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The Dutch Identity: A New Tool for the Study of Item Response Theory Models IRT

Holland, Paul W.
Publication Year:
Report Number:
RR-87-27, PSRTR-87-78
ETS Research Report
Document Type:
Page Count:
Subject/Key Words:
Dutch Identity, Item Response Theory (IRT), Mathematical Models, Psychometrics, Statistical Analysis


The Dutch identity is a useful way to reexpress the basic equations of item response theory (IRT) that relate the manifest probabilities to the item response functions (IRFs) and the latent trait distribution. The identity may be exploited in several ways. For example: (a) to show how IRT models behave for large numbers of items--they are submodels of second-order log-linear models for 2J tables; (b) to suggest new ways to assess the dimensionality of IRT models--factor analysis of matrices composed of second-order interactions from log-linear models; (c) to give insight into the structure of latent class models; and (d) to illuminate the problem of identifying the IRFs and the latent trait distribution from sample data.

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