Psychometrika

, Volume 52, Issue 3, pp 393–408

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

Authors

  • Yoshio Takane
    • Department of PsychologyMcGill University
  • Jan de Leeuw
    • University of Leiden
Article

DOI: 10.1007/BF02294363

Cite this article as:
Takane, Y. & de Leeuw, J. Psychometrika (1987) 52: 393. doi:10.1007/BF02294363
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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.

Key words

marginal maximum likelihood estimationdichotomous dataordered and unordered categorical datapair comparison data

Copyright information

© The Psychometric Society 1987