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Optimal Designs for the Rasch Model

Published online by Cambridge University Press:  01 January 2025

Ulrike Grasshoff ,
Heinz Holling  and
Rainer Schwabe
Ulrike Grasshoff
Affiliation:
Otto-von-Guericke University Magdeburg
Heinz Holling*
Affiliation:
University of Münster
Rainer Schwabe
Affiliation:
Otto-von-Guericke University Magdeburg
*
Requests for reprints should be sent to Heinz Holling, Institute of Psychology, University of Münster, Fliednerstr. 21, 48149 Münster, Germany. E-mail: holling@psy.uni-muenster.de
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Abstract

In this paper, optimal designs will be derived for estimating the ability parameters of the Rasch model when difficulty parameters are known. It is well established that a design is locally D-optimal if the ability and difficulty coincide. But locally optimal designs require that the ability parameters to be estimated are known. To attenuate this very restrictive assumption, prior knowledge on the ability parameter may be incorporated within a Bayesian approach. Several symmetric weight distributions, e.g., uniform, normal and logistic distributions, will be considered. Furthermore, maximin efficient designs are developed where the minimal efficiency is maximized over a specified range of ability parameters.

Keywords

optimal designBayesian designmaximin efficient designitem response theoryRasch model

Information

Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 4 , October 2012 , pp. 710 - 723
Copyright
Copyright © 2012 The Psychometric Society

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