cdi.kli: Cognitive Diagnostic Indices based on Kullback-Leibler Information

Description

This function computes several cognitive diagnostic indices grounded on the Kullback-Leibler information (Rupp, Henson & Templin, 2009, Ch. 13) at the test, item, attribute and item-attribute level. See Henson and Douglas (2005) and Henson, Roussos, Douglas and He (2008) for more details.

Usage

cdi.kli(object)
# S3 method for cdi.kli
summary(object, digits=2,  ...)

Value

A list with following entries

test_disc: Test discrimination which is the sum of all global item discrimination indices
attr_disc: Attribute discriminations
glob_item_disc: Global item discriminations (Cognitive diagnostic index)
attr_item_disc: Attribute-specific item discrimination
KLI: Array with Kullback-Leibler informations of all items (first dimension) and skill classes (in the second and third dimension)
skillclasses: Matrix containing all used skill classes in the model
hdist: Matrix containing Hamming distance between skill classes
pjk: Used probabilities
q.matrix: Used Q-matrix
summary: Data frame with test- and item-specific discrimination statistics

Arguments

object: Object of class din or gdina. For the summary method, it is the result of cdi.kli.
digits: Number of digits for rounding
...: Further arguments to be passed

References

Henson, R., DiBello, L., & Stout, B. (2018). A generalized approach to defining item discrimination for DCMs. Measurement: Interdisciplinary Research and Perspectives, 16(1), 18-29. http://dx.doi.org/10.1080/15366367.2018.1436855

Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29, 262-277. http://dx.doi.org/10.1177/0146621604272623

Henson, R., Roussos, L., Douglas, J., & He, X. (2008). Cognitive diagnostic attribute-level discrimination indices. Applied Psychological Measurement, 32, 275-288. http://dx.doi.org/10.1177/0146621607302478

Rupp, A. A., Templin, J., & Henson, R. A. (2010). Diagnostic Measurement: Theory, Methods, and Applications. New York: The Guilford Press.

Examples

Run this code

#############################################################################
# EXAMPLE 1: Examples based on CDM::sim.dina
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

mod <- CDM::din( sim.dina, q.matrix=sim.qmatrix )
summary(mod)
  ##  Item parameters
  ##         item guess  slip   IDI rmsea
  ##  Item1 Item1 0.086 0.210 0.704 0.014
  ##  Item2 Item2 0.109 0.239 0.652 0.034
  ##  Item3 Item3 0.129 0.185 0.686 0.028
  ##  Item4 Item4 0.226 0.218 0.556 0.019
  ##  Item5 Item5 0.059 0.000 0.941 0.002
  ##  Item6 Item6 0.248 0.500 0.252 0.036
  ##  Item7 Item7 0.243 0.489 0.268 0.041
  ##  Item8 Item8 0.278 0.125 0.597 0.109
  ##  Item9 Item9 0.317 0.027 0.656 0.065

cmod <- CDM::cdi.kli( mod )

# attribute discrimination indices
round( cmod$attr_disc, 3 )
  ##      V1     V2     V3
  ##   1.966  2.506 11.169

# look at global item discrimination indices
round( cmod$glob_item_disc, 3 )
  ##  > round( cmod$glob_item_disc, 3 )
  ##  Item1 Item2 Item3 Item4 Item5 Item6 Item7 Item8 Item9
  ##  0.594 0.486 0.533 0.465 5.913 0.093 0.040 0.397 0.656

# correlation of IDI and global item discrimination
stats::cor( cmod$glob_item_disc, mod$IDI )
  ##  [1] 0.6927274

# attribute-specific item indices
round( cmod$attr_item_disc, 3 )
  ##           V1    V2    V3
  ##  Item1 0.648 0.648 0.000
  ##  Item2 0.000 0.530 0.530
  ##  Item3 0.581 0.000 0.581
  ##  Item4 0.697 0.000 0.000
  ##  Item5 0.000 0.000 8.870
  ##  Item6 0.000 0.140 0.000
  ##  Item7 0.040 0.040 0.040
  ##  Item8 0.000 0.433 0.433
  ##  Item9 0.000 0.715 0.715

## Note that attributes with a zero entry for an item
## do not differ from zero for the attribute specific item index