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Optimal Design for the Rasch Poisson-Gamma Model

  • Ulrike Graßhoff
  • Heinz HollingEmail author
  • Rainer Schwabe
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Many tests, measuring human intelligence, yield count data. Often, these data can be analyzed by the Rasch Poisson counts model which incorporates parameters representing the ability of the respondents and the difficulty of the items. In a generalized version, the so-called Rasch Poisson-Gamma counts model, the ability parameter is specified as random with an underlying Gamma distribution. We will develop locally D-optimal calibration designs for an extended version of this model which includes two binary covariates in order to explain the difficulty of an item.

Notes

Acknowledgements

This work was supported by grant Ho1286-6 of the Deutsche Forschungsgemeinschaft.

References

  1. 1.
    Doebler, A., Holling, H.: A processing speed test based on rule-based item generation: an analysis with the Rasch Poisson Counts model. Learn. Individ. Differ. (2015, in press)Google Scholar
  2. 2.
    Graßhoff, U., Holling, H., Schwabe, R.: Optimal design for count data with binary predictors in item response theory. In: Uciński, D., Atkinson, A.C., Patan, M. (eds.) mODa10 -Advances in Model-Oriented Design and Analysis, pp. 117–124. Springer, Cham (2013)CrossRefGoogle Scholar
  3. 3.
    Rasch, G.: Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research, Copenhagen (1960)Google Scholar
  4. 4.
    Verhelst, N.D., Kamphuis, F.H.: A Poisson-Gamma model for speed tests. Measurement and Research Department Reports, 2009–2. Cito, Arnhem (2009)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Ulrike Graßhoff
    • 1
  • Heinz Holling
    • 2
    Email author
  • Rainer Schwabe
    • 3
  1. 1.School of Business and EconomicsHumboldt UniversityBerlinGermany
  2. 2.Institute of PsychologyUniversity of MünsterMünsterGermany
  3. 3.Institute for Mathematical StochasticsOtto-von-Guericke UniversityMagdeburgGermany

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