## 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.

## Key words

optimal design Bayesian design maximin efficient design item response theory Rasch model## Notes

### Acknowledgements

This research was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HO 1286/6-1. The authors would like to thank Norbert Gaffke for helpful discussions.

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