gradedness | R Documentation |
Checks if a knowledge structure is
forward- or backward-graded in any item;
downgradable.
is.forward.graded(K)
is.backward.graded(K)
is.downgradable(K)
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. |
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).
A knowledge structure K
is downgradable, if its inner fringe is empty
only for a single state (the empty set). See Doignon and Falmagne (2015).
For forward- and backward-gradedness, a named logical vector with as many
elements as columns in K
.
For downgradability, a single logical value.
Doignon, J.-P., & Falmagne, J.-C. (2015). Knowledge spaces and learning spaces. arXiv. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.48550/arXiv.1511.06757")}
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(4), 248–255. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/j.jmp.2012.05.001")}
blim
, jacobian
, getKFringe
.
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
is.downgradable(K) # not downgradable
all(K[, "a"] | getKFringe(K)[, "a"]) # every K or outer fringe contains a
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