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Homogeneous Case of the Continuous Response Model

Published online by Cambridge University Press:  01 January 2025

Fumiko Samejima
Fumiko Samejima*
Affiliation:
Bowling Green State University
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Abstract

In line with the latent trait model, the continuous response level is defined and considered, in contrast to the discrete response levels, which have already been explored by the author. Discussions are mainly focused on the homogeneous case and the open response situation. The operating density characteristic of the continuous item score is defined. Also the basic function, information functions and the positive-exponent family are discussed on the continuous response level, in connection with the sufficient condition that a unique maximum estimate is provided for the response pattern, which consists of the continuous item scores.

Type
Original Paper
Information
Psychometrika , Volume 38 , Issue 2 , June 1973 , pp. 203 - 219
Copyright
Copyright © 1973 The Psychometric Society

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References

Ashford, J. R. An approach to the analysis of data for semi-quantal responses in biological assay. Biometrics, 1959, 15, 573–581CrossRefGoogle Scholar
Birnbaum, A. Some latent trait models and their use in inferring an examinee's ability. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-WesleyGoogle Scholar
Gurland, J., Lee, I., Dahm, P. A.. Polychotomous quantal response in biological assay. Biometrics, 1960, 16, 382–398CrossRefGoogle Scholar
Lazarsfeld, P. F. Latent structure analysis. In Koch, S. (Eds.), Psychology: A study of a science. Vol. 3. New York: McGraw-Hill. 1959, 476–542Google Scholar
Lord, F. M., Novick, M. R. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-WesleyGoogle Scholar
Samejima, F. A general model for the operating characteristic of graded item response. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 55, 1967.Google Scholar
Samejima, F. General considerations on the homogeneous case of graded item response. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 57, 1968(a).Google Scholar
Samejima, F. Further considerations on the homogeneous case of graded item response. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 59, 1968(b).Google Scholar
Samejima, F. Sufficient conditions for unique maximum in the heterogeneous case of graded item response. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 61, 1968(c).Google Scholar
Samejima, F. Application of the graded response model to the nominal response and multiple-choice situations. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 63, 1968(d).Google Scholar
Samejima, F. Considerations on the Bayes modal estimator. Chapel Hill, N. C.: UNC Psychometric Laboratory Report, 70, 1968(e).Google Scholar
Samejima, F. Estimation of latent ability using a response pattern of graded scores. Psychometric Monograph, 1969, No. 17.Google Scholar
Samejima, F. A general model for free response data. Psychometric Monograph, 1972, No. 18.Google Scholar