ind_gen: Inductive Generation Procedure

In DAKS: Data Analysis and Knowledge Spaces

Description

ind_gen generates inductively a set of competing quasi orders.

Usage

ind_gen(b)

Arguments

b	a required matrix of the numbers of counterexamples for all pairs of items, for instance obtained from a call to ob_counter.

Value

If the argument b is of required type, ind_gen returns a list of the inductively generated quasi orders.

Note

The function iita calls ind_gen for constructing the set of competing quasi orders according to the inductive generation procedure.

The set of competing quasi orders is a list of objects of the class set. These objects (quasi orders) consist 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, Ali Uenlue

References

Sargin, A. and Uenlue, 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.

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

ob_counter for computation of numbers of counterexamples; iita, the interface that provides the three inductive item tree analysis methods under one umbrella; z_test for one- and two-sample Z-tests. See also DAKS-package for general information about this package.

Examples

ob <- ob_counter(pisa)
ind_gen(ob)

Example output

Loading required package: relations
Loading required package: sets
[[1]]
{(1L, 5L)}

[[2]]
{(1L, 4L), (1L, 5L)}

[[3]]
{(1L, 4L), (1L, 5L), (2L, 5L)}

[[4]]
{(1L, 4L), (1L, 5L), (2L, 4L), (2L, 5L)}

[[5]]
{(1L, 4L), (1L, 5L), (2L, 4L), (2L, 5L), (3L, 5L)}

[[6]]
{(1L, 3L), (1L, 4L), (1L, 5L), (2L, 4L), (2L, 5L), (3L, 5L)}

[[7]]
{(1L, 3L), (1L, 4L), (1L, 5L), (2L, 4L), (2L, 5L), (3L, 4L), (3L, 5L)}

[[8]]
{(1L, 3L), (1L, 4L), (1L, 5L), (2L, 3L), (2L, 4L), (2L, 5L), (3L, 4L),
 (3L, 5L)}

[[9]]
{(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 3L), (2L, 4L), (2L, 5L),
 (3L, 4L), (3L, 5L)}

[[10]]
{(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 3L), (2L, 4L), (2L, 5L),
 (3L, 4L), (3L, 5L), (4L, 5L)}

[[11]]
{(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 1L), (2L, 3L), (2L, 4L),
 (2L, 5L), (3L, 4L), (3L, 5L), (4L, 5L), (5L, 4L)}

[[12]]
{(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 1L), (2L, 3L), (2L, 4L),
 (2L, 5L), (3L, 4L), (3L, 5L), (4L, 3L), (4L, 5L), (5L, 3L), (5L, 4L)}

[[13]]
{(1L, 2L), (1L, 3L), (1L, 4L), (1L, 5L), (2L, 1L), (2L, 3L), (2L, 4L),
 (2L, 5L), (3L, 1L), (3L, 2L), (3L, 4L), (3L, 5L), (4L, 1L), (4L, 2L),
 (4L, 3L), (4L, 5L), (5L, 1L), (5L, 2L), (5L, 3L), (5L, 4L)}

DAKS documentation built on May 2, 2019, 6:43 a.m.