Abstract
The authors developed a new latent trait model for polytomous data. A unique feature of this model is that it explains the psychological process through which a subject reaches correct or wrong responses. This model is an integration of two parts. One part discriminates states of knowledge, namely, it classifies them into three categories, i.e., a) complete knowledge, b) partial knowledge, and c) complete ignorance. Another feature of the model is that we have two different kinds of manifest data, i.e. confidence data and correct/wrong responses. The subject is required to choose whether he is confident of his answer or not. In this paper, we make use of confidence data as auxiliary information in making effective estimation of parameters. Then the new model was applied to mathematics test data of high school students.
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