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Checking the Assumptions of Rasch's Model for Speed Tests

Published online by Cambridge University Press:  01 January 2025

M. G. H. Jansen  and
C. A. W. Glas
M. G. H. Jansen*
Affiliation:
University of Groningen
C. A. W. Glas
Affiliation:
University of Twente
*
Requests for reprints should be sent to Margo Jansen, Department of Education, University of Groningen, Grote Rozenstraat 38, 9712 TJ Groningen, The Netherlands. E-Mail: g.g.h.jansen@ppsw.rug.nl
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Abstract

Two new tests for a model for the response times on pure speed tests by Rasch (1960) are proposed. The model is based on the assumption that the test response times are approximately gamma distributed, with known index parameters and unknown rate parameters. The rate parameters are decomposed in a subject ability parameter and a test difficulty parameter. By treating the ability as a gamma distributed random variable, maximum marginal likelihood (MML) estimators for the test difficulty parameters and the parameters of the ability distribution are easily derived. Also the model tests proposed here pertain to the framework of MML. Two tests or modification indices are proposed. The first one is focused on the assumption of local stochastic independence, the second one on the assumption of the test characteristic functions. The tests are based on Lagrange multiplier statistics, and can therefore be computed using the parameter estimates under the null model. Therefore, model violations for all items and pairs of items can be assessed as a by-product of one single estimation run. Power studies and applications to real data are included as numerical examples.

Keywords

speed testRasch modelLagrange multiplier testlocal stochastic independencemodel fitscore testtest characteristic curve
Type
Theory and Methods
Information
Psychometrika , Volume 70 , Issue 4 , December 2005 , pp. 671 - 684
Copyright
Copyright © 2005 The Psychometric Society

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