PROBABILITY ESTIMATION OF DICHOTOMOUS RESPONSE PATTERNS BY LOGISTIC FRACTIONAL-FACTORIAL REPRESENTATION

SHIZUHIKO NISHISATO

doi:10.4992/psycholres1954.12.87

SHIZUHIKO NISHISATO

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JOURNAL FREE ACCESS

1970 Volume 12 Issue 3 Pages 87-95

DOI https://doi.org/10.4992/psycholres1954.12.87

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Published: 1970 Received: June 06, 1970 Available on J-STAGE: February 24, 2009 Accepted: - Advance online publication: - Revised: -
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Date of correction: February 24, 2009 Reason for correction: - Correction: ABSTRACT Details: Wrong : A method for estimating probabilities of 2ⁿ dichotomous response patterns is proposed. Incorporated in the method are two techniques: the fractional replicate principle, which would mitigate the size problem (the number of possible patterns and the number of parameters): a logistic representation of probabilities, which would assure the efficient use of the fractional principle, and which eliminates the possibility that an estimate may exceed the range of the probability measure. Numerical examples suggest that the proposed method may be very useful whenever some approximation to the probability is required.
Right : A method for estimating probabilities of 2ⁿ dichotomous response patterns is proposed. Incorporated in the method are two techniques: the fractional replicate principle, which would mitigate the size problem (the number of possible patterns and the number of parameters): a logistic representation of probabilities, which would assure the efficient use of the fractional principle, and which eliminates the possibility that an estimate may exceed the range of the probability measure. Numerical examples suggest that the proposed method may be very useful whenever some approximation to the probability is required.

Date of correction: February 24, 2009 Reason for correction: - Correction: CITATION Details: Wrong : ANSCOMBE, F. J. 1956 On estimating the binominal response ralations. Biometrika, 43, 461-464.
BAHADUR, R. R. 1961 A representation of the joint distribution of responses to n dichotomous items. In Solomon, H. (Ed.) Studies in Item Analysis and Prediction. Stanford University Press, Chapter 9, 158-168.
BOCK, R. D. 1963 Programming univariate and multivariate analysis of variance. Technometrics, 5, 95-117.
DYKE, G. V., & PATTERSON, H. D. 1952 Analysis of factorial arrangements when the data are proportions. Biometrics, 8, 1-12.
HITCHCOCK, S. E. 1962 A note on the estimation of the parameters of the logistic function, using the minimum logic X² method. Biometrika, 49, 250-252.
JOHNSON, N. L., & LEONE, F. C. 1964 Statistics and experimental design: In engineering and the physical sciences. New York: John Wiley & Sons, Inc., Vol. 2.
NISHISATO, S. 1965 Minimum entropy clustering of test items. The University of North Carolina Unpublished Ph. D. Dissertation.

Right : ANSCOMBE, F. J. 1956 On estimating the binominal response ralations. Biometrika, 43, 461-464.
BAHADUR, R. R. 1961 A representation of the joint distribution of responses to n dichotomous items. In Solomon, H.(Ed.) Studies in Item Analysis and Prediction. Stanford University Press, Chapter 9, 158-168.
BOCK, R. D. 1963 Programming univariate and multivariate analysis of variance. Technometrics, 5, 95-117.
DYKE, G. V., & PATTERSON, H. D. 1952 Analysis of factorial arrangements when the data are proportions. Biometrics, 8, 1-12.
HITCHCOCK, S. E. 1962 A note on the estimation of the parameters of the logistic function, using the minimum logit χ2 method. Biometrika, 49, 250-252.
JOHNSON, N. L., & LEONE, F. C. 1964 Statistics and experimental design: In engineering and the physical sciences. New York: John Wiley & Sons, Inc., Vol.2.
NISHISATO, S. 1965 Minimum entropy clustering of test items. The University of North Carolina Unpublished Ph. D. Dissertation.

Date of correction: February 24, 2009 Reason for correction: - Correction: PDF FILE Details: -

Abstract

A method for estimating probabilities of 2ⁿ dichotomous response patterns is proposed. Incorporated in the method are two techniques: the fractional replicate principle, which would mitigate the size problem (the number of possible patterns and the number of parameters): a logistic representation of probabilities, which would assure the efficient use of the fractional principle, and which eliminates the possibility that an estimate may exceed the range of the probability measure. Numerical examples suggest that the proposed method may be very useful whenever some approximation to the probability is required.

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