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Fitting a Response Model for n Dichotomously Scored Items

Published online by Cambridge University Press:  01 January 2025

R. Darrell Bock  and
Marcus Lieberman
R. Darrell Bock
Affiliation:
University of Chicago
Marcus Lieberman
Affiliation:
Institute for Educational Research, Downers Grove, Illinois
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Abstract

A method of estimating the parameters of the normal ogive model for dichotomously scored item-responses by maximum likelihood is demonstrated. Although the procedure requires numerical integration in order to evaluate the likelihood equations, a computer implemented Newton-Raphson solution is shown to be straightforward in other respects. Empirical tests of the procedure show that the resulting estimates are very similar to those based on a conventional analysis of item “difficulties” and first factor loadings obtained from the matrix of tetrachoric correlation coefficients. Problems of testing the fit of the model, and of obtaining invariant parameters are discussed.

Type
Original Paper
Information
Psychometrika , Volume 35 , Issue 2 , June 1970 , pp. 179 - 197
Copyright
Copyright © 1970 The Psychometric Society

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Footnotes

*

Research reported in this paper was supported by NSF Grant 1025 to the University of Chicago.

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