Differential Item Functioning in the GDINA Model
This function assesses item-wise differential item functioning in the GDINA model by using the Wald test (de la Torre, 2011; Hou, de la Torre & Nandakumar, 2014). It is necessary that a multiple group GDINA model is previously fitted.
gdina.dif(object) ## S3 method for class 'gdina.dif' summary(object, ...)
object |
Object of class |
... |
Further arguments to be passed |
The p values are also calculated by a Holm adjustment
for multiple comparisons (see p.holm in
output difstats).
In the case of two groups, an effect size of differential item functioning
(labeled as UA (unsigned area) in difstats value) is defined as
the weighted absolute difference of item response functions. The DIF measure
for item j is defined as
UA_j=∑_l w( α_l ) | P( X_j=1 | α_l, G=1 ) - P( X_j=1 | α_l, G=2 ) |
where w( α_l )=[ P( α_l | G=1 ) + P( α_l | G=2 ) ]/2.
A list with following entries
difstats |
Data frame containing results of item-wise Wald tests |
coef |
Data frame containing all (group-wise) item parameters |
delta_all |
List of δ vectors containing all item parameters |
varmat_all |
List of covariance matrices of all δ item parameters |
prob.exp.group |
List with groups and items containing expected latent class sizes and expected probabilities for each group and each item. Based on this information, effect sizes of differential item functioning can be calculated. |
de la Torre, J. (2011). The generalized DINA model framework. Psychometrika, 76, 179-199.
Hou, L., de la Torre, J., & Nandakumar, R. (2014). Differential item functioning assessment in cognitive diagnostic modeling: Application of the Wald test to investigate DIF in the DINA model. Journal of Educational Measurement, 51, 98-125.
See the GDINA::dif function in the
GDINA package for similar functionality.
## Not run:
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# EXAMPLE 1: DIF for DINA simulated data
#############################################################################
# simulate some data
set.seed(976)
N <- 2000 # number of persons in a group
I <- 9 # number of items
q.matrix <- matrix( 0, 9,2 )
q.matrix[1:3,1] <- 1
q.matrix[4:6,2] <- 1
q.matrix[7:9,c(1,2)] <- 1
# simulate first group
guess <- rep( .2, I )
slip <- rep(.1, I)
dat1 <- CDM::sim.din( N=N, q.matrix=q.matrix, guess=guess, slip=slip,
mean=c(0,0) )$dat
# simulate second group with some DIF items (items 1, 7 and 8)
guess[ c(1,7)] <- c(.3, .35 )
slip[8] <- .25
dat2 <- CDM::sim.din( N=N, q.matrix=q.matrix, guess=guess, slip=slip,
mean=c(0.4,.25) )$dat
group <- rep(1:2, each=N )
dat <- rbind( dat1, dat2 )
#*** estimate multiple group GDINA model
mod1 <- CDM::gdina( dat, q.matrix=q.matrix, rule="DINA", group=group )
summary(mod1)
#*** assess differential item functioning
dmod1 <- CDM::gdina.dif( mod1)
summary(dmod1)
## item X2 df p p.holm UA
## 1 I001 10.1711 2 0.0062 0.0495 0.0428
## 2 I002 1.9933 2 0.3691 1.0000 0.0276
## 3 I003 0.0313 2 0.9845 1.0000 0.0040
## 4 I004 0.0290 2 0.9856 1.0000 0.0044
## 5 I005 2.3230 2 0.3130 1.0000 0.0142
## 6 I006 1.8330 2 0.3999 1.0000 0.0159
## 7 I007 40.6851 2 0.0000 0.0000 0.1184
## 8 I008 6.7912 2 0.0335 0.2346 0.0710
## 9 I009 1.1538 2 0.5616 1.0000 0.0180
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.