, Volume 46, Issue 1, pp 79–92 | Cite as

When are item response models consistent with observed data?

  • Paul W. Holland


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.

Key words

latent-trait models local independence item-characteristic curves 


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  1. 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.Google Scholar
  2. Bock, D. & Lieberman, M. Fitting a response model forn dichotomously scored items.Psychometrika, 1970,35, 179–197.Google Scholar
  3. Lawley, D. N. On problems connected with item selection and test construction.Proceedings of the Royal Society of Edinburgh, 1947,61, 273–287.Google Scholar
  4. Lazarsfeld, P. The algebra of dichotomous systems. In H. Solomon (ed.),Studies in item analysis and prediction. Stanford, California: Stanford University Press, 1961.Google Scholar
  5. Lazarsfeld, P. & Henry, N.Latent structure analysis. Boston: Houghton-Mifflin, 1968.Google Scholar
  6. Lord, F. A theory of test scores.Psychometric Monographs, 1952, 7.Google Scholar
  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.Google Scholar
  8. Lord, F. & Novick, M.Statistical theories of mental tests. Reading, Massachusetts: Addison-Wesley, 1968.Google Scholar
  9. Rasch, G.Probabilistic models for some intelligence and attainment tests. Copenhagen: Neilson & Lydiche, 1960.Google Scholar
  10. Tucker, L. Maximum validity of a test with equivalent items.Psychometrika, 1946,11, 1–13.Google Scholar

Copyright information

© The Psychometric Society 1981

Authors and Affiliations

  • Paul W. Holland
    • 1
  1. 1.Division of Measurement, Statistics, and Data Analysis ResearchEducational Testing ServicePrinceton

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