corr_iita: Corrected Inductive Item Tree Analysis
In DAKS: Data Analysis and Knowledge Spaces

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

corr_iita performs the corrected inductive item tree analysis procedure and returns the corresponding diff values.

1	corr_iita(dataset, A)

`dataset`	a required data frame or matrix consisting of binary, 1 or 0, numeric data.
`A`	a required list of competing quasi orders (surmise relations), for instance obtained from a call to `ind_gen`.

Corrected inductive item tree analysis is a data analysis method for deriving knowledge structures (more precisely, surmise relations) from binary data. Details on this procedure can be found in iita. The set of competing quasi orders is passed via the argument A, so any selection set of quasi orders can be used.

The set of competing quasi orders must be 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.'

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

If the arguments dataset and A are of required types, corr_iita returns a named list of the following components:

`diff.value`	a vector of the diff values corresponding to the competing quasi orders in `A`.
`error.rate`	a vector of the error rates corresponding to the competing quasi orders in `A`.

The function iita can be used to perform one of the three inductive item tree analysis procedures (including the corrected inductive item tree analysis method) selectively. Whereas for the function corr_iita a selection set of competing quasi orders has to be passed via the argument A manually, iita automatically generates a selection set from the data using the inductive generation procedure implemented in ind_gen.

The latter approach using iita is common so far, in knowledge space theory, where the inductive data analysis methods have been utilized for exploratory derivations of surmise relations from data. The function corr_iita, on the other hand, can be used to select among surmise relations for instance obtained from querying experts or from competing psychological theories.

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/.

orig_iita for original inductive item tree analysis; mini_iita for minimized corrected inductive item tree analysis; iita, the interface that provides the three inductive item tree analysis methods under one umbrella; pop_variance for population asymptotic variances of diff coefficients; variance for estimated asymptotic variances of diff coefficients; pop_iita for population inductive item tree analysis. See also DAKS-package for general information about this package.