Information Matrices and Standard Errors for MLEs of Item Parameters in IRT

Psychometrika

Volumn 79, Issue 2, 2014, Pages 232-254

  Yuan, Ke Hai ^a   Cheng, Ying ^a   Patton, Jeff ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

model misspecification; Monte Carlo; observed information matrix; sandwich type covariance matrix; standard errors

Indexed keywords

MONTE CARLO METHOD; STATISTICAL MODEL; THEORETICAL MODEL;

LIKELIHOOD FUNCTIONS; MODELS, THEORETICAL; MONTE CARLO METHOD;

EID: 84897023975     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-013-9334-4     Document Type: Article

References (41)

1. Baker, F. B., & Kim, S. H. (2004). Item response theory: parameter estimation techniques (2nd ed.). New York: Dekker.
2. Bentler, P. M. (1995). EQS structural equations program manual. Encino: Multivariate Software.
3. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: application of an EM algorithm. Psychometrika, 46, 443-459.
4. Bock, R. D., & Lieberman, M. (1970). Fitting a response model for n dichotomously scored items. Psychometrika, 35, 179-197.
5. Casella, G., & Berger, R. L. (2001). Statistical inference (2nd ed.). Pacific Grove: Duxbury Press.
6. Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm (with discussion). Journal of the Royal Statistical Society. Series B, 39, 1-38.
7. Drasgow, F., & Parsons, C. K. (1983). Application of unidimensional item response theory models to multidimensional data. Applied Psychological Measurement, 7, 189-199.
8. du Toit, M. (2003) IRT from SSI: bilog-mg, multilog, parscale, testfact. Lincolnwood: Scientific Software International.
9. Efron, B., & Hinkley, D. V. (1978). Assessing the accuracy of the maximum likelihood estimator: observed versus expected Fisher information. Biometrika, 65, 457-487.
10. Efron, B., & Tibshirani, R. J. (1993). An introduction to the bootstrap. New York: Chapman & Hall.
11. Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah: Erlbaum.
12. Firth, D. (1993). Bias reduction of maximum likelihood estimates. Biometrika, 80, 27-38.
13. Harrison, D. A. (1986). Robustness of IRT parameter estimation to violations on the unidimensionality assumption. Journal of Educational Statistics, 11, 91-115.
14. Hayes, A. F., & Cai, L. (2007). Using heteroscedasticity-consistent standard error estimators in OLS regression: an introduction and software implementation. Behavior Research Methods, 39, 709-722.
15. Huber, P. J. (1967). The behavior of maximum likelihood estimates under nonstandard conditions. In Proceedings of the fifth Berkeley symposium on mathematical statistics and probability (pp. 221-233). Berkeley: University of California Press.
16. Kirisci, L., Hsu, T.-C., & Yu, L. (2001). Robustness of item parameter estimation programs to assumptions of unidimensionality and normality. Applied Psychological Measurement, 25, 146-162.
17. Li, Y. H. (2002). Analytically asymptotic standard errors of multidimensional IRT item parameters. In S. P. Shohov (Ed.), Advances in psychology research (Vol. 13, pp. 87-108). New York: Nova Science Publishers.
18. Li, Y. H., & Lissitz, R. W. (2004). Applications of the analytically derived asymptotic standard errors of item response theory item parameter estimates. Journal of Educational Measurement, 41, 85-117.
19. Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13-22.
20. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley.
21. 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.
22. Maronna, R. A., Martin, R. D., & Yohai, V. J. (2006). Robust statistics: theory and methods. New York: Wiley.
23. Maydeu-Olivares, A., Cai, L., & Hernandez, A. (2011). Comparing the fit of IRT and factor analysis models. Structural Equation Modeling, 18, 333-356.
24. Mislevy, R. J. (1986). Bayes model estimation in item response models. Psychometrika, 51, 177-195.
25. Mislevy, R. J., & Bock, R. D. (1990). BILOG: maximum likelihood item analysis and test scoring with logistic models for binary items. Chicago: Scientific Software International.
26. Mislevy, R. J., & Sheehan, K. M. (1989). Information matrices in latent-variable models. Journal of Educational Statistics, 14, 335-350.
27. Muthén, L. K., & Muthén, B. O. (2007). Mplus user's guide (5th ed.). Los Angeles: Muthén & Muthén.
28. Ogasawara, H. (2010). Asymptotic expansions for the pivots using log-likelihood derivatives with an application in item response theory. Journal of Multivariate Analysis, 101, 2149-2167.
29. Reise, S. P., & Yu, J. (1990). Parameter recovery in the graded response model using MULTILOG. Journal of Educational Measurement, 27, 133-144.
30. Schuster, C., & Yuan, K.-H. (2011). Robust estimation of latent ability in item response models. Journal of Educational and Behavioral Statistics, 36, 720-735.
31. Stout, W. F. (1987). A nonparametric approach for assessing latent trait dimensionality. Psychometrika, 52, 79-98.
32. Stout, W. F., Habing, B., Douglas, J., Kim, H. R., Roussos, L. A., & Zhang, J. (1996). Conditional covariance-based nonparametric multidimensionality assessment. Applied Psychological Measurement, 20, 331-354.
33. Thissen, D., & Wainer, H. (1982). Some standard errors in item response theory. Psychometrika, 47, 397-412.
34. Toland, M. D. (2008). Determining the accuracy of item parameter standard error of estimates in BILOG-MG3. Doctoral dissertation. Retrieved from ProQuest LLC (UMI Number 3317288).
35. Tsutakawa, R. K. (1984). Estimation of two-parameter logistic item response curves. Journal of Educational Statistics, 9, 263-276.
36. Wainer, H., & Thissen, D. (1987). Estimating ability with the wrong model. Journal of Educational Statistics, 12, 339-368.
37. White, H. (1982). Maximum likelihood estimation of misspecified models. Econometrica, 50, 1-25.
38. Woods, C. M., & Lin, N. (2009). Item response theory with estimation of the latent density using Davidian curves. Applied Psychological Measurement, 33, 102-117.
39. Woods, C. M., & Thissen, D. (2006). Item response theory with estimation of the latent population distribution using spline-based densities. Psychometrika, 71, 281-301.
40. Yuan, K.-H., & Hayashi, K. (2006). Standard errors in covariance structure models: asymptotics versus bootstrap. British Journal of Mathematical & Statistical Psychology, 59, 397-417.
41. Zhang, J., & Stout, W. F. (1999). The theoretical DETECT index of dimensionality and its application to approximate simple structure. Psychometrika, 64, 213-249.