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Estimation of Latent Ability Using a Response Pattern of Graded Scores

Samejima, Fumi
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Bayesian Statistics, Item Analysis, Item Response Theory, Statistical Analysis


Estimation of latent ability using the entire response pattern of free-response items is discussed, first in the general case and then in the case where the items are scored in a graded way, especially when the thinking process required for solving each item is assumed to be homogeneous. Advantages of the present methods are investigated by comparing them with those which make use of conventional dichotomous items or test scores, theoretically as well as empirically, in terms of the amounts of information, the standard errors of estimators, and the mean-square errors of estimators. The utility of the Bayes modal estimator as a computational compromise for the Bayes estimator is also discussed and observed. The relationship between the formula for the item characteristic function and the philosophy of scoring is observed with respect to dichotomous items.

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