Titlebook: Rasch Models; Foundations, Recent Gerhard H. Fischer,Ivo W. Molenaar Book 1995 Springer-Verlag New York, Inc. 1995 Item response theory.La

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Derivations of the Rasch Modelrk, unique properties of the RM. In the latter case, we would have to conclude that the RM plays a rather singular role within IRT. As we shall see, this is actually so. The derivations in this chapter lay a foundation both for the RM and for the metric scale properties of Rasch measurement.

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Linear Logistic Models for Changewith the unidimensionality requirement of the RM. The present chapter discusses properties of these models of change, gives estimation equations, uniqueness results, and hypothesis tests, and mentions typical applications.

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Dynamic Generalizations of the Rasch Modelscussed in the literature. The second class comprises two parts: models which violate the assumption of local stochastic independence, and models which do not. This latter class is shown to be a generalization of mathematical learning models which were popular in the fifties and sixties.

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Linear and Repeated Measures Models for the Person Parametersas a repeated measures example, does fear decrease after behavior therapy? The present chapter presents linear and repeated measures models for the person parameter, that can be used to investigate these kind of hypotheses.

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Mixture Distribution Rasch Models and introducing class-specific score probabilities as model parameters. The model can be used to test the fit of the ordinary Rasch model. By means of an example it is illustrated that this goodness-of-fit test can be more powerful for detecting model violations than the conditional likelihood ratio test by Andersen.

CORE

The One Parameter Logistic Modelnce the discrimination indices are not estimated, but imputed by hypothesis, it is important to test the adequacy of their values. Two i tem-oriented tests which are especially powerful against misspecification of the discrimination indices are discussed in detail. An example is added.