Discrimination Indices at Item-Attribute, Item and Test Level
Computes discrimination indices at the probability metric (de la Torre, 2008; Henson, DiBello & Stout, 2018).
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, ...)
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_{ \boldmath{α} } ≤ft( ∑_{h=1}^{H_j} | P(X_j=h| \boldmath{α} ) - P(X_j=h| \boldmath{α}^{(-k)} ) | \right )
where \boldmath{α}^{(-k)} and \boldmath{α} 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} ∑_{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_{ \boldmath{α}_1,\boldmath{α}_2, h} | P(X_j=h| \boldmath{α}_1 ) - P(X_j=h| \boldmath{α}_2 ) |
and can be found as idi in the values list.
A list with following entries
discrim_item_attribute |
Discrimination indices DI_{jk} at item level for each attribute |
idi |
Item discrimination index IDI_j |
discrim_test |
Discrimination index at test level |
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 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).
## 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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.