linking.robust: Robust Linking of Item Intercepts

In sirt: Supplementary Item Response Theory Models

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 class 'linking.robust'
summary(object,...)

## S3 method for class '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
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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_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)

## 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)

## End(Not run)

sirt documentation built on May 29, 2024, 8:43 a.m.