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Applying the Principles of Specific Objectivity and of Generalizability to the Measurement of Change

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 Psychologie, Universität Wien, Liebiggasse 5, A-1010 Vienna, AUSTRIA.
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Abstract

A formal framework for measuring change in sets of dichotomous data is developed and implications of the principle of specific objectivity of results within this framework are investigated. Building upon the concept of specific objectivity as introduced by G. Rasch, three equivalent formal definitions of that postulate are given, and it is shown that they lead to latent additivity of the parametric structure. If, in addition, the observations are assumed to be locally independent realizations of Bernoulli variables, a family of models follows necessarily which are isomorphic to a logistic model with additive parameters, determining an interval scale for latent trait measurement and a ratio scale for quantifying change. Adding the further assumption of generalizability over subsets of items from a given universe yields a logistic model which allows a multidimensional description of individual differences and a quantitative assessment of treatment effects; as a special case, a unidimensional parameterization is introduced also and a unidimensional latent trait model for change is derived. As a side result, the relationship between specific objectivity and additive conjoint measurement is clarified.

Keywords

latent trait theoryitem response theorymeasurement of changelogistic latent trait modelsspecific objectivityconjoint measurementadditivity
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 4 , December 1987 , pp. 565 - 587
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

This research was supported in part by Österreichische Forschungsgemeinschaft under grant No. 01/0054. The author is indebted to A. Kriegl, E. E. Roskam, I. W. Molenaar, J. O. Ramsey, and J. Irtel for valuable critical comments on a previous draft of this paper.

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