Identification of parametric Rasch-type models

Journal of Statistical Planning and Inference

Volumn 143, Issue 1, 2013, Pages 116-130

  San Martín, Ernesto ^a   Rolin, Jean Marie ^b  

^a PONTIFICIA UNIVERSIDAD CATÓLICA DE CHILE   (Chile)

^b UNIVERSITÉ CATHOLIQUE DE LOUVAIN   (Belgium)

Author keywords

Fixed effects Rasch model; Generalized Linear Mixed Model; Latent regression models; LLTM; Location scale distributions; MIRID; Random effects Rasch model

Indexed keywords

EID: 84866291091     PISSN: 03783758     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jspi.2012.06.014     Document Type: Article

References (51)

1. Adams R.J., Wilson M., Wang W. Multidimensional random coefficients multinomial logit model. Applied Psychological Measurement 1997, 21:1-23.
2. Adams R.J., Wu M.L. The mixed-coefficients multinomial logit model: a generalization form of the Rasch model. Multivariate and Mixture Distribution Rasch Models 2007, 57-75. Springer. M. von Davier, C.H. Carstensen (Eds.).
3. Basu D. Statistical Information and Likelihood (with Discussion). Sankhyā 1975, 37:1-71.
4. Bechger T.M., Maris G., Verstralen H.H.F.M., Béguin A.A. Using classical test theory in combination with item response theory. Applied Psychological Measurement 2003, 27:319-334.
5. Bechger T.M., Verstralen H.H.F.M., Verhelst N.D. Identifiability of Nonlinear Logistic Test Models. Psychometrika 2001, 66:357-372.
6. Bechger T.M., Verstralen H.H.F.M., Verhelst N.D. Equivalent linear logistic test models. Psychometrika 2002, 67:123-136.
7. Butler S.M., Louis T.A. Consistency of maximum likelihood estimators in general random effects models for binary data. Annals of Statistics 1997, 25:351-377.
8. Butter R., De Boeck P., Verhelst N. An item response model with internal restrictions on item difficulty. Psychometrika 1998, 63:47-63.
9. Catchpol E.A., Morgan B.J.T. Detecting parameter redundancy. Biometrika 1997, 84:187-196.
10. Chen M.-H., Dey D. Bayesian modeling of correlated binary responses via scale mixture of multivariate normal link functions. Sankhyā: The Indian Journal of Statistics 1998, 60:322-343.
11. Cox D.R., Hinkley D.V. Theoretical Statistics 1974, Chapman and Hall, London.
12. De Boeck P., Wilson M. Explanatory Item Response Models. A Generalized Linear and Nonlinear Approach 2004, Springer, New York.
13. Embretson S.E., Reise S.P. Item Response Theory for Psychologists 2000, Lawrence Erlbaum Associates, Publishers, New Jersey.
14. Engle R.E., Hendry D.F., Rixhard J.F. Exogeneity. Econometrica 1983, 51:277-304.
15. Fahrmeir L., Tutz G. Multivariate Statistical Modelling Based on Generalized Linear Models 2001, Springer, New York. second edition.
16. Farrell R.H. Multivariate Calculation. Use of Continuous Groups 1985, Springer, New York.
17. Fischer G. Logistic latent trait models with linear constraints. Psychometrika 1983, 48:3-26.
18. Fischer G.H. Derivations of the Rasch model. Rasch Models. Foundations, Recent Developments and Applications 1995, Springer, New York, (Chapter 2). G.H. Fischer, I.W. Molenaar (Eds.).
19. Fischer G.H. Remarks on "Equivalent Linear Logistic Test Models" by Bechger, Verstralen, and Verhelst (2002). Psychhometrika 2004, 69:305-315.
20. Fischer R.A. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London, Series A 1922, 222:309-368.
21. Florens J.P., Mouchart M., Rolin J.M. Elements of Bayesian Statistics 1990, Marcel and Dekker, New York.
22. Fox J.T., Kim K., Ryan S., Bajari P. The random coefficients logit model is identified. Journal of Econometrics 2012, 166:204-212.
23. Halmos P. Finite-Dimensional Vector Spaces 1987, Springer, New York.
24. Hendry D.F. Dynamic Econometrics 1995, Oxford University Press, Oxford.
25. Laplace P.S. Mémoire sur la probabilité des causes par les événements 1774, Académie Royal des Sciences de Paris, Paris.
26. Lazarsfeld P.F. A conceptual introduction to latent structure analysis. Mathematical Thinking in the Social Sciences 1954, 349-387. Russell & Russell, New York. P.F. Lazarsfeld (Ed.).
27. Maris G., Bechger T. Equivalent MIRID models. Psychometrika 2004, 69:627-639.
28. Marsaglia G. Conditional means and covariance of normal variable with singular covariance matrix. Journal of the American Statistical Association 1964, 59:1203-1204.
29. McCullagh P. What is a statistical model? (with Discussion). Annals of Statistics 2002, 30:1225-1310.
30. Molenaar I.W. Estimation of item parameters. Rasch Models. Foundations, Recent Developments and Applications 1995, Springer, New York, (Chapter 3). G.H. Fischer, I.W. Molenaar (Eds.).
31. Molenbergs G., Verbeke G. An introduction to generalized (non)linear mixed model. Explanatory Item Response Models. A Generalized Linear and Nonlinear Approach 2004, 111-153. Springer, New York. P. De Boeck, M. Wilson (Eds.).
32. Mouchart M., San Martín E. Specification and identification issues in models involving a latent hierarchical structure. Journal of Statistical Planning and Inference 2003, 111:143-163.
33. Muthen B. A structural probit model with latent variables. Journal of the American Statistical Association 1979, 74:807-811.
34. Oulhaj A., Mouchart M. The role of the exogenous randomness in the identification of conditional models. Metron-International Journal of Statistics 2006, 64:253-261.
35. Piegorsch W. Complementary log regression for generalized linear models. American Statistician 1992, 46:94-99.
36. Rabe-Hesketh S., Skrondal A. Parametrization of multivariate random effects models for categorical data. Biometrics 2001, 57:1256-1264.
37. Rasch G. An individualistic approach to item analysis. Readings in Mathematical Social Sciences 1966, 89-107. MIT Press, Massachusetts. P.F. Lazarsfeld, N.W. Henry (Eds.).
38. Rasch G. An item analysis which takes individual differences into account. British Journal of Mathematical and Statistical Psychology 1966, 19:49-57.
39. Reichenbach H. The Direction of Time 1956, University of California Press, Los Angeles.
40. Rijmen F., De Boeck P. A relation between a between-item multidimensional IRT model and the mixture Rasch model. Psychometrika 2005, 70:481-496.
41. San Martín E., González J., Tuerlinckx F. Identified parameters, parameters of interest and their relationships. Measurement: Interdisciplinary Research and Perspective 2009, 7:97-105.
42. San Martín E., Jara A., Rolin J.-M., Mouchart M. On the Bayesian nonparametric generalization of IRT-type models. Psychometrika 2011, 76:385-409.
43. San Martin, E., Rolin, J.M., Castro, L.M. Identification of the 1PL model with guessing parameter: parametric and semi-parametric results. Psychometrika, in press.
44. Sijtsma K., Molenaar I.W. Introduction to Nonparametric Item Response Theory 2002, Sage Publications, Thousand Oaks.
45. Smits D.J., De Boeck P. A componential IRT model for guilt. Multivariate Behavioral Research 2003, 38:161-188.
46. Smits D.J., De Boeck P., Verhelst N. Estimation of the MIRID: a program and a SAS-based approach. Behavior Research Methods, Instruments, and Computers 2003, 35:537-549.
47. Smits D.J.M., Moore S. Latent item predictors with fixed effects. Explanatory Item Response Models. A Generalized Linear and Nonlinear Approach 2004, 267-287. Springer, New York. P. De Boeck, M. Wilson (Eds.).
48. Snijders T., Bosker R. Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling 1999, Sage, London.
49. Spivak M. Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus 1965, Perseus Book Publishing, Cambridge.
50. Verbekee G., Molenberghs G. Linear Mixed Models for Longitudinal Data 2009, Springer, New York.
51. Wu M. The role of plausible values in large-scale surveys. Studies in Educational Evaluation 2005, 31:114-128.