Probabilistic Knowledge Space and Item Response Theories: Towards a Unified Test Theory


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Current psychological test theory has its origin in the GUTTMAN-model, developed more than 50 years ago. This model allows the linear ranking of persons (regarding their abilities) and test items (regarding their difficulties). Since then, test theory parted into two different directions. On the one hand, based on the RASCH-model and generalized by MOKKEN’s monotone homogeneity model, a family of linear-scale probabilistic models (Item-Response-Theories) arose, on the other hand, starting with AIRASIAN, BART, and KRUS, a family of non-linear deterministic models (Knowledge Space Theory) has been developed. Although there exist scattered approaches to create specific probabilistic non-linear deterministic models, respectively, to create “de-linearized” (linear-scale) probabilistic models, those activities did not arise from the idea of conflating the splitted directions of psychological test theories.
Thus, the explicit aim of the current project is the fusion of mentioned splitted directions of theories in order to develop a superior probabilistic test theory that includes the existing models as special cases. The related work is basically of psychological-mathematical nature. In addition, this theoretical work must be accompanied by the development of related software that supports the theoretical model evolution and that enables the application to practical requirements. Software development, therefore, will be based on current technologies and the integration of existing software components.
There is a tremendous practical impact of a comprehensive test theory in addition with the related software products: It allows (a) an exact acquisition of personal profiles and item difficulties even in highly complex structures and noisy datasets. Additional, despite the mentioned conditions, it allows (b) an adaptive testing and gathering a person’s exact knowledge and capability profile with comparably low effort. This is important, for example, for a further stage of intercultural knowledge profiling, e.g. by the International Mathematics and Science Studies, that recently attained wide popularity with the results of the last PISA study. Exact measures of knowledge and capability, furthermore, are from importance for (c) personalized interventions, e.g. individual training. Modeled and empirically validated complex structures of knowledge and capability may also be used to optimize (d) the internal structure of single courses up to (e) complete curricula.

Publications: List of publications (pdf)

Media: Proposal (pdf, restricted access)


  • Dietrich Albert
  • Michael D. Kickmeier-Rust
  • Ali Ünlü

Graz Partner: Department of Psychology, University of Graz, Austria/Europe

Duration: 01.05.2004 – 31.10.2006 (30 months)

Funding: This project is granted by the Austrian Science Fund (FWF). Grant No.: P17071-N04

  • Total Budget: € 96,656.18
  • Total Funding: € 96,656.18
  • CSS Budget: € 96,656.18