discrim.index {CDM} | R Documentation |
Discrimination Indices at Item-Attribute, Item and Test Level
Description
Computes discrimination indices at the probability metric (de la Torre, 2008; Henson, DiBello & Stout, 2018).
Usage
discrim.index(object, ...)
## S3 method for class 'din'
discrim.index(object, ...)
## S3 method for class 'gdina'
discrim.index(object, ...)
## S3 method for class 'mcdina'
discrim.index(object, ...)
## S3 method for class 'discrim.index'
summary(object, file=NULL, digits=3, ...)
Arguments
object |
|
file |
Optional file name for a file in which the summary output should be sunk |
digits |
Number of digits for rounding |
... |
Further arguments to be passed |
Details
If item j
possesses H_j
categories, the item-attribute
specific discrimination for attribute k
according to Henson et al. (2018) is defined as
DI_{jk}=\frac{1}{2} \max_{ \bm{\alpha} }
\left( \sum_{h=1}^{H_j} | P(X_j=h| \bm{\alpha} ) -
P(X_j=h| \bm{\alpha}^{(-k)} ) |
\right )
where \bm{\alpha}^{(-k)}
and \bm{\alpha}
differ only
in attribute k
. The index DI_{jk}
can be found as the
value discrim_item_attribute
. The test-level discrimination index
is defined as
\overline{DI}=\frac{1}{J} \sum_{j=1}^J \max_k DI_{jk}
and can be found
in discrim_test
.
According to de la Torre (2008) and de la Torre, Rossi and van der Ark (2018), the item discrimination index (IDI) is defined as
IDI_j=\max_{ \bm{\alpha}_1,\bm{\alpha}_2, h}
| P(X_j=h| \bm{\alpha}_1 ) - P(X_j=h| \bm{\alpha}_2 ) |
and can be found as idi
in the values list.
Value
A list with following entries
discrim_item_attribute |
Discrimination indices |
idi |
Item discrimination index |
discrim_test |
Discrimination index at test level |
References
de la Torre, J. (2008). An empirically based method of Q-matrix validation
for the DINA model: Development and applications.
Journal of Educational Measurement, 45, 343-362.
http://dx.doi.org/10.1111/j.1745-3984.2008.00069.x
de la Torre, J., van der Ark, L. A., & Rossi, G. (2018). Analysis of clinical data from a cognitive diagnosis modeling framework. Measurement and Evaluation in Counseling and Development, 51(4), 281-296. https://doi.org/10.1080/07481756.2017.1327286
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
See Also
See cdi.kli
for discrimination indices based on the
Kullback-Leibler information.
For a fitted model mod
in the GDINA package, discrimination indices can be
extracted by the method extract(mod,"discrim")
(GDINA::extract
).
Examples
## Not run:
#############################################################################
# EXAMPLE 1: DINA and GDINA model
#############################################################################
data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")
#-- fit GDINA and DINA model
mod1 <- CDM::gdina( sim.dina, q.matrix=sim.qmatrix )
mod2 <- CDM::din( sim.dina, q.matrix=sim.qmatrix )
#-- compute discrimination indices
dimod1 <- CDM::discrim.index(mod1)
dimod2 <- CDM::discrim.index(mod2)
summary(dimod1)
summary(dimod2)
## End(Not run)