Estimation of a Ramsay-Curve Item Response Theory Model by the Metropolis-Hastings Robbins-Monro Algorithm

Educational and Psychological Measurement

Volumn 74, Issue 2, 2014, Pages 343-369

  Monroe, Scott ^a   Cai, Li ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

density estimation; EM algorithm; item response theory; MH RM; Ramsay curve

Indexed keywords

EID: 84894315592     PISSN: 00131644     EISSN: 15523888     Source Type: Journal    
DOI: 10.1177/0013164413499344     Document Type: Article

References (37)

1. Abrahamowicz M.,Ramsay J. O.Multicategorical spline model for item response theory.Psychometrika. 1992;57:5-27.
2. Baker F. B.,Kim S.-H.Item response theory: Parameter estimation techniques. 2004). Item response theory: Parameter estimation techniques (2nd ed.). New York, NY: Marcel Dekker.New York, NY: Marcel Dekker; 2004:.
3. Bock R. D.,Aitkin M.Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm.Psychometrika. 1981;46:443-459.
4. Borkar V. S.Stochastic approximation: A dynamical systems viewpoint. Cambridge, England: Cambridge University Press; 2008:.
5. Cai L.SEM of another flavour: Two new applications of the supplemented EM algorithm.British Journal of Mathematical and Statistical Psychology. 2008;61:309-329.
6. Cai L.High-dimensional exploratory item factor analysis by a Metropolis-Hastings Robbins-Monro algorithm.Psychometrika. 2010;75:33-57.
7. Cai L.Seattle, WA: Vector Psychometric Group; 2012:.
8. Cai L.,Maydeu-Olivares A.,Coffman D. L.,Thissen D.Limited-information goodness-of-fit testing of item response theory models for sparse 2p tables.British Journal of Mathematical and Statistical Psychology. 2006;59:173-194.
9. Cai L.,Thissen D.,du Toit S. H. C.Lincolnwood, IL: Scientific Software International; 2011:.
10. de Boor C.A practical guide to splines. 2001). A practical guide to splines (Revised ed.). New York, NY: Springer-Verlag.New York, NY: Springer-Verlag; 2001:.
11. Dempster A. P.,Laird N. M.,Rubin D. B.Maximum likelihood from incomplete data via the EM algorithm (with discussion).Journal of the Royal Statistical Society. 1977;39:1-38.
12. Diebolt J.,Ip E. H. S.Markov chain Monte Carlo in practice. Gilks W.Richardson S.Spiegelhalter D., ed. London, England: Chapman & Hall; 1996:259-273.
13. Duncan K. A.,MacEachern S. N.Nonparametric Bayesian modelling for item response.Statistical Modelling. 2008;8:41-66.
14. Fisher R. A.Theory of statistical estimation.Proceedings of the Cambridge Philosophical Society. 1925;22:700-725.
15. Fox J. P.Stochastic EM for estimating the parameters of a multilevel IRT model.British Journal of Mathematical and Statistical Psychology. 2003;56:65-81.
16. Gu F.,Skorupski W. P.,Hoyle L.,Kingston N. M.Standard errors and confidence intervals from bootstrapping for Ramsay-curve item response theory model item parameters.Applied Psychological Measurement. 2011;35:562-565.
17. Hastings W. K.Monte Carlo sampling methods using Markov chains and their applications.Biometrika. 1970;57:97-109.
18. LangerM. M. (2008). A reexamination of Lord's Wald test for differential item functioning using item response theory and modern error estimation (Unpublished doctoral dissertation). University of North Carolina at Chapel Hill.
19. Lord F. M.Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum; 1980:.
20. Lord F. M.,Novick M. R.Statistical theories of mental test scores. Reading, MA: Addison-Wesley; 1968:.
21. Louis T. A.Finding the observed information matrix when using the EM algorithm.Journal of the Royal Statistical Society-Series B. 1982;44:226-233.
22. Metropolis N.,Rosenbluth A. W.,Rosenbluth M. N.,Teller A. H.,Teller E.Equations of state calculations by fast computing machines.Journal of Chemical Physics. 1953;21:1087-1092.
23. Mislevy R. J.Estimating latent distributions.Psychometrika. 1984;49:359-381.
24. Patz R. A.,Junker B. W.A straightforward approach to Markov chain Monte Carlo methods for item response models.Journal of Educational and Behavioral Statistics. 1999;24:146-178.
25. Polyak B. T.,Juditsky A. B.Acceleration of stochastic approximation by averaging.SIAM Journal of control and optimization. 1992;30:838-855.
26. Ramsay J. O.Differential equation models for statistical inference.Canadian Journal of Statistics. 2000;28:225-240.
27. Ramsay J. O.,Winsberg S.Maximum marginal likelihood estimation for semiparametric item analysis.Psychometrika. 1991;56:365-379.
28. Robbins H.,Monro S.A stochastic approximation method.Annals of Mathematical Statistics. 1951;22:400-407.
29. Samejima F.Estimation of latent ability using a response pattern of graded scores.Psychometric Monographs. 1969;17:1-100.
30. von Neumann J.Various techniques used in connection with random digits.National Bureau of Standards Applied Mathematics Series. 1951;12:36-38.
31. Woods C. M.Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables.Psychological Methods. 2006;11:253-270.
32. Woods C. M.Ramsay curve IRT for Likert-type data.Applied Psychological Measurement. 2007;31:195-212.
33. Woods C. M.Ramsay curve item response theory for the three-parameter item response theory model.Applied Psychological Measurement. 2008;36:447-465.
34. Woods C. M.,Lin N.Item response theory with estimation of the latent density using Davidian curves.Applied Psychological Measurement. 2008;33:102-117.
35. Woods C. M.,Thissen D.Item response theory with estimation of the latent population distribution using spline-based densities.Psychometrika. 2006;71:281-301.
36. Wu C. F. J.On the convergence properties of the EM algorithm.Annals of Statistics. 1983;11:95-103.
37. Yang J. S.,Hansen M.,Cai L.Characterizing sources of uncertainty in item response theory scale scores.Educational and Psychological Measurement. 2012;72:264-290.