equating.rasch.Rd
This function does the linking in the generalized logistic item response model. Only item difficulties (\(b\) item parameters) are allowed. Mean-mean linking and the methods of Haebara and Stocking-Lord are implemented (Kolen & Brennan, 2004).
equating.rasch(x, y, theta=seq(-4, 4, len=100), alpha1=0, alpha2=0)
x | Matrix with two columns: First column items, second column item difficulties |
---|---|
y | Matrix with two columns: First columns item, second column item difficulties |
theta | Vector of theta values at which the linking functions
should be evaluated. If a weighting according to a prespecified normal
distribution \(N( \mu,\sigma^2)\) is aimed, then choose
|
alpha1 | Fixed \(\alpha_1\) parameter in the generalized item response model |
alpha2 | Fixed \(\alpha_2\) parameter in the generalized item response model |
Estimated linking constants according to the methods
Mean.Mean
(Mean-mean linking), Haebara
(Haebara method)
and Stocking.Lord
(Stocking-Lord method).
Descriptives of the linking. The linking error
(linkerror
) is calculated under the assumption of simple
random sampling of items
Original and transformed item parameters of anchor items
Original and transformed item parameters of all items
Kolen, M. J., & Brennan, R. L. (2004). Test Equating, Scaling, and Linking: Methods and Practices. New York: Springer.
For estimating standard errors (due to inference with respect to
the item domain) of this procedure see equating.rasch.jackknife
.
For linking several studies see linking.haberman
or
invariance.alignment
.
A robust alternative to mean-mean linking is implemented in
linking.robust
.
For linking under more general item response models see the plink package.
############################################################################# # EXAMPLE 1: Linking item parameters of the PISA study ############################################################################# data(data.pisaPars) pars <- data.pisaPars # linking the two studies with the Rasch model mod <- sirt::equating.rasch(x=pars[,c("item","study1")], y=pars[,c("item","study2")]) ## Mean.Mean Haebara Stocking.Lord ## 1 0.08828 0.08896269 0.09292838 if (FALSE) { #*** linking using the plink package # The plink package is not available on CRAN anymore. # You can download the package with # utils::install.packages("plink", repos="http://www2.uaem.mx/r-mirror") library(plink) I <- nrow(pars) pm <- plink::as.poly.mod(I) # linking parameters plink.pars1 <- list( "study1"=data.frame( 1, pars$study1, 0 ), "study2"=data.frame( 1, pars$study2, 0 ) ) # the parameters are arranged in the columns: # Discrimination, Difficulty, Guessing Parameter # common items common.items <- cbind("study1"=1:I,"study2"=1:I) # number of categories per item cats.item <- list( "study1"=rep(2,I), "study2"=rep(2,I)) # convert into plink object x <- plink::as.irt.pars( plink.pars1, common.items, cat=cats.item, poly.mod=list(pm,pm)) # linking using plink: first group is reference group out <- plink::plink(x, rescale="MS", base.grp=1, D=1.7) # summary for linking summary(out) ## ------- group2/group1* ------- ## Linking Constants ## ## A B ## Mean/Mean 1.000000 -0.088280 ## Mean/Sigma 1.000000 -0.088280 ## Haebara 1.000000 -0.088515 ## Stocking-Lord 1.000000 -0.096610 # extract linked parameters pars.out <- plink::link.pars(out) }