# Likelihood-Ratio Test DIF statistic

### Description

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

### Usage

1 | ```
LRT(data, member)
``` |

### Arguments

`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.

### Value

A vector with the values of the LRT DIF statistics.

### Note

Because of the fitting of the modified Rasch model with `glmer`

the process can be very time consuming (see the **Details** section of `difLRT`

).

### 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 Education, University of Liege

Research Group of Quantitative Psychology and Individual Differences, KU Leuven

David.Magis@ulg.ac.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

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.

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.

### See Also

`difLRT`

, `dichoDif`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
## 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)
``` |