ita function

Item Tree Analysis (ITA)

Item tree analysis (ITA) on a set of binary responses.

ita(R, L = NULL, makeK = FALSE, search = c("local", "global"))

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?
• search: local (default) or global threshold search.

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. Its attempts to minimize the total discrepancy between R and K.

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

Returns

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: either NULL or the method used for threshold search.

• L: the selected or requested threshold.

• P: the precedence matrix containing the number of violations.

• I: the precedence relation as a logical incidence matrix at threshold L.

References

Schrepp, M. (1999). On the empirical construction of implications between bi-valued test items. Mathematical Social Sciences, 38 (3), 361--375. 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 (locally) optimal threshold L

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

## Plotting the precedence relation
if(requireNamespace("relations") &&
   requireNamespace("Rgraphviz")) {
  plot(relations::as.relation(i$I))
}