skillspace.hierarchy.RdThe function skillspace.hierarchy defines a reduced skill space
for hierarchies in skills (see e.g. Leighton, Gierl, & Hunka, 2004).
The function skillspace.full defines a full skill space
for dichotomous skills.
skillspace.hierarchy(B, skill.names) skillspace.full(skill.names)
| B | A matrix or a string containing restrictions of the hierarchy.
If Alternatively, a string can be also conveniently used for defining a hierarchy (see Examples). |
|---|---|
| skill.names | Vector of names in skills |
The reduced skill space output can be used as an argument in din
or gdina to directly test for a hierarchy in attributes.
A list with following entries
Reachability matrix
Reduced skill space fulfilling the specified hierarchy
Complete skill space
Indices of skill patterns in
skillspace.complete which were removed for defining
skillspace.reduced
Leighton, J. P., Gierl, M. J., & Hunka, S. M. (2004). The attribute hierarchy method for cognitive assessment: A variation on Tatsuoka's rule space approach. Journal of Educational Measurement, 41, 205-237.
See din (Example 6) for an application of
skillspace.hierarchy for model comparisons.
See the GDINA::att.structure function in the
GDINA package for similar functionality.
############################################################################# # EXAMPLE 1: Toy example with 3 skills ############################################################################# K <- 3 # number of skills skill.names <- paste0("A", 1:K ) # names of skills # create a zero matrix for hierarchy definition B0 <- 0*diag(K) rownames(B0) <- colnames(B0) <- skill.names #*** Model 1: A1 > A2 > A3 B <- B0 B[1,2] <- 1 # A1 > A2 B[2,3] <- 1 # A2 > A3 sp1 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp1$skillspace.reduced ## A1 A2 A3 ## 1 0 0 0 ## 2 1 0 0 ## 4 1 1 0 ## 8 1 1 1 #*** Model 2: A1 > A2 and A1 > A3 B <- B0 B[1,2] <- 1 # A1 > A2 B[1,3] <- 1 # A1 > A3 sp2 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp2$skillspace.reduced ## A1 A2 A3 ## 1 0 0 0 ## 2 1 0 0 ## 4 1 1 0 ## 6 1 0 1 ## 8 1 1 1 #*** Model 3: A1 > A3, A2 is not included in a hierarchical way B <- B0 B[1,3] <- 1 # A1 > A3 sp3 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp3$skillspace.reduced ## A1 A2 A3 ## 1 0 0 0 ## 2 1 0 0 ## 3 0 1 0 ## 4 1 1 0 ## 6 1 0 1 ## 8 1 1 1 #~~~ Hierarchy specification using strings #*** Model 1: A1 > A2 > A3 B <- "A1 > A2 A2 > A3" sp1 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp1$skillspace.reduced # Model 1 can be also written in one line for B B <- "A1 > A2 > A3" sp1b <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp1b$skillspace.reduced #*** Model 2: A1 > A2 and A1 > A3 B <- "A1 > A2 A1 > A3" sp2 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp2$skillspace.reduced #*** Model 3: A1 > A3 B <- "A1 > A3" sp3 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp3$skillspace.reduced if (FALSE) { ############################################################################# # EXAMPLE 2: Examples from Leighton et al. (2004): Fig. 1 (p. 210) ############################################################################# skill.names <- paste0("A",1:6) # 6 skills #*** Model 1: Linear hierarchy (A) B <- "A1 > A2 > A3 > A4 > A5 > A6" sp1 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp1$skillspace.reduced #*** Model 2: Convergent hierarchy (B) B <- "A1 > A2 > A3 A2 > A4 A3 > A5 > A6 A4 > A5 > A6" sp2 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp2$skillspace.reduced #*** Model 3: Divergent hierarchy (C) B <- "A1 > A2 > A3 A1 > A4 > A5 A1 > A4 > A6" sp3 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp3$skillspace.reduced #*** Model 4: Unstructured hierarchy (D) B <- "A1 > A2 \n A1 > A3 \n A1 > A4 \n A1 > A5 \n A1 > A6" # This specification of B is equivalent to writing separate lines: # B <- "A1 > A2 # A1 > A3 # A1 > A4 # A1 > A5 # A1 > A6" sp4 <- CDM::skillspace.hierarchy( B=B, skill.names=skill.names ) sp4$skillspace.reduced }