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).
linking.robust(itempars) # S3 method for linking.robust summary(object,...) # S3 method for linking.robust plot(x, ...)
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. |
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object | Object of class |
x | Object of class |
... | Further arguments to be passed |
A list with following entries
Index for optimal scale parameter
Optimal scale parameter
Linking constant for optimal scale parameter
Standard error for linking constant obtained with optimal scale parameter
Linking constant dependent on the scale parameter
Standard error of the linking constant dependent on the scale parameter
DIF standard deviation (non-robust estimate)
DIF standard deviation (robust estimate using the MAD measure)
Original item parameters
Used vector of scale parameters
Number of items
Used data frame of item parameters
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
Other functions for linking: linking.haberman
,
equating.rasch
See also the plink package.
############################################################################# # 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) }