A Dynamic Generalization of the Rasch Model

Norman D. Verhelst · Cees A. W. Glas

79 citations0/0 files storedPsychometrika

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Educational Technology and Assessment

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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References

1961Probabilistic Models for Some Intelligence and Attainment Tests 1962Individual Choice Behavior 1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1963Handbook of mathematical psychology: I.1952A theory of test scores.1984Estimating Latent Distributions 1974Conditional Inference and Models for Measuring.1984Loglinear Rasch Model Tests

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