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Optimal Designs For The Rasch Model

by Graßhoff, U.; Holling, H.; Schwabe, R..

Series: 2010-22, Preprints

62K05 Optimal designs
62P15 Applications to psychology
62J12 Generalized linear models

When calibrating a test, optimal design provides means for an efficient procedure. In this paper, optimal designs will be derived for estimating the difficulty parameters of the Rasch model, when abilities are assumed to be 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 difficulties to be estimated are known. To attenuate this very restrictive assumption, prior knowledge on the difficulty may be incorporated within a Bayesian approach. Several symmetric weight istributions, 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 difficulties.

optimal design, Bayesian design, maximin efficient design, item response theory, Rasch model