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 et al. (2008) for more details.

Usage

cdi.kli(object)

## S3 method for class 'cdi.kli':
summary(object, digits = 2 ,  \dots)

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

Value

A list with following entries
test_discTest discrimination which is the sum of all global item discrimination indices
attr_discAttribute discriminations
glob_item_discGlobal item discriminations (Cognitive diagnostic index)
attr_item_discAttribute-specific item discrimination
KLIArray with Kullback-Leibler informations of all items (first dimension) and skill classes (in the second and third dimension)
skillclassesMatrix containing all used skill classes in the model
hdistMatrix containing Hamming distance between skill classes
pjkUsed probabilities
q.matrixUsed Q-matrix
summaryData frame with test- and item-specific discrimination statistics

References

Henson, R., & Douglas, J. (2005). Test construction for cognitive diagnosis. Applied Psychological Measurement, 29, 262-277. Henson, R., Roussos, L., Douglas, J., & He, X. (2008). Cognitive diagnostic attribute-level discrimination indices. Applied Psychological Measurement, 32, 275-288. 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 sim.dina
#############################################################################	

data(sim.dina)
data(sim.qmatrix)

mod <- 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 <- 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

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