Abstract
The problem of deciding whether a set of mental test data is consistent with any one of a large class of item response models is considered. The “classical” assumption of locla independence is weakened to a new condition, local nonnegative dependence (LND). Necessary and sufficient conditions are derived for a LND item response model to fit a set of data. This leads to a condition that a set of data must satisfy if it is to be representable by any item response model that assumes both local independence and monotone item characteristic curves. An example is given to show that LND is strictly weaker than local independence. Thus rejection of LND models implies rejection of all item response models that assume local independence for a given set of data.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability (Part 5). In F. Lord & M. Novick,Statistical theories of mental test scores. Reading, Massachusetts: Addison-Wesley, 1947.
Bock, D. & Lieberman, M. Fitting a response model forn dichotomously scored items.Psychometrika, 1970,35, 179–197.
Lawley, D. N. On problems connected with item selection and test construction.Proceedings of the Royal Society of Edinburgh, 1947,61, 273–287.
Lazarsfeld, P. The algebra of dichotomous systems. In H. Solomon (ed.),Studies in item analysis and prediction. Stanford, California: Stanford University Press, 1961.
Lazarsfeld, P. & Henry, N.Latent structure analysis. Boston: Houghton-Mifflin, 1968.
Lord, F. A theory of test scores.Psychometric Monographs, 1952, 7.
Lord, F. An application of confidence intervals and of maximum likelihood to the estimation of an examinee's ability.Psychometrika, 1953,18, 57–76.
Lord, F. & Novick, M.Statistical theories of mental tests. Reading, Massachusetts: Addison-Wesley, 1968.
Rasch, G.Probabilistic models for some intelligence and attainment tests. Copenhagen: Neilson & Lydiche, 1960.
Tucker, L. Maximum validity of a test with equivalent items.Psychometrika, 1946,11, 1–13.
Author information
Authors and Affiliations
Additional information
This research was supported in part by Grant NIE-G-78-0157 to ETS from the NIE, by the Program Statistics Research Project, and by TOEFL Program Research. I would like to thank Dr. Douglas Jones of ETS for stimulating discussions during the early stages of this research, Dr. Frederick Lord of ETS for his encouragement of this work and comments on earlier drafts of this paper and Professor Robert Berk of Rutgers University for pointing out that conditions (a), (b) and (c) of Theorem 2 were also sufficient for LND and Monotonicity. Dr. Donald Alderman of ETS provided financial support for the development of a computer program to apply these results to data from the TOEFL program.
Rights and permissions
About this article
Cite this article
Holland, P.W. When are item response models consistent with observed data?. Psychometrika 46, 79–92 (1981). https://doi.org/10.1007/BF02293920
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02293920