, Volume 52, Issue 3, pp 393–408 | Cite as

On the relationship between item response theory and factor analysis of discretized variables

  • Yoshio Takane
  • Jan de Leeuw


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.

Key words

marginal maximum likelihood estimation dichotomous data ordered and unordered categorical data pair comparison data 


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Copyright information

© The Psychometric Society 1987

Authors and Affiliations

  • Yoshio Takane
    • 1
  • Jan de Leeuw
    • 2
  1. 1.Department of PsychologyMcGill UniversityMontrealCanada
  2. 2.University of LeidenThe Netherlands

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