A dynamic generalization of the Rasch model. Verhelst, N. & Glas, C. A. W. Psychometrika, 58:395–415, 1993.
A dynamic generalization of the Rasch model [link]Paper  doi  abstract   bibtex   
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.
@article{verhelst_dynamic_1993,
	title = {A dynamic generalization of the {Rasch} model},
	volume = {58},
	url = {http://dx.doi.org/10.1007/BF02294648},
	doi = {10.1007/BF02294648},
	abstract = {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.},
	urldate = {2010-06-17},
	journal = {Psychometrika},
	author = {Verhelst, N. and Glas, C. A. W.},
	year = {1993},
	pages = {395--415}
}

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