contrastMatrix: Contrast matrix for computing generalized Lord's chi-squared...
In difR: Collection of Methods to Detect Dichotomous Differential Item Functioning (DIF)

Description Usage Arguments Details Value Author(s) References See Also Examples

This command sets the appropriate contrast matrix C for computing the generalized Lord's chi-squared statistics in the framework of DIF detection among multiple groups.

1 2	contrastMatrix(nrFocal, model)

`nrFocal`	numeric: the number of focal groups.
`model`	character: the logistic model to be fitted (either `"1PL"`, `"2PL"`, `"3PL"` or `"3PLc"`). See Details.

The contrast matrix C is necessary to calculate the generalized Lord's chi-squared statistic. It is designed to perform accurate tests of equality of item parameters accross the groups of examinees (see Kim, Cohen and Park, 1995). This is a subroutine for the command genLordChi2 which returns the DIF statistics.

The number of focal groups has to be specified by the argument nrFocal. Moreover, four logistic IRT models can be considered: the 1PL, 2PL and 3PL models can be set by using their acronyms (e.g. "1PL" for 1PL model, and so on). It is also possible to consider the constrained 3PL model, where all pseudo-guessing values are equal across the groups of examinees and take some predefined values which do not need to be supplied here. This model is specified by the value "3PLc" for argument model.

A contrast matrix designed to test equality of item parameter estimates from the specified model and with nrFocal focal groups. The output matrix has a number of rows equal to nrFocal times the number of tested parameters (one for 1PL model, two for 2PL and constrained 3PL models, three for 3PL model). The number of columns is equal to (nrFocal+1) times the number of tested parameters. See Kim, Cohen and Park (1995) for further details.

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/

Kim, S.-H., Cohen, A.S. and Park, T.-H. (1995). Detection of differential item functioning in multiple groups. Journal of Educational Measurement, 32, 261-276. doi: 10.1111/j.1745-3984.1995.tb00466.x

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

genLordChi2, difGenLord

## Not run: 

 # Contrast matrices with 1PL model and several focal groups
 contrastMatrix(2, "1PL")
 contrastMatrix(3, "1PL")
 contrastMatrix(4, "1PL")

 # Contrast matrices with 2PL, constrained and unconstrained 3PL models and three 
 # focal groups
 contrastMatrix(3, "2PL")
 contrastMatrix(3, "3PLc")
 contrastMatrix(3, "3PL")

## End(Not run)