ita: Item Tree Analysis (ITA)

In pks: Probabilistic Knowledge Structures

Item Tree Analysis (ITA)

Description

Performs an item tree analysis (ITA) on a set of binary responses.

Usage

ita(R, L = NULL, makeK = FALSE)

Arguments

R	a subject-by-problem indicator matrix representing the responses.
L	the threshold of violations acceptable for the precedence relation. If NULL (default), an optimal threshold is searched for.
makeK	should the corresponding knowledge structure be returned?

Details

ITA seeks to establish a precedence relation among a set of binary items. For each pair of items (p, q), it counts how often p is not solved if q is solved, which constitutes a violation of the relation. ITA searches for a threshold L for the maximum number of violations consistent with a (transitive) precedence relation.

See van Leeuwe (1974) and Schrepp (1999) for details.

Value

An object of class ita having the following components:

K	the knowledge structure corresponding to the precedence relation.
discrepancy	the discrepancy between R and K (fit), between K and R (complexity), and their sum (total).
transitiveL	the vector of transitive thresholds.
searchL	has the threshold value been optimized?
L	the selected or requested threshold.
P	the precedence matrix containing the number of violations.

References

Schrepp, M. (1999). On the empirical construction of implications between bi-valued test items. Mathematical Social Sciences, 38(3), 361–375. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0165-4896(99)00025-6")}

Van Leeuwe, J.F. (1974). Item tree analysis. Nederlands Tijdschrift voor de Psychologie en haar Grensgebieden, 29(6), 475–483.

See Also

blim.

Examples

data(chess)

ita(chess$R)  # find optimal threshold L

i <- ita(chess$R, L = 6, makeK = TRUE)
identical(sort(as.pattern(i$K)),
          sort(as.pattern(chess$dst1)))

pks documentation built on May 5, 2023, 3:08 p.m.