difR (version 6.1.0)

SimPolyDif: 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)}))

Value

A list with several arguments:

data

the matrix with DIF items.

ipars

the item parameters.

thetas

the person parameters.

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).

Author

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

Details

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

References

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

Examples

if (FALSE) {
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")

}