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An Irt-Based Model for Dichotomous Longitudinal Data

Published online by Cambridge University Press:  01 January 2025

Gerhard H. Fischer
Gerhard H. Fischer*
Affiliation:
University of Vienna
*
Requests for reprints should be sent to G. H. Fischer, Institut für Psychologic, Universitfit Wien, Liebiggasse 5, A-1010 Vienna, AUSTRIA
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Abstract

The LLRA (linear logistic model with relaxed assumptions; Fischer, 1974, 1977a, 1977b, 1983a) was developed, within the framework of generalized Rasch models, for assessing change in dichotomous item score matrices between two points in time; it allows to quantify change on latent trait dimensions and to explain change in terms of treatment effects, treatment interactions, and a trend effect. A remarkable feature of the model is that unidimensionality of the item set is not required. The present paper extends this model to designs with any number of time points and even with different sets of items presented on different occasions, provided that one unidimensional subscale is available per latent trait. Thus unidimensionality assumptions within subscales are combined with multidimensionality of the item set. Conditional maximum likelihood methods for parameter estimation and hypothesis testing are developed, and a necessary and sufficient condition for unique identification of the model, given the data, is derived. Finally, a sample application is presented.

Keywords

Rasch modelslogistic modelsmeasurement of change
Type
Original Paper
Information
Psychometrika , Volume 54 , Issue 4 , December 1989 , pp. 599 - 624
Copyright
Copyright © 1989 The Psychometric Society

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Footnotes

To my friend Josef Roppert who has taught me how to apply statistical reasoning to substantive problems.

This research was supported in part by Österreichische Forschungsgemeinschaft under grant No. 01/0054. The author wishes to thank B. Wild for the numerical computation of the sample application in section 5.

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