pks (version 0.4-1)

gradedness: Forward- or Backward-Gradedness of a Knowledge Structure

Description

Checks if a knowledge structure is forward- or backward-graded in any item.

Usage

is.forward.graded(K)
is.backward.graded(K)

Arguments

K

a state-by-problem indicator matrix representing the knowledge structure. An element is one if the problem is contained in the state, and else zero. K should have non-empty colnames.

Value

A named logical vector with as many elements as columns in K.

Details

A knowledge structure \(K\) is forward-graded in item \(q\), if \(S \cup \{q\}\) is in \(K\) for every state \(S \in K\).

A knowledge structure \(K\) is backward-graded in item \(q\), if \(S - \{q\}\) is in \(K\) for every state \(S \in K\).

See Spoto, Stefanutti, and Vidotto (2012).

References

Spoto, A., Stefanutti, L., & Vidotto, G. (2012). On the unidentifiability of a certain class of skill multi map based probabilistic knowledge structures. Journal of Mathematical Psychology, 56, 248--255. 10.1016/j.jmp.2012.05.001

See Also

blim, jacobian.

Examples

# NOT RUN {
K <- as.binmat(c("0000", "1000", "1100", "1010", "0110", "1110", "1111"))
is.forward.graded(K)   # forward-graded in a
is.backward.graded(K)  # not backward-graded in a
# }