difR (version 6.1.0)

LordChi2: Lord's chi-square DIF statistic

Description

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

Usage

LordChi2(mR, mF)

Value

A vector with the values of the Lord's chi-square DIF statistics.

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.

Author

David Magis
Data science consultant at IQVIA Belux
Brussels, Belgium
Sebastien Beland
Faculte des sciences de l'education
Universite de Montreal (Canada)

Gilles Raiche
Universite du Quebec a Montreal

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.

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.

Magis, D., Beland, S., Tuerlinckx, F. and De Boeck, P. (2010). A general framework and an R package for the detection of dichotomous differential item functioning. Behavior Research Methods, 42, 847-862. tools:::Rd_expr_doi("10.3758/BRM.42.3.847")

See Also

itemParEst, itemRescale, difLord, dichoDif

Examples

if (FALSE) {

 # 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)
 }