linking.robust: Robust Linking of Item Intercepts

Description

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).

Usage

linking.robust(itempars)
# S3 method for linking.robust
summary(object,...)
# S3 method for linking.robust
plot(x, ...)

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

…

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

Standard error of the linking constant dependent on the scale parameter

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

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. 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. 10.1177/0013164411416975

Examples

Run this code

# NOT RUN {
#############################################################################
# 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)

# }
# NOT RUN {
#############################################################################
# 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)
# }