sirt (version 0.36-30)

equating.rasch: 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=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.

See Also

For linking under more general item response models see the plink package. For linking several studies see linking.haberman.

Examples

#############################################################################
# EXAMPLE 1: Linking item parameters of the PISA study
#############################################################################

data(data.pisaPars)
pars <- data.pisaPars

# linking the tow studies with the Rasch model
mod <- equating.rasch(x=pars[,c("item","study1")], y=pars[,c("item","study2")])
##   Mean.Mean    Haebara Stocking.Lord
## 1   0.08828 0.08896269    0.09292838

# Linking with plink package
library(plink)
# define common items
I <- nrow(pars)
pm <- as.poly.mod(I)
# define item parameters for plink
plink.pars <- list( "study1" = cbind( 1 , pars$study1 , 0 ) ,
        "study2" = cbind( 1 , pars$study2 , 0 ) )
# set parameter structure for plink
x <- as.irt.pars( pars=plink.pars, cbind(1:I , 1:I), cat=list(rep(2,I),rep(2,I)) , 
        poly.mod=list(pm,pm) )
# linking with plink
out <- plink(x, rescale="MS", base.grp=2, D=1.7)
summary(out)        # summary
##   -------  group1/group2*  -------
##   Linking Constants
##                        A        B
##   Mean/Mean     1.000000 0.088280
##   Mean/Sigma    1.000000 0.088280
##   Haebara       1.000000 0.088605
##   Stocking-Lord 1.000000 0.096617
constants <- link.con(out) # Extract linking constants
constants