LRT: Likelihood-Ratio Test DIF statistic
In difR: Collection of Methods to Detect Dichotomous Differential Item Functioning (DIF)

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

Calulates Likelihoo-Ratio Test (LRT) statistics for DIF detection.

1	LRT(data, member)

`data`	numeric: the data matrix (one row per subject, one column per item).
`member`	numeric: the vector of group membership with zero and one entries only. See Details.

This command computes the likelihood-ratio test statistic (Thissen, Steinberg and Wainer, 1988) in the specific framework of differential item functioning. It forms the basic command of difLRT and is specifically designed for this call.

The data are passed through the data argument, with one row per subject and one column per item. Missing values are allowed but must be coded as NA values.

The vector of group membership, specified with member argument, must hold only zeros and ones, a value of zero corresponding to the reference group and a value of one to the focal group.

The LRT DIF statistic is computed for each item separately, using all other items as anchor items.

A vector with the values of the LRT DIF statistics.

Because of the fitting of the modified Rasch model with glmer the process can be very time consuming (see the Details section of difLRT).

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/

Bates, D. and Maechler, M. (2009). lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-31. http://CRAN.R-project.org/package=lme4

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

Thissen, D., Steinberg, L. and Wainer, H. (1988). Use of item response theory in the study of group difference in trace lines. In H. Wainer and H. Braun (Eds.), Test validity. Hillsdale, NJ: Lawrence Erlbaum Associates.

difLRT, dichoDif

## Not run: 

 # Loading of the verbal data
 data(verbal)
 attach(verbal)

 # Excluding the "Anger" variable
 verbal <- verbal[colnames(verbal)!="Anger"]

 # Keeping the first 5 items and the first 50 subjects
 # (this is an artificial simplification to reduce the computational time)
 # Sixth column holds the group membership
 verbal <- verbal[1:50, c(1:5, 25)]

 # Likelihood-ratio statistics
 LRT(verbal[,1:5], verbal[,6])
 
## End(Not run)