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Psychometrika

, Volume 39, Issue 1, pp 111–121 | Cite as

Normal ogive model on the continuous response level in the multidimensional latent space

  • Fumiko Samejima
Article

Abstract

The homogeneous case of the continuous response model is expanded to the multi-dimensional latent space, and the normal ogive model is presented. The operating density characteristic of the continuous item response and the vector of basic functions are developed. It is found out that there is a vector of sufficient statistics for estimating the subject's vector of latent traits, given the item parameter vectors. The relationship between the model and the linear factor analysis is observed. The matrix of item response information functions is introduced. Some additional observations are also made.

Keywords

Basic Function Public Policy Parameter Vector Response Model Item Response 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Anderson, T. W. and H. Rubin. Statistical inference in factor analysis.Proceedings of the third Berkeley symposium on mathematical statistics and probability, 1956,5, 111–150.Google Scholar
  2. Anderson, T. W. Some scaling models and estimation procedures in the latent class model. In U. Grenander (Ed.),Probability and statistics. New York: Wiley, 1959, 9–38.Google Scholar
  3. Bartlett, M. S. The statistical conception of mental factors.British Journal of Psychology 1937,28, 97–104.Google Scholar
  4. Bartlett, M. S. Methods of estimating mental factors. London:Nature, 1938,141, 609–610.Google Scholar
  5. Lawley, D. N. and A. E. Maxwell.Factor analysis as a statistical method. (2nd edition) New York: American Elsevier, 1971.Google Scholar
  6. Lord, F. M. and M. R. Novick.Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.Google Scholar
  7. McDonald, R. P. A note on the derivation of the general latent class model.Psychometrika, 1962,27, 203–206.Google Scholar
  8. Samejima, F. Estimation of latent ability using a response pattern of graded scores.Psychometrika Monograph, 1969, No. 17.Google Scholar
  9. Samejima, F. A general model for free response data.Psychometrika Monograph, 1972, No. 18.Google Scholar
  10. Samejima, F. Homogeneous case of the continuous response model.Psychometrika, 1973,38, 203–219.Google Scholar

Copyright information

© Psychometric Society 1974

Authors and Affiliations

  • Fumiko Samejima
    • 1
  1. 1.University of TennesseeUSA

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