RajuZ {difR}R Documentation

Raju's area DIF statistic

Description

Calculates the Raju's statistics for DIF detection.

Usage

 RajuZ(mR, mF)
 

Arguments

mR numeric: the matrix of item parameter estimates (one row per item) for the reference group. See Details.
mF numeric: the matrix of item parameter estimates (one row per item) for the focal group. See Details.

Details

This command computes the Raju's area statistic (Raju, 1988, 1990) in the specific framework of differential item functioning. It forms the basic command of difRaju and is specifically designed for this call.

The matrices mR and mF must have the same format as the output of the command itemParEst and one the possible models (1PL, 2PL or constrained 3PL). The number of columns therefore equals two, five or six, respectively. Note that the unconstrained 3PL model cannot be used in this method: all pseudo-guessing parameters must be equal in both groups of subjects. Moreover, item parameters of the focal must be on the same scale of that of the reference group. If not, make use of e.g. equal means anchoring (Cook and Eignor, 1991) and itemRescale to transform them adequately.

Value

A matrix with one row per item and three columns, holding respectively Raju's area between the two item characteristic curves, its standard error and the Raju DIF statistic (the latter being the ratio of the first two columns).

Author(s)

Sebastien Beland
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
sebastien.beland.1@hotmail.com
David Magis
Research Group of Quantitative Psychology and Individual Differences
Katholieke Universiteit Leuven
David.Magis@psy.kuleuven.be, http://ppw.kuleuven.be/okp/home/
Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

Cook, L. L. and Eignor, D. R. (1991). An NCME instructional module on IRT equating methods. Educational Measurement: Issues and Practice, 10, 37-45.

Raju, N.S. (1988). The area between two item characteristic curves. Psychometrika, 53, 495-502.

Raju, N. S. (1990). Determining the significance of estimated signed and unsigned areas between two item response functions. Applied Psychological Measurement, 14, 197-207.

See Also

itemParEst, itemRescale, difRaju, dichoDif

Examples

# Loading of the verbal data
data(verbal)
attach(verbal)

# Splitting the data into reference and focal groups
nF<-sum(Gender)
nR<-nrow(verbal)-nF
data.ref<-verbal[,1:24][order(Gender),][1:nR,]
data.focal<-verbal[,1:24][order(Gender),][(nR+1):(nR+nF),]

# Pre-estimation of the item parameters (1PL model)
mR<-itemParEst(data.ref,model="1PL")
mF<-itemParEst(data.focal,model="1PL")
mF<-itemRescale(mR, mF)
RajuZ(mR, mF)

# Pre-estimation of the item parameters (2PL model)
mR<-itemParEst(data.ref,model="2PL")
mF<-itemParEst(data.focal,model="2PL")
mF<-itemRescale(mR, mF)
RajuZ(mR, mF)

# Pre-estimation of the item parameters (constrained 3PL model)
mR<-itemParEst(data.ref,model="3PL",c=0.05)
mF<-itemParEst(data.focal,model="3PL",c=0.05)
mF<-itemRescale(mR, mF)
RajuZ(mR, mF)

[Package difR version 1.1 Index]