imp2state {DAKS}R Documentation

Transformation from Implications to Knowledge States

Description

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

Usage

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.

Value

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.

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.'

Author(s)

Anatol Sargin anatol.sargin@math.uni-augsburg.de, Ali Uenlue ali.uenlue@math.uni-augsburg.de

References

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

Sargin, A. and Uenlue, A. (2009) DAKS: An R package for data analysis in knowledge space theory. Manuscript submitted for publication. http://www.math.uni-augsburg.de/~uenlueal/

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))

[Package DAKS version 2.0-0 Index]