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Some Neglected Problems in IRT

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 Gerhard H. Fischer, Institut für Psychologie, Universität Wien, Liebiggasse 5, A-1010 Wien, AUSTRIA.
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Abstract

The paper addresses three neglected questions from IRT. In section 1, the properties of the “measurement” of ability or trait parameters and item difficulty parameters in the Rasch model are discussed. It is shown that the solution to this problem is rather complex and depends both on general assumptions about properties of the item response functions and on assumptions about the available item universe. Section 2 deals with the measurement of individual change or “modifiability” based on a Rasch test. A conditional likelihood approach is presented that yields (a) an ML estimator of modifiability for given item parameters, (b) allows one to test hypotheses about change by means of a Clopper-Pearson confidence interval for the modifiability parameter, or (c) to estimate modifiability jointly with the item parameters. Uniqueness results for all three methods are also presented. In section 3, the Mantel-Haenszel method for detecting DIF is discussed under a novel perspective: What is the most general framework within which the Mantel-Haenszel method correctly detects DIF of a studied item? The answer is that this is a 2PL model where, however, all discrimination parameters are known and the studied item has the same discrimination in both populations. Since these requirements would hardly be satisfied in practical applications, the case of constant discrimination parameters, that is, the Rasch model, is the only realistic framework. A simple Pearson x2 test for DIF of one studied item is proposed as an alternative to the Mantel-Haenszel test; moreover, this test is generalized to the case of two items simultaneously studied for DIF.

Keywords

measurementIRTRasch modelmeasurement of changeDIFMantel-Haenszel statistic
Type
Original Paper
Information
Psychometrika , Volume 60 , Issue 4 , December 1995 , pp. 459 - 487
Copyright
Copyright © 1995 The Psychometric Society

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Footnotes

Presidential Address delivered at the 30th Annual Meeting of the Psychometric Society, 16–18 June 1995 in Minneapolis.

This research was supported in part by the Fonds zur Förderung der Wissenschaftlichen Forschung under Grant No. P10118-HIS.

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