Maximum-likelihood estimation of noncompensatory IRT models with the MH-RM algorithm

Applied Psychological Measurement

Volumn 38, Issue 5, 2014, Pages 339-358

  Philip Chalmers, R ^a   Flora, David B ^a  

^a YORK UNIVERSITY   (Canada)

Author keywords

Multidimensional item response theory; Noncompensatory models; Stochastic estimation

Indexed keywords

EID: 84927721811     PISSN: 01466216     EISSN: 15523497     Source Type: Journal    
DOI: 10.1177/0146621614520958     Document Type: Article

References (33)

1. Ackerman, T. A. (1989). Unidimensional IRT calibration of compensatory and noncompensatory multidimensional items. Applied Psychological Measurement, 13, 113-127.
2. Babcock, B. (2011). Estimating a noncompensatory IRT model using Metropolis within Gibbs sampling. Applied Psychological Measurement, 35, 317-329.
3. Baker, F. B., & Kim, S. H. (2004). Item response theory: Parameter estimation techniques (2nd ed.). New York, NY: Marcel Dekker.
4. Birnbaum, A. (1968). Some latent trait models and their use in inferring an examinee's ability. In F. M. Lord & M. R. Novick (Eds.), Statistical theories of mental test scores (pp. 395-479). Reading, MA: Addison-Wesley.
5. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm. Psychometrika, 46, 443-459.
6. Bollen, K. A. (1989). Structural equations with latent variables. New York, NY: Wiley.
7. Bolt, D. M., & Lall, V. F. (2003). Estimation of compensatory and noncompensatory multidimensional item response models using Markov Chain Monte Carlo. Applied Psychological Measurement, 27, 395-414.
8. Cai, L. (2010a). High-dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins- Monro algorithm. Psychometrika, 75, 33-57.
9. Cai, L. (2010b). Metropolis-Hastings Robbins-Monro algorithm for confirmatory item factor analysis. Journal of Educational and Behavioral Statistics, 35, 307-335.
10. Chalmers, R. P. (2012). mirt: A multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. Retrieved from http://www.jstatsoft.org/v48/i06
11. Diebolt, J., & Ip, E. H. S. (1996). Stochastic EM: Method and application. In W. Gilks, S. Richardson, & D. Spiegel-halter (Eds.), Markov chain Monte Carlo in practice (pp. 259-273). London, England: Chapman & Hall.
12. Edwards, M. C. (2010). A Markov Chain Monte Carlo approach to confirmatory item factor analysis. Psychometrika, 75, 474-497.
13. Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Erlbaum.
14. Hastings, W. K. (1970). Monte Carlo simulation methods using Markov chains and their applications. Biometrika, 57, 97-109.
15. Knol, D. L., & Berger, M. P. F. (1991). Empirical comparison between factor analysis and multidimensional item response models. Multivariate Behavioral Research, 26, 457-477.
16. Lazarsfeld, P. F. (1950). The logical and mathematical foundation of latent structure analysis. In S. A. Stouffer, L. Guttman, E. A. Suchman, P. F. Lazarsfeld, S. A. Star, & J. A. Clausen (Eds.), Measurement and prediction (pp. 362-412). New York, NY: Wiley. Lord, F. M. (1977, July). Discussion: Section 2. In D. J. Weiss (Ed.), Proceedings of the 1977 Computerized Adaptive Testing Conference (pp. 99-103). Minneapolis, MN.
17. Lord, F. M. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum.
18. Louis, T. A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society: Series B, 44, 226-233.
19. Maris, E. (1995). Psychometric latent response models. Psychometrika, 60, 523-547.
20. Maris, E. (1999). Estimating multiple classification latent class models. Psychometrika, 64, 187-212.
21. McDonald, R. P. (1962). A general approach to nonlinear factor analysis. Psychometrika, 27, 397-415.
22. McDonald, R. P. (1999). Test theory: A unified treatment. Mahwah, NJ: Erlbaum.
23. Metropolis, N., Rosenbluth, A. W., Teller, A. H., & Teller, E. (1953). Equations of state space calculations by fast computing machines. Journal of Chemical Physics, 21, 1087-1091.
24. Mulaik, S. A. (2010). Foundations of factor analysis (2nd ed.). Boca Raton, FL: Chapman & Hall.
25. R Core Team. (2013). R: A language and environment for statistical computing [Computer software]. Vienna, Austria. Available from http://www.R-project.org/
26. Reckase, M. D. (2009). Multidimensional item response theory. New York, NY: Springer.
27. Robbins, H., & Monro, S. (1951). A stochastic approximation method. The Annals of Mathematical Statistics, 22, 400-407.
28. Schilling, S., & Bock, R. D. (2005). High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature. Psychometrika, 70, 533-555.
29. Sympson, J. B. (1977, July). A model for testing with multidimensional items. In D. J. Weiss (Ed.), Proceedings of the 1977 Computerized Adaptive Testing Conference (pp. 82-98). Minneapolis, MN.
30. Thissen, D., & Steinberg, L. (2009). Item response theory. In R. E. Millsap & A. Maydeu-Olivares (Eds.), The SAGE handbook of quantitative methods in psychology (pp. 148-177). Los Angeles, CA: Sage.
31. Whitely, S. E. (1980). Multicomponent latent trait models for ability tests. Psychometrika, 60, 181-198.
32. Wood, R., Wilson, D., Gibbons, R., Schilling, S., Muraki, E., & Bock, R. (2003). TESTFACT 4 for Windows: Test scoring, item statistics, and full-information item factor analysis [Computer software]. Scientific Software International. Chicago, IL: Scientific Software International.
33. Zhang, J. (2012). Calibration of response data using MIRT models with simple and mixed structures. Applied Psychological Measurement, 36, 375-398.