SimPolyDif: Generation of DIF for polytomous items

In difR: Collection of Methods to Detect Dichotomous and Polytomous Differential Item Functioning (DIF)

Generation of DIF for polytomous items

Description

Function to generate DIF for polytomous items using the GPCM.

Usage

 SimPolyDif(It, ItDIFa, ItDIFb,
                       NR, NF, a, b, d, ncat=3,
                       Ga=rep(0,ItDIFa), Gb=rep(0,ItDIFb),
                       D=1, 
                       thR=NULL,thF=NULL,muR=0,muF=0,sigR=1,sigF=1,
                       ItDIFd=NULL, Gd = lapply(1:It, function(x){rep(0,ncat)}))
 

Arguments

It	It: Number of items
ItDIFa	Vector of integers specifying which items have DIF for a parameters.
ItDIFb	Vector of integers specifying which items have DIF for b parameters.
NR	Number of respondents for reference group.
NF	Number of respondents for focal group (generalize to multiple focal groups).
a	Item slope for reference group.
b	Item difficulty for reference group.
d	Step parameters, as a list whose length is the same as the number of items, for the reference group.
ncat	Number of categories per item. Currently the same number for all items.
Gb	Vector of difference in b's for focal group(s).
Ga	Vector of difference in a's for focal group(s).
D	Scaling parameter for GPCM. Defaults to 1.
thR	Optional vector of latent variable values for reference group.
thF	Optional vector of latent variable values for focal group.
muR	Mean of latent variable for reference group. Used if latent scores not supplied.
muF	Mean of latent variable for reference group. Used if latent scores not supplied.
sigR	Standard deviation of latent variable for reference group. Used if latent scores not supplied.
sigF	Standard deviation of latent variable for reference group. Used if latent scores not supplied.
ItDIFd	Vector of integers specifying which items have DIF for step parameters.
Gd	List of differences in d's for focal group(s).

Details

This function is based on traditional parameterizations of the GPCM that have an overall difficulty parameter and step parameters.

Value

A list with several arguments:

data	the matrix with DIF items.
ipars	the item parameters.
thetas	the person parameters.

Author(s)

Carl F. Falk
Department of Psychology
McGill University (Canada)
[e-mail], https://www.mcgill.ca/psychology/carl-f-falk
Sebastien Beland
Faculte des sciences de l'education
Universite de Montreal (Canada)
[e-mail]

References

Muraki, E. (1992). A generalized partial credit model: Application of an EM algorithm. Applied Psychological Measurement, 16, 159–176.

Examples

## Not run: 
set.seed(1234)

# original item parameters
a <- rlnorm(10, -0.5)  # slopes
b <- runif(10, -2, 2)  # difficulty
d <- list()
d[[1]] <- c(0, 2, .5, -.15, -1.1)
d[[2]] <- c(0, 2, .25, -.45, -.75)
d[[3]] <- c(0, 1, .5, -.65, -1)
d[[4]] <- c(0, 2, .5, -.85, -2)
d[[5]] <- c(0, 1, .25, -.05, -1)
d[[6]] <- c(0, 2, .5, -.95, -1)
d[[7]] <- c(0, 1, .25, -.35, -2)
d[[8]] <- c(0, 2, .5, -.15, -1)
d[[9]] <- c(0, 1, .25, -.25, -2)
d[[10]] <- c(0, 2, .5, -.35, -1)

# Uniform DIF
It <- 10; NR <- 1000; NF <- 1000
ItDIFa <- NULL; Ga <- NULL
ItDIFb <- c(1, 3)
Gb <- rep(.5, 2)

Out.Unif <- SimPolyDif(It, ItDIFa, ItDIFb, NR, NF, a, b, d,
                       ncat = 5, Ga = Ga, Gb = Gb)
Out.Unif$ipars
Data <- Out.Unif$data
difPolyLogistic(as.data.frame(Data[, 1:It]),
                group = Data[, It + 1], focal.name = "G2")

# Nonuniform DIF
ItDIFa <- c(1, 2)
Ga <- rep(.25, 2)
ItDIFb <- c(1, 3)
Gb <- rep(.5, 2)

Out.NUnif <- SimPolyDif(It, ItDIFa, ItDIFb, NR, NF, a, b, d,
                        ncat = 5, Ga = Ga, Gb = Gb)
Out.NUnif$ipars
Data <- Out.NUnif$data
difPolyLogistic(as.data.frame(Data[, 1:It]),
                group = Data[, It + 1], focal.name = "G2")

# Also changing step parameters
ItDIFd <- c(2)
Gd <- list(c(0, .25, -.25, .25, -.25))

Out.NUnif2 <- SimPolyDif(It, ItDIFa, ItDIFb, NR, NF, a, b, d,
                         ncat = 5, Ga = Ga, Gb = Gb,
                         ItDIFd = ItDIFd, Gd = Gd)
Out.NUnif2$ipars
Data <- Out.NUnif2$data
difPolyLogistic(as.data.frame(Data[, 1:It]),
                group = Data[, It + 1], focal.name = "G2")


## End(Not run)

difR documentation built on June 8, 2025, 1:03 p.m.