Optimal Design for the Rasch Poisson-Gamma Model
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.
This work was supported by grant Ho1286-6 of the Deutsche Forschungsgemeinschaft.
- 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
- 3.Rasch, G.: Probabilistic Models for Some Intelligence and Attainment Tests. Danish Institute for Educational Research, Copenhagen (1960)Google Scholar
- 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