Estimation of Latent Ability Using a Response Pattern of Graded Scores

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Abstract
This monograph is a part of a more comprehensive treatment of estimation of latent traits, when the entire response pattern is used.The fundamental structure of the whole theory comes from the latent trait model, which was initiated by Lazarsfeld as the latent structure analysis [Lazarsfeld, 1959], and also by Lord and others as a theory of mental test scores [Lord, 1952]. Similarities and differences in their mathematical structures and tendencies were discussed by Lazarsfeld [Lazarsfeld, 1960] and the recent book by Lord and Novick with contributions by Birnbaum [Lord & Novick, 1968] provides the dichotomous case of the latent trait model in the context of mental measurement.

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