ob_counter: Computation of Numbers of Counterexamples

Description Usage Arguments Details Value Note Author(s) References See Also Examples


ob_counter computes from a dataset for all item pairs the corresponding numbers of counterexamples.





a required data frame or matrix consisting of binary, 1 or 0, numeric data.


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.'

The data must contain only ones and zeros, which encode solving or failing to solve an item, respectively.


If the argument dataset is of required type, ob_counter returns a matrix of the numbers of counterexamples for all pairs of items.


The function ind_gen can be used to inductively generate from the returned matrix of the numbers of counterexamples a set of quasi orders.

The function iita calls ob_counter.


Anatol Sargin, Ali Uenlue


Sargin, A. and Uenlue, A. (2009) Inductive item tree analysis: Corrections, improvements, and comparisons. Mathematical Social Sciences, 58, 376–392.

Uenlue, 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. URL http://www.jstatsoft.org/v37/i02/.

See Also

ind_gen for inductive generation procedure using numbers of counterexamples; iita, the interface that provides the three inductive item tree analysis methods under one umbrella. See also DAKS-package for general information about this package.



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