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On the Relationship between iTem Response Theory and Factor Analysis of Discretized Variables

Published online by Cambridge University Press:  01 January 2025

Yoshio Takane  and
Jan de Leeuw
Yoshio Takane*
Affiliation:
McGill University
Jan de Leeuw
Affiliation:
University of Leiden
*
Requests for reprints should be sent to Yoshio Takane, Department of Psychology, McGill University 1205 Dr. Penfield Ave., Montreal, PQ H3A 1B1 CANADA.
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Abstract

Equivalence of marginal likelihood of the two-parameter normal ogive model in item response theory (IRT) and factor analysis of dichotomized variables (FA) was formally proved. The basic result on the dichotomous variables was extended to multicategory cases, both ordered and unordered categorical data. Pair comparison data arising from multiple-judgment sampling were discussed as a special case of the unordered categorical data. A taxonomy of data for the IRT and FA models was also attempted.

Keywords

marginal maximum likelihood estimationdichotomous dataordered and unordered categorical datapair comparison data
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 3 , September 1987 , pp. 393 - 408
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

The work reported in this paper has been supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada.

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