Identifiability of nonlinear logistic test models

Psychometrika

Volumn 66, Issue 3, 2001, Pages 357-371

  Bechger, Timo M ^a   Verhelst, Norman D ^b   Verstralen, Huub H F M ^b  

^a Cito group   (Netherlands)

^b NONE

Author keywords

Componential item response theory; Identifiability; Item response theory; Linear logistic test model; Nonlinear logistic test models

Indexed keywords

EID: 0035594863     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/bf02294439     Document Type: Article

References (40)

1. Aitchison, W., & Silvey, S.D. (1958). Maximum likelihood estimation of parameters subject to restraints. Annals of Mathematical Statistics, 28, 813-828.
2. Andersen, E.B. (1995). Polytomous Rasch models and their estimation. In G.H. Fisher & I.W. Molenaar (Eds.). Rasch models: Foundations, recent developments and applications. New York, NY: Springer Verlag.
3. Andres, J. (1990). Grundlagen Linearer Strukturgleichungsmodelle [Foundations of linear structural equation models). New York, NY: Peter Lang.
4. Baker, F.B. (1993). Sensitivity of the linear logistic test model to misspecification of the weight matrix. Applied Psychological Measurement, 17, 201 -211.
5. Basilevsky, A. (1983). Applied matrix algebra in the statistical sciences. New York, NY: North-Holland.
6. Bechger, T.M., Verstralen, H.H.F.M., & Verhelst, N.D. (2000). Equivalent linear logistic test models (Cito R&D Report 2000-4). Arnhem, The Netherlands: Cito.
7. Bekker, P.A. (1989). Identification in restricted factor models. Journal of Econometrics, 41, 5-16.
8. Bekker, P.A., Merckens, A., & Wansbeek, T.J. (1994). Identification, equivalent models, and computer algebra. Boston, MA: Academic Press.
9. Borden, R.S. (1998). A course in advanced calculus. New York, NY: Dover Publications.
10. Butter, R.P. (1994). Item response models with internal restrictions on item difficulty. Unpublished doctoral dissertation, Catholic University of Leuven, Belgium.
11. Butter, R.P., De Boeck, P., & Verhelst, N.D. (1998). An item response model with internal restrictions on item difficulty. Psychometrika, 63, 47-63.
12. Dieudonné, J. (1969). Foundations of modern analysis. New York, NY: Academic Press.
13. Fisher, F.M. (1966). The identification problem in Econometrics. New York, NY: McGraw-Hill.
14. Fischer, G.H. (1983). Logistic latent trait models with linear constraints. Psychometrika, 48, 3-26.
15. Fischer, G.H. (1995). The linear logistic test model. In G.H. Fisher & I.W. Molenaar (Eds.), Rasch models: Foundations, recent developments and applications. New York, NY: Springer Verlag.
16. Fischer, G.H., & Ponocny, I. (1994). An extension of the partial credit model with an application to the measurement of change. Psychometrika, 59, 177-192.
17. Fischer, G.H., & Ponocny, I. (1995). Extended rating scale and partial credit models for assessing change. In G.H. Fischer & I.W. Molenaar (Eds.). Rasch models: Foundations, recent developments and applications, (chap. 10). New York, NY: Springer Verlag.
18. Fuller, S.A., Sinyakov, M.N., & Tischchenko, S.V. (2000). Linearity and the mathematics of several variables. Singapore: World Scientific.
19. Gabrielsen, A. (1978). Consistency and identifiability. Journal of Econometrics, 8, 261-263.
20. Gill, L., & Lewbel, A. (1992). Testing the rank and definiteness of estimated matrices with application to factor, state-space and ARMA models. Journal of the American Statistical Association, 87, 766-776.
21. Glas, C.A.W., & Verhelst, N.D. (1995). Testing the Rasch model. In G.H. Fischer & I.W. Molenaar (Eds.), Rasch models: Their foundations, recent developments and applications. New York, NY: Springer Verlag.
22. Henrion, D., & Sebel, M. (1993, July). Numerical methods for polynomial rank evaluation. Paper presented at the IFAC conference on systems structure and control, Nantes, France.
23. Krantz, S.G., & Parks, H.R. (1992). A primer on real analytic functions. Basel, Switzerland: Birkhauser Verlag.
24. Lang, S. (1987). Linear algebra (3rd ed.). New York, NY: Springer Verlag.
25. Lang, S. (1996). Calculus of several variables. (3rd ed.). New York, NY: Springer Verlag.
26. Luijben, Th. C.W. (1991). Equivalent models in covariance structure analysis. Psychometrika, 56, 653-665.
27. Parthasarathy, T. (1983). On global univalence theorems (Lecture Notes in Mathematics). New York, NY: Springer Verlag.
28. Ponocny, I., & Pononcny-Seliger, E. (1997). Applications of the program LpcM in the field of measuring change. In M. Wilson (Ed.), Objective measurement: Theory into practice (Vol. 4, pp. 231-238). Norwood, NJ: Ablex.
29. Rao, C.R. (1947). Large sample tests of statistical hypothesis concerning several parameters with applications to the problems of estimation. Proceedings Cambridge Philosophical Society, 44, 50-57.
30. Rasch, G. (1960). Probabilistic models for some intelligence and attainment tests. Copenhagen: Danish Institute for Educational Research. (Expanded edition, University of Chigago Press, 1980)
31. Rasch, G. (1966). An individualistic approach to item analysis. In P.F. Lazersfeld & N.W. Henry (Eds.), Readings in mathematical social science. Cambridge, MA: The MIT Press.
32. Rothenberg, T.J. (1971). Identification in parametric models. Econometrica, 39, 577-591.
33. Shapiro, A. (1983). On local identifiability in structural models (Unpublished Research Report). Pretoria, South Africa: University of South Africa, Department of Mathematics and Applied Mathematics.
34. Shapiro, A. (1985). Identifiability of factor analysis: Some results and open problems. Linear Algebra and Its Applications, 70, 1-7.
35. Shapiro, A. (1986). Asymptotic theory of overparameterized structural models. Journal of the American Statistical Association, 81, 142-149.
36. Shapiro, A., & Browne, M.W. (1983). On the investigation of local identifiability: A counterexample. Psychometrika, 48, 303-304.
37. Silvey, S.D. (1959). The Lagrange multiplier test. Annals of Mathematical Statistics, 30, 398-407.
38. Smits, D.J.M. (1999). A componential model for guilt feelings: An application of the LLTM and the MIRID. Unpublished masters thesis, University of Leuven, Department of Psychological Science, Leuven, Belgium.
39. Wald, A. (1950). Note on the identifiability of economic relations. In T.C. Koopmans (Ed.), Statistical inference in dynamic economic models, (Cowles Commission Monograph No. 10). New York, NY: Wiley.
40. Wu, M.L., Adams, R.J., & Wilson, M. (1998). ConQuest: Generalised item reponse modelling [computer program]. Melbourne: Australian Council for Educational Research (ACER) Press.