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Optimal Designs for the Rasch Model

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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. Copyright The Psychometric Society 2012

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  • Ulrike Graßhoff & Heinz Holling & Rainer Schwabe, 2012. "Optimal Designs for the Rasch Model," Psychometrika, Springer;The Psychometric Society, vol. 77(4), pages 710-723, October.
    • Handle: RePEc:spr:psycho:v:77:y:2012:i:4:p:710-723
    DOI: 10.1007/s11336-012-9276-2
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    1. Ulrike Graßhoff & Rainer Schwabe, 2008. "Optimal design for the Bradley–Terry paired comparison model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(3), pages 275-289, July.
    2. Martijn Berger & C. Joy King & Weng Wong, 2000. "Minimax d-optimal designs for item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 377-390, September.
    3. Holger Dette, 1997. "Designing Experiments with Respect to ‘Standardized’ Optimality Criteria," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(1), pages 97-110.
    4. D. Firth & J. P. Hinde, 1997. "On Bayesian D‐optimum Design Criteria and the Equivalence Theorem in Non‐linear Models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 793-797.
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