LordChi2 {difR}R Documentation

Lord's chi-square DIF statistic

Description

Calculates the Lord's chi-square statistics for DIF detection.

Usage

 LordChi2(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 Lord's chi-square statistic (Lord, 1980) in the specific framework of differential item functioning. It forms the basic command of difLord and is specifically designed for this call.

The matrices mR and mF must have the same format as the output of the command itemParEst with one the possible models (1PL, 2PL, 3PL or constrained 3PL). The number of columns therefore equals two, five, nine or six, respectively. 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 vector with the values of the Lord's chi-square DIF statistics.

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.

Lord, F. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum Associates.

See Also

itemParEst, itemRescale, difLord, 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)
LordChi2(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)
LordChi2(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)
LordChi2(mR, mF)

[Package difR version 1.1 Index]