RajuZ {difR} | R Documentation |

## 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 |

`mF` |
numeric: the matrix of item parameter estimates (one row per item) for the focal group. See |

`signed` |
logical: should the |

### 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 |

### Author(s)

Sebastien Beland

Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)

Universite du Quebec a Montreal

sebastien.beland.1@hotmail.com, http://www.cdame.uqam.ca/

David Magis

Department of Psychology, University of Liege

Research Group of Quantitative Psychology and Individual Differences, KU Leuven

David.Magis@uliege.be, http://ppw.kuleuven.be/okp/home/

Gilles Raiche

Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca, http://www.cdame.uqam.ca/

### 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. doi: 10.3758/BRM.42.3.847

Raju, N.S. (1988). The area between two item characteristic curves. *Psychometrika, 53*, 495-502. 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. 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*version 5.1 Index]