Robust Linking of Item Intercepts
linking.robust.Rd
This function implements a robust alternative of mean-mean linking which employs trimmed means instead of means. The linking constant is calculated for varying trimming parameters \(k\). The treatment of differential item functioning as outliers and application of robust statistics is discussed in Magis and De Boeck (2011, 2012).
Arguments
- itempars
Data frame of item parameters (item intercepts). The first column contains the item label, the 2nd and 3rd columns item parameters of two studies.
- object
Object of class
linking.robust
- x
Object of class
linking.robust
- ...
Further arguments to be passed
Value
A list with following entries
- ind.kopt
Index for optimal scale parameter
- kopt
Optimal scale parameter
- meanpars.kopt
Linking constant for optimal scale parameter
- se.kopt
Standard error for linking constant obtained with optimal scale parameter
- meanpars
Linking constant dependent on the scale parameter
- se
Standard error of the linking constant dependent on the scale parameter
- sd
DIF standard deviation (non-robust estimate)
- mad
DIF standard deviation (robust estimate using the MAD measure)
- pars
Original item parameters
- k.robust
Used vector of scale parameters
- I
Number of items
- itempars
Used data frame of item parameters
References
Magis, D., & De Boeck, P. (2011). Identification of differential item functioning in multiple-group settings: A multivariate outlier detection approach. Multivariate Behavioral Research, 46(5), 733-755. doi:10.1080/00273171.2011.606757
Magis, D., & De Boeck, P. (2012). A robust outlier approach to prevent type I error inflation in differential item functioning. Educational and Psychological Measurement, 72(2), 291-311. doi:10.1177/0013164411416975
See also
Other functions for linking: linking.haberman
,
equating.rasch
See also the plink package.
Examples
#############################################################################
# EXAMPLE 1: Linking data.si03
#############################################################################
data(data.si03)
res1 <- sirt::linking.robust( itempars=data.si03 )
summary(res1)
## Number of items=27
## Optimal trimming parameter k=8 | non-robust parameter k=0
## Linking constant=-0.0345 | non-robust estimate=-0.056
## Standard error=0.0186 | non-robust estimate=0.027
## DIF SD: MAD=0.0771 (robust) | SD=0.1405 (non-robust)
plot(res1)
if (FALSE) {
#############################################################################
# EXAMPLE 2: Linking PISA item parameters data.pisaPars
#############################################################################
data(data.pisaPars)
# Linking with items
res2 <- sirt::linking.robust( data.pisaPars[, c(1,3,4)] )
summary(res2)
## Optimal trimming parameter k=0 | non-robust parameter k=0
## Linking constant=-0.0883 | non-robust estimate=-0.0883
## Standard error=0.0297 | non-robust estimate=0.0297
## DIF SD: MAD=0.1824 (robust) | SD=0.1487 (non-robust)
## -> no trimming is necessary for reducing the standard error
plot(res2)
#############################################################################
# EXAMPLE 3: Linking with simulated item parameters containing outliers
#############################################################################
# simulate some parameters
I <- 38
set.seed(18785)
itempars <- data.frame("item"=paste0("I",1:I) )
itempars$study1 <- stats::rnorm( I, mean=.3, sd=1.4 )
# simulate DIF effects plus some outliers
bdif <- stats::rnorm(I,mean=.4,sd=.09)+( stats::runif(I)>.9 )* rep( 1*c(-1,1)+.4, each=I/2 )
itempars$study2 <- itempars$study1 + bdif
# robust linking
res <- sirt::linking.robust( itempars )
summary(res)
## Number of items=38
## Optimal trimming parameter k=12 | non-robust parameter k=0
## Linking constant=-0.4285 | non-robust estimate=-0.5727
## Standard error=0.0218 | non-robust estimate=0.0913
## DIF SD: MAD=0.1186 (robust) | SD=0.5628 (non-robust)
## -> substantial differences of estimated linking constants in this case of
## deviations from normality of item parameters
plot(res)
}