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

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References

Atkinson, A.C., Donev, A.N., & Tobias, R.D. (2007). Optimum experimental designs, with SAS. Oxford: Oxford University Press.CrossRefGoogle Scholar
Berger, M.P.F., King, C.Y.J., & Wong, W.K. (2000). Minimax D-optimal designs for item response theory models. Psychometrika, 65, 377–390.CrossRefGoogle Scholar
Berger, M.P.F., & Wong, W.K. (2009). An introduction to optimal designs for social and biomedical research. Chichester: Wiley.CrossRefGoogle Scholar
Braess, D., & Dette, H. (2007). On the number of support points of maximin and Bayesian optimal designs. Annals of Statistics, 35, 772–792.CrossRefGoogle Scholar
Buyske, S. (2005). Optimal design in educational testing. In Berger, M.P.F., & Wong, W.K. (Eds.), Applied optimal designs (pp. 1–19). New York: Wiley.Google Scholar
Chaloner, K. (1993). A note on optimal Bayesian design for nonlinear problems. Journal of Statistical Planning and Inference, 37, 229–235.CrossRefGoogle Scholar
Chaloner, K., & Larntz, K. (1989). Optimal Bayesian design applied to logistic regression experiments. Journal of Statistical Planning and Inference, 21, 191–208.CrossRefGoogle Scholar
Dette, H. (1997). Designing experiments with respect to ‘standardized’ optimality criteria. Journal of the Royal Statistical Society. Series B, 59, 97–110.CrossRefGoogle Scholar
Dette, H., & Neugebauer, H.-M. (1996). Bayesian optimal one point designs for one parameter nonlinear models. Journal of Statistical Planning and Inference, 52, 17–31.CrossRefGoogle Scholar
Firth, D., & Hinde, J.P. (1997). On Bayesian D-optimum design criteria and the equivalence theorem in non-linear models. Journal of the Royal Statistical Society. Series B, 59, 793–797.CrossRefGoogle Scholar
Graßhoff, U., & Schwabe, R. (2008). Optimal design for the Bradley–Terry paired comparison model. Statistical Methods and Applications, 17, 275–289.CrossRefGoogle Scholar
Kiefer, J. (1974). General equivalence theory for optimum designs (approximate theory). Annals of Statistics, 2, 849–879.CrossRefGoogle Scholar
van der Linden, W.J. (2005). Linear models for optimal test design. New York: Springer.CrossRefGoogle Scholar
van der Linden, W.J., & Pashley, P.J. (2010). Item selection and ability estimation adaptive testing. In van der Linden, W.J., & Glas, C.A.W. (Eds.), Elements of adaptive testing (pp. 3–30). New York: Springer.CrossRefGoogle Scholar