10-22
Optimal Designs For The Rasch Model
by Graßhoff, U.; Holling, H.; Schwabe, R.
Preprint series: 10-22, Preprints
- MSC:
- 62K05 Optimal designs
- 62P15 Applications to psychology
- 62J12 Generalized linear models
Abstract: 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.
Keywords: optimal design, Bayesian design, maximin efficient design, item response theory, Rasch model
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