sirt (version 1.14-0)

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 $k$.

Usage

linking.robust(itempars)
"summary"(object,...)
"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

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 <- 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 <- 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 <- 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)