RajuZ: Raju's area DIF statistic

In difR: Collection of Methods to Detect Dichotomous and Polytomous Differential Item Functioning (DIF)

Raju's area DIF statistic

Description

Calculates the Raju's statistics for DIF detection.

Usage

RajuZ(mR, mF, signed = FALSE)
 

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.
signed	logical: should the signed area be computed, or the unsigned (i.e. in absolute value) ara? Default is FALSE, i.e. the unsigned area. 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.

By default, the unsigned area, given by Equation (57) in Raju (1990), is computed. It makes use of Equations (14), (15), (23) and (46) for the numerator, and Equations (17), (33) to (39), and (52) for the denominator of the Z statistic. However, the signed area, given by Equation (56) in Raju (1990), can be used instead. In this case, Equations (14), (21) and (44) are used for the numerator, and Equations (17), (25) and (48) for the denominator. The choice of the type of area is fixed by the logical signed argument, with default value FALSE.

Value

A list with two components:

res	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).
signed	the value of the signed argument.

Author(s)

David Magis
Data science consultant at IQVIA Belux
Brussels, Belgium
Sebastien Beland
Faculte des sciences de l'education
Universite de Montreal (Canada)
[e-mail]
Gilles Raiche
Universite du Quebec a Montreal
[e-mail]

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.

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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.3758/BRM.42.3.847")}

Raju, N.S. (1988). The area between two item characteristic curves. Psychometrika, 53, 495-502. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/BF02294403")}

Raju, N. S. (1990). Determining the significance of estimated signed and unsigned areas between two item response functions. Applied Psychological Measurement, 14, 197-207. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1177/014662169001400208")}

See Also

itemParEst, itemRescale, difRaju, dichoDif

Examples

## Not run: 

 # 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)

 # Signed and unsigned Raju statistics
 RajuZ(mR, mF)
 RajuZ(mR, mF, signed = TRUE)

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

 # Signed and unsigned Raju statistics
 RajuZ(mR, mF)
 RajuZ(mR, mF, signed = TRUE)
 
 # 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)
 
 # Signed and unsigned Raju statistics
 RajuZ(mR, mF)
 RajuZ(mR, mF, signed = TRUE)
 
## End(Not run)
 

difR documentation built on June 8, 2025, 1:03 p.m.