About the Theory
Schrepp (1999, 2003) developed IITA (Inductive itemm Tree Analysis) as a means to derive
a surmise relation from dichotomous response patterns. Sargin and Ünlü (2009;
Ünlü & Sargin, 2010) implemented two advanced versions of that procedure.
The three inductive item tree analysis algorithms are exploratory methods for extracting
quasi orders (surmise relations) from data. In each algorithm, competing binary relations
are generated (in the same way for all three versions), and a fit measure (differing from
version to version) is computed for every relation of the selection set in order to find
the quasi order that fits the data best. In all three algorithms, the idea is to estimate
the numbers of counterexamples for each quasi order, and to find, over all competing quasi
orders, the minimum value for the discrepancy between the observed and expected numbers of
counterexamples. The three data analysis methods differ in their choices of estimates for
the expected numbers of counterexamples. (For an item pair (i,j), the number of subjects
solving item j but failing to solve item i, is the corresponding number of counterexamples.
Their response patterns contradict the interpretation of (i,j) as `mastering item j implies
mastering item i.')
- Sargin, A. and Ünlü, A. (2009) Inductive item tree analysis: Corrections, improvements,
and comparisons. Mathematical Social Sciences, 58, 376--392.
- Schrepp, M. (1999) On the empirical construction of implications between bi-valued test
items. Mathematical Social Sciences, 38, 361--375.
- Schrepp, M. (2003) A method for the analysis of hierarchical dependencies between items
of a questionnaire. Methods of Psychological Research, 19, 43--79.
- Ünlü, A. and Sargin, A. (2010) DAKS: An R package for data analysis methods in knowledge space theory.
Journal of Statistical Software, 37(2), 1--31.
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:
- The accompanying binary dataset is part of the empirical 2003 Programme for International
Student Assessment (PISA) data. It contains the item responses by 340 German students on a
5-item dichotomously scored mathematical literacy test. The dataset was obtained after
dichotomizing the original multiple-choice or open format test data. Wording of the test items
used in the assessment is not known (not available publicly).
- 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.
- 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).
- Strict Linear Order
- Fictitious data set describing a linear order 1 ≾ 2 ≾ 3 ≾ 4 ≾ 5 almost
Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces.
Heller, J. & Wickelmaier, F. (2013). Minimum discrepancy estimation in probabilistic knowledge structures.
Electronic Notes in Discrete Mathematics, 42,
OECD Programme for International Student Assessment (PISA)
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,
Wickelmaier, F., Heller, J., & Anselmi, P. (2016). pks: Probabilistic Knowledge Structures.
version 0.4-0. https://CRAN.R-project.org/package=kst
Do not forget to press the "Done" button when you have finished!
Please note that each item must be solved at least once within a non-trivial pattern,
i.e. within a pattern unequal to the full item set Q.
About this App
This App was created within the TquanT
TquanT was co-funded by the Erasmus+ Programme of the European Commission.
© 2018 Christoph Anzengruber & Cord Hockemeyer, University of Graz, Austria