imp2state function

Transformation from Implications to Knowledge States

imp2state transforms a set of implications (ought to be a surmise relation) to the corresponding set of knowledge states (the quasi ordinal knowledge space).

imp2state(imp, items)

Arguments

• imp: a required object of class set

  representing the set of implications, for instance obtained from a call to iita.

• items: a required numeric giving the number of items of the domain taken as basis for imp.

Returns

If the arguments imp and items are of required types, imp2state returns a matrix consisting of ones or zeros (the quasi ordinal knowledge space), in which each row represents the $1$/$0$-pattern of a knowledge state.

References

Doignon, J.-P. and Falmagne, J.-C. (1999) Knowledge Spaces. Berlin, Heidelberg, and New York: Springer-Verlag.

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

For any set of implications the returned knowledge structure is a quasi ordinal knowledge space. In case of a surmise relation this is Birkhoff's theorem. For details refer to Doignon and Falmagne (1999, Theorem 1.49) .

A set of implications, an object of the class set, consists of $2$-tuples $(i, j)$ of the class tuple, where a $2$-tuple $(i, j)$ is interpreted as `mastering item $j$ implies mastering item $i$.'

See Also

state2imp for transformation from knowledge states to implications. See also DAKS-package for general information about this package.

Examples

x <- iita(pisa, v = 1)
imp2state(x$implications, ncol(pisa))