ob_counter function

Computation of Numbers of Counterexamples

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

ob_counter(dataset)

Arguments

• dataset: a required data frame or matrix consisting of binary, $1$ or $0$, numeric data.

Details

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.

Returns

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

References

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 package for data analysis methods in knowledge space theory. Journal of Statistical Software, 37 (2), 1--31. URL http://www.jstatsoft.org/v37/i02/.

Author(s)

Anatol Sargin, Ali Uenlue

Note

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.

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.

Examples

ob_counter(pisa)