gdina.dif: Differential Item Functioning in the GDINA Model

In CDM: Cognitive Diagnosis Modeling

Differential Item Functioning in the GDINA Model

Description

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.

Usage

gdina.dif(object)

## S3 method for class 'gdina.dif'
summary(object, ...)

Arguments

object	Object of class gdina
...	Further arguments to be passed

Details

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.

Value

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.

References

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 Also

See the GDINA::dif function in the GDINA package for similar functionality.

Examples

## Not run: 
#############################################################################
# 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)

CDM documentation built on Aug. 25, 2022, 5:08 p.m.