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On the relationship between item response theory and factor analysis of discretized variables. (English) Zbl 0628.62104

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.

MSC:

62P15 Applications of statistics to psychology
62H25 Factor analysis and principal components; correspondence analysis
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