, Volume 52, Issue 3, pp 393-408

First online:

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

  • Yoshio TakaneAffiliated withDepartment of Psychology, McGill University
  • , Jan de LeeuwAffiliated withUniversity of Leiden

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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