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

Yoshio Takane · Jan de Leeuw

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

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.

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References

1969Statistical Theories of Mental Test Scores 1968ESTIMATION OF LATENT ABILITY USING A RESPONSE PATTERN OF GRADED SCORES1 1960Individual Choice Behavior: A Theoretical Analysis.1969Latent Structure Analysis.1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1969Estimation of Latent Ability Using a Response Pattern of Graded Scores 1984A General Structural Equation Model with Dichotomous, Ordered Categorical, and Continuous Latent Variable Indicators 1960A theory of data.

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