Estimating difficulty from polytomous categorical data

Psychometrika

Volumn 75, Issue 2, 2010, Pages 331-350

  Revuelta, Javier ^a  

^a UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

Generalized logit linear item response model; Identifiability; Nested effects parameterization; Nominal categories model; Polytomous item response theory

Indexed keywords

EID: 77953723512     PISSN: 00333123     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11336-009-9145-9     Document Type: Article

References (30)

1. Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle. In B. N. Petrov & F. Csaki (Eds.), The second international symposium on information theory. Budapest: Akadmiai Kiado.
2. Arendasy, M., & Sommer, M. (2005). The effect of different types of perceptual manipulations on the dimensionality of automatically generated figural matrices. Intelligence, 33, 307-324.
3. Bechger, T. M., Maris, G., Verstralen, H. H. F. M., & Verhelts, N. D. (2005). The Nedelsky model for multiple-choice items. In L. A. van der Ark, M. A. Croon & Sijtsma (Eds.), New developments in categorical data analysis for the social and behavioral sciences. Mahwah: Lawrence Erlbaum Associates.
4. 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.
5. Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29-51.
6. Bock, R. D. (1975). Multivariate statistical methods in the behavioral sciences. New York: Wiley.
7. 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.
8. Bock, R. D., & Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: application of an EM algorithm. Psychometrika, 46, 443-459.
9. Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: a theoretical account of the processing in the Raven progressive matrices test. Psychological Review, 97(3), 404-431.
10. Haladyna, T. (2004). Developing and validating multiple-choice test items (3rd ed.). Mahwah: Lawrence Erlbaum Associates.
11. Hambleton, R. K., & Swaminathan, H. (1985). Item response theory: principles and applications. Boston: Kluwer Academic.
12. Hutchinson, T. P. (1991). Ability, partial information, guessing: statistical modelling applied to multiple-choice items. Adelaide: Rumsby Scientific Publishing.
13. Maxwell, S. E., & Delaney, H. D. (1990). Designing experiments and analyzing data. Belmont: Wadsworth.
14. Maydeu-Olivares, A., & Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables. Psychometrika, 71, 713-732.
15. Mislevy, R. J. (1984). Estimating latent distributions. Psychometrika, 49, 359-381.
16. Nocedal, J., & Wright, S. J. (2006). Numerical optimization. New York: Springer.
17. Revuelta, J. (2004). Analysis of distractor difficulty in multiple-choice items. Psychometrika, 69, 217-234.
18. Revuelta, J. (2005). An item response model for nominal data based on the rising selection ratios criterion. Psychometrika, 70, 305-324.
19. Revuelta, J. (2008). The generalized logit-linear item response model for binary-designed items. Psychometrika, 73, 385-405.
20. Revuelta, J. (2009). Identifiability and equivalence of GLLIRM models. Psychometrika, 74, 257-272.
21. Rothenberg, T. (1971). Identification in parametric models. Econometrica, 39, 577-591.
22. San Martin, E., del Pino, G., & De Boeck, P. (2006). IRT models for ability-based guessing. Applied Psychological Measurement, 30, 183-203.
23. Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6, 461-464.
24. Sternberg, R. J. (2000). Handbook of intelligence. Cambridge: Cambridge University Press.
25. Thissen, D. (1982). Marginal maximum likelihood estimation for the one parameter logistic model. Psychometrika, 47, 175-186.
26. Thissen, D., Chen, W. H., & Bock, R. D. (2003). Multilog 7. 0. Scientific Software International. Lincolnwood, IL.
27. Thissen, D., & Steinberg, L. (1984). A response model for multiple-choice items. Psychometrika, 49, 501-519.
28. Thissen, D., & Steinberg, L. (1986). A taxonomy of item response models. Psychometrika, 51, 567-577.
29. Thissen, D., Steinberg, L., & Fitzpatrick, A. R. (1989). Multiple-choice items: the distractors are also part of the item. Journal of Educational Measurement, 26, 161-176.
30. Townsend, J. T., & Nozawa, G. (1997). Serial exhaustive models can violate the race model inequality: implications for architecture and capacity. Psychological Review, 104, 595-602.