Cognitive Diagnostic Indices based on Kullback-Leibler Information
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.
cdi.kli(object) ## S3 method for class 'cdi.kli' summary(object, digits=2, ...)
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 |
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.
See discrim.index for computing discrimination indices at the
probability metric.
See Henson, DiBello and Stout (2018) for an overview of different discrimination indices.
############################################################################# # 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
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.