# equating.rasch: Equating in the Generalized Logistic Rasch Model In alexanderrobitzsch/sirt: Supplementary Item Response Theory Models

 equating.rasch R Documentation

## Equating in the Generalized Logistic Rasch Model

### Description

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).

### Usage

equating.rasch(x, y, theta=seq(-4, 4, len=100),
alpha1=0, alpha2=0)


### Arguments

 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 theta=stats::qnorm( seq(.001, .999, len=100), mean=mu, sd=sigma) alpha1 Fixed \alpha_1 parameter in the generalized item response model alpha2 Fixed \alpha_2 parameter in the generalized item response model

### Value

 B.est Estimated linking constants according to the methods Mean.Mean (Mean-mean linking), Haebara (Haebara method) and Stocking.Lord (Stocking-Lord method). descriptives Descriptives of the linking. The linking error (linkerror) is calculated under the assumption of simple random sampling of items anchor Original and transformed item parameters of anchor items transf.par Original and transformed item parameters of all items

### References

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.

### Examples

#############################################################################
# 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

## Not run:
# The plink package is not available on CRAN anymore.
I <- nrow(pars)
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))
poly.mod=list(pm,pm))
summary(out)
##   -------  group2/group1*  -------
##
##                        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