delineate function

Delineate a Knowledge Structure by a Skill Function

Computes the knowledge structure delineated by a skill function.

delineate(skillfun, itemID = 1)

Arguments

• skillfun: a data frame or a matrix representing the skill function. It consists of an item indicator and a problem-by-skill indicator matrix.
• itemID: index of the column in skillfun that holds the item indicator.

Details

The skill function $(Q, S, \mu)$ indicates for each item in $Q$

which subsets of skills in $S$ are required to solve the item. Thus, $\mu(q)$ is a set containing sets of skills. An item may have multiple entries in skillfun, each in a separate row identified by the same itemID.

See Doignon and Falmagne (1999, Chap. 4).

Returns

A list of two components: - K: the knowledge structure delineated by the skill function.

• classes: a list of equivalence classes of competence states; the members of these classes are mapped onto the same knowledge state by the problem function induced by the skill function $\mu$.

References

Doignon, J.-P., & Falmagne, J.-C. (1999). Knowledge spaces. Berlin: Springer.

See Also

blim.

Examples

# Skill function
# mu(e) = {{s, t}, {s, u}},  mu(f) = {{u}}
# mu(g) = {{s}, {t}},        mu(h) = {{t}}
sf <- read.table(header = TRUE, text = "
  item s t u
     e 1 1 0
     e 1 0 1
     f 0 0 1
     g 1 0 0
     g 0 1 0
     h 0 1 0
")
delineate(sf)

## See ?probability for further examples.