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A General Least Squares Solution for Successive Intervals

Published online by Cambridge University Press:  01 January 2025

Gertrude W. Diederich ,
Samuel J. Messick  and
Ledyard R Tucker
Gertrude W. Diederich
Affiliation:
Princeton University
Samuel J. Messick
Affiliation:
Princeton University and Educational Testing Service
Ledyard R Tucker
Affiliation:
Princeton University and Educational Testing Service
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Abstract

A general least squares solution for successive intervals is presented, along with iterative procedures for obtaining stimulus scale values, discriminal dispersions, and category boundaries. Because provisions for weighting were incorporated into the derivation, the solution may be applied without loss of rigor to the typical experimental matrix of incomplete data, i.e., to a data matrix with missing entries, as well as to the rarely occurring matrix of complete data. The use of weights also permits adjustments for variations in the reliability of estimates obtained from the data. The computational steps involved in the solution are enumerated, the amount of labor required comparing favorably with other procedures. A quick, yet accurate, graphical approximation suggested by the least squares derivation is also described.

Type
Original Paper
Information
Psychometrika , Volume 22 , Issue 2 , June 1957 , pp. 159 - 173
Copyright
Copyright © 1957 Psychometric Society

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Footnotes

*

This research was jointly supported in part by Princeton University, the Office of Naval Research under contract N6onr-270-20, and the National Science Foundation under grant NSF G-642, and in part by Educational Testing Service.

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