Basic Local Independence Model (BLIM)
Basic Local Independence Model (BLIM)
About the Theory
In Knowledge Space Theory, a knowledge structure 𝒦 is any family of subsets of a set Q of items (or test problems) which contains the empty set {} and the full item set Q. Such a knowledge structure can be used together with the BLIM model to simulate response patterns.The Basic Local Independence Model (BLIM)
Assumption Given the knowledge state K of a person, the responses are stochastically independent over problems and the response to each problem q∈Q only depends on the probabilities βq of a careless error and ηq of a lucky guess for item q. In this app, we simplify the BLIM a bit further by assuming identical β and η values for all items.Example Spaces
As example data, knowledge spaces provided by the R package pks (Heller & Wickelmaier, 2013; Wickelmaier et al., 2016) are used. Concretely, the following spaces are used:- Density
- Taagepera et al. (1997) applied knowledge space theory to specific science problems. The density test was administered to 2060 students, a sub structure of five items is included here.
- Matter
- Taagepera et al. (1997) applied knowledge space theory to specific science problems. The conservation of matter test was administered to 1620 students, a sub structure of five items is included here.
- Doignon & Falmagne
- Fictitious data set from Doignon and Falmagne (1999, chap. 7).
References
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer. Heller, J. & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures. Electronic Notes in Discrete Mathematics, 42, 49-56. Schrepp, M., Held, T., & Albert, D. (1999). Component-based construction of surmise relations for chess problems. In D. Albert & J. Lukas (Eds.), Knowledge spaces: Theories, empirical research, and applications (pp. 41--66). Mahwah, NJ: Erlbaum. Taagepera, M., Potter, F., Miller, G.E., & Lakshminarayan, K. (1997). Mapping students' thinking patterns by the use of knowledge space theory. International Journal of Science Education, 19, 283--302. Wickelmaier, F., Heller, J., & Anselmi, P. (2016). pks: Probabilistic Knowledge Structures. R package version 0.4-0. https://CRAN.R-project.org/package=kstAbout this App
This App was created within the TquanT project.TquanT was co-funded by the Erasmus+ Programme of the European Commission.
© 2018 Christoph Anzengruber & Cord Hockemeyer, University of Graz, Austria