Identifiability and equivalence of GLLIRM models

Psychometrika

Volumn 74, Issue 2, 2009, Pages 257-272

  Revuelta, Javier ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Equivalence; Generalized logit linear item response model; Identifiability; Item response theory; Nominal categories model

Indexed keywords

EID: 67349272996     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-008-9084-x     Document Type: Article

References (36)

1. Andersen, E. B. (1980). Discrete statistical models with social science applications. Amsterdam: North-Holland.
2. R. Bartels 1985 Identification in econometrics The American Statistician 39 102 104
3. T. M. Bechger G. Maris 2004 Structural equation modelling of multiple facet data. Extending models for multitrait-multimethod data Psicológica 25 253 274 (Pubitemid 39526218)
4. T. M. Bechger N. D. Verhelst H. F. M. Verstralen 2001 Identifiability of nonlinear logistic test models Psychometrika 66 357 371 (Pubitemid 33338968)
5. T. M. Bechger H. F. M. Verstralen N. D. Verhelst 2002 Equivalent linear logistic test models Psychometrika 67 123 136
6. Bejar, I. I. (1993). A generative approach to educational and psychological measurement. In N. Frederiksen, R. J. Mislevy & I. I. Bejar (Eds.), Test theory for a new generation of tests (pp. 199-217). Mahwah: Lawrence Erlbaum.
7. I. I. Bejar R. R. Lawless M. E. Morley M. E. Wagner R. E. Bennett J. Revuelta 2002 A feasibility study of on-the-fly adaptive testing Journal of Technology, Learning and Assessment 2 4 29
8. 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 tests scores. Reading: Addison-Wesley.
9. R. D. Bock 1972 Estimating item parameters and latent ability when responses are scored in two or more nominal categories Psychometrika 37 29 51
10. Bock, R. D. (1997). The nominal categories model. In W. J. van der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory. New York: Springer.
11. R. D. Bock M. Aitkin 1981 Marginal maximum likelihood estimation of item parameters: Application of an EM algorithm Psychometrika 46 443 459
12. Bock, R. D., & Moustaki, I. (2007). Item response theory in a general framework. In C. R. Rao & S. Sinharay (Eds.), Handbook of statistics. Psychometrics. Amsterdam: Elsevier.
13. S. Embretson 1999 Generating items during testing. Psychometric issues and models Psychometrika 64 407 433
14. G. H. Fischer 1981 On the existence and uniqueness of maximum-likelihood estimates in the Rasch model Psychometrika 46 59 77
15. G. H. Fischer 1983 Logistic latent trait model with linear constraints Psychometrika 48 3 26
16. Fischer, G. H. (1995). The linear logistic test model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: foundations, recent developments and applications. New York: Springer.
17. Fischer, G. H. (1997). Unidimensional linear logistic Rasch models. In W. v. der Linden & R. K. Hambleton (Eds.), Handbook of modern item response theory. New York: Springer.
18. G. H. Fischer 2004 Remarks on "Equivalent linear logistic test models" by Bechger, Verstralen, and Verhelst (2002) Psychometrika 69 305 315 (Pubitemid 39603760)
19. Fischer, G. H., & Molenaar, I. W. (1995). Rasch models. Foundations, recent developments and applications. New York: Springer.
20. G. H. Fischer I. Ponocny 1994 An extension of the partial credit model with an application to the measurement of change Psychometrika 56 177 192 (Pubitemid 24794408)
21. Hsiao, C. (1983). Identification. In Z. Griliches & M. D. Intriligator (Eds.), Handbook of econometrics, Vol. I. Amsterdam: North-Holland.
22. Irvine, S. H., Kyllonen, P. C. (2002). Item generation for test development. Mahwah: Lawrence Erlbaum Associates.
23. Lehmann, E. L. (1983). Theory of point estimation. New York: Wiley.
24. C. F. Manski 1988 Identification of binary response models Journal of the American Statistical Association 83 729 738
25. G. Maris T. M. Bechger 2004 Equivalent MIRID models Psychometrika 69 627 639 (Pubitemid 40366647)
26. Pringle, R. M., & Rayner, A. A. (1971). Generalized inverse matrix with application to statistics. London: Charles Griffin & Co.
27. Rao, C. R. (1973). Linear statistical inference and its applications. New York: Wiley.
28. Rao, C. R., & Mitra, S. K. (1971). Generalized inverse of matrices and its applications. New York: Wiley.
29. Rao, C. R., & Toutenburg, H. (1995). Linear models. Least squares and alternatives. New York: Springer.
30. J. Revuelta 2008 The generalized logit-linear item response model for binary-designed items Psychometrika 73 3 385 405
31. J. Richmond 1974 Identifiability in linear models Econometrica 42 731 736
32. T. Rothenberg 1971 Identification in parametric models Econometrica 39 577 591
33. D. Thissen L. Steinberg 1986 A taxonomy of item response models Psychometrika 51 567 577
34. R. C. Tsai 2000 Remarks on the identifiability of Thurstonian ranking models. Case V, III or neither? Psychometrika 65 233 240
35. A. Wald 1949 Note on the consistency of the maximum likelihood estimate The Annals of Mathematical Statistics 20 595 601
36. Wansbeek, T., & Meijer, E. (2000). Measurement error and latent variables in econometrics. Amsterdam: North-Holland.