Differential item functioning for cognitive diagnosis models

This function is used to detect differential item functioning using the Wald test (Hou, de la Torre, & Nandakumar, 2014; Ma, Terzi, & de la Torre, 2021) and the likelihood ratio test (Ma, Terzi, & de la Torre, 2021). The forward anchor item search procedure developed in Ma, Terzi, and de la Torre (2021) was implemented.

Usage

dif(
  dat,
  Q,
  group,
  model = "GDINA",
  sequential = FALSE,
  method = "wald",
  anchor.items = NULL,
  dif.items = "all",
  p.adjust.methods = "holm",
  approx = FALSE,
  SE.type = 2,
  FS.args = list(on = FALSE, alpha.level = 0.05, maxit = 10, verbose = FALSE),
  ...
)

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

Arguments

dat

item responses from two or more groups; missing data need to be coded as NA

Q

Q-matrix specifying the association between items and attributes

group

a factor or a vector indicating the group each individual belongs to. Its length must be equal to the number of individuals.

model

model for each item.

sequential

Logical; whether a sequential model is fit to the data. Default is FALSE.

method

DIF detection method; It can be "wald" for Hou, de la Torre, and Nandakumar's (2014) Wald test method, and "LR" for likelihood ratio test (Ma, Terzi, Lee,& de la Torre, 2017).

anchor.items

which items will be used as anchors? Default is NULL, which means none of the items are used as anchors. For LR method, it can also be an integer vector giving the item numbers for anchors or "all", which means all items are treated as anchor items.

dif.items

which items are subject to DIF detection? Default is "all". It can also be an integer vector giving the item numbers.

p.adjust.methods

adjusted p-values for multiple hypothesis tests. This is conducted using p.adjust function in stats, and therefore all adjustment methods supported by p.adjust can be used, including "holm", "hochberg", "hommel", "bonferroni", "BH" and "BY". See p.adjust for more details. "holm" is the default.

approx

Whether an approximated LR test is implemented? If TRUE, parameters of items except the studied one will not be re-estimated.

SE.type

Type of standard error estimation methods for the Wald test.

FS.args

arguments for the forward anchor item search procedure developed in Ma, Terzi, and de la Torre (2021). A list with the following elements:

on - logical; TRUE if activate the forward anchor item search procedure. Default = FALSE.
alpha.level - nominal level for Wald or LR test. Default = .05.
maxit - maximum number of iterations allowed. Default = 10.
verbose - logical; print information for each iteration or not? Default = FALSE.

...

arguments passed to GDINA function for model calibration

object

dif object for S3 method

Value

A data frame giving the Wald statistics and associated p-values.

Methods (by generic)

summary(dif): print summary information

References

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.

Ma, W., Terzi, R., & de la Torre, J. (2021). Detecting differential item functioning using multiple-group cognitive diagnosis models. Applied Psychological Measurement.

Author

Wenchao Ma, The University of Minnesota, wma@umn.edu Jimmy de la Torre, The University of Hong Kong

Examples

if (FALSE) { # \dontrun{

####################################
#          Example 1.              #
#        two-group DIF             #
####################################

set.seed(123456)
N <- 3000
Q <- sim30GDINA$simQ
gs <- matrix(.2,ncol = 2, nrow = nrow(Q))
# By default, individuals are simulated from uniform distribution
# and deltas are simulated randomly
sim1 <- simGDINA(N,Q,gs.parm = gs,model="DINA")
sim2 <- simGDINA(N,Q,gs.parm = gs,model=c(rep("DINA",nrow(Q)-1),"DINO"))
dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat"))
gr <- rep(c("G1","G2"),each=N)

# DIF using Wald test
dif.wald <- dif(dat, Q, group=gr, method = "Wald")
dif.wald
# DIF using LR test
dif.LR <- dif(dat, Q, group=gr, method="LR")
dif.LR
# DIF using Wald test + forward search algorithm
dif.wald.FS <- dif(dat, Q, group=gr, method = "Wald", FS.args = list(on = TRUE, verbose = TRUE))
dif.wald.FS
# DIF using LR test + forward search algorithm
dif.LR.FS <- dif(dat, Q, group=gr, method = "LR", FS.args = list(on = TRUE, verbose = TRUE))
dif.LR.FS

####################################
#          Example 2.              #
#        two-group DIF             #
#    with attribute structure.     #
####################################
# --- User-specified attribute structure ----#
Q <- sim30GDINA$simQ
K <- ncol(Q)
# linear structure A1->A2->A3->A4->A5
linear <- list(c(1,2),
               c(2,3),
               c(3,4),
               c(4,5))
struc <- att.structure(linear,K)
set.seed(123)
# data simulation
N <- 1000
true.lc <- sample(c(1:2^K),N,replace=TRUE,prob=struc$att.prob)
table(true.lc) #check the sample
true.att <- attributepattern(K)[true.lc,]
 gs <- matrix(rep(0.1,2*nrow(Q)),ncol=2)
 # data simulation
 simD <- simGDINA(N,Q,gs.parm = gs, model = "ACDM",attribute = true.att)
 dat <- extract(simD,"dat")
gr <- rep(1:2,each=N/2)
dif.wald <- dif(dat, Q, group=gr, method = "Wald",
                att.str = diverg, att.dist = "saturated")
dif.wald


####################################
#          Example 3.              #
#        Three-group DIF           #
####################################

set.seed(123456)
N <- 500
Q <- sim30GDINA$simQ
gs <- matrix(.2,ncol = 2, nrow = nrow(Q))
# By default, individuals are simulated from uniform distribution
# and deltas are simulated randomly
sim1 <- simGDINA(N,Q,gs.parm = gs,model="DINA")
sim2 <- simGDINA(N,Q,gs.parm = gs,model=c(rep("DINA",nrow(Q)-1),"DINO"))
sim3 <- simGDINA(N,Q,gs.parm = gs,model="DINA")
dat <- rbind(extract(sim1,"dat"),extract(sim2,"dat"),extract(sim3,"dat"))
gr <- rep(c("G1","G2","G3"),each=N)

# DIF using Wald test - omnibus test
dif.wald <- dif(dat, Q, group=gr, method = "Wald")
dif.wald
# pairwise comparison between all pair of groups
dif.pair = pairwiseDIF(dif.wald)
dif.pair
# draw plot to show the DIF
plot(dif.pair, withSE = TRUE)
} # }