Society, Series B, 48, 249-250.
16. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen, Denmark: Nielson & Lydiche.
17. Rost, J. (1990). Rasch models in latent classes: an integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.
18. Rost, J. (1991). A logistic mixture distribution model for polychotomous item responses. British Journal of Mathematical and Statistical Psychology, 44, 75-92.
19. Rost, J., & von Davier, M. (1995). Mixture distribution Rasch models. In I. W. Moelenaar (Ed.), Rasch models: Foundations, recent developments and applications (pp. 257-268). New York, NY: Springer Verlag.
20. Schwartz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6, 461-464.
21. von Davier, M., & Carstensen, C. H. (Eds.). (2007). Multivariate and mixture distribution Rasch models. New York, NY: Springer.
22. von Davier, M., & Rost, J. (1995). Polytomous mixed Rasch models. In I. W. Moelenaar (Ed.), Rasch models: Foundations, recent developments and applications (pp. 371-379). New York, NY: Springer Verlag.
23. Wagner-Menghin, M.M. (2007). The mixed-Rasch model: An example for analyzing the meaning of response latencies in a personality questionnaire. In E. V. Smith Jr. & R. M. Smith (Eds.), Rasch measurement: Advanced and specialized applications (pp. 103-120). Maple Grove, MN: JAM Press.
24. Willse, J.T. (2009). mixRasch: Mixture Rasch Models with JMLE (Version 0.1). Retrieved fromhttp://CRAN.R-project.org/package=mixRasch.
25. Wright, B.D. (1984). Despair and hope for educational measurement. Contemporary Education Review, 3, 281-288.
26. Wright, B.D., & Masters, G.N. (1981). Rating scale analysis. Chicago, IL: Mesa Press.