A dynamic generalization of the Rasch model |
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Authors: | N. D. Verhelst C. A. W. Glas |
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Affiliation: | (1) National Institute of Educational Measurement (Cito), Arnhem, The Netherlands |
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Abstract: | In the present paper a model for describing dynamic processes is constructed by combining the common Rasch model with the concept of structurally incomplete designs. This is accomplished by mapping each item on a collection of virtual items, one of which is assumed to be presented to the respondent dependent on the preceding responses and/or the feedback obtained. It is shown that, in the case of subject control, no unique conditional maximum likelihood (CML) estimates exist, whereas marginal maximum likelihood (MML) proves a suitable estimation procedure. A hierarchical family of dynamic models is presented, and it is shown how to test special cases against more general ones. Furthermore, it is shown that the model presented is a generalization of a class of mathematical learning models, known as Luce's beta-model. |
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Keywords: | Rasch model missing data incomplete designs dynamic models mathematical learning theory |
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