genMantelHaenszel {difR} | R Documentation |

## Generalized Mantel-Haenszel DIF statistic

### Description

Calculates the generalized Mantel-Haenszel statistics for DIF detection among multiple groups.

### Usage

```
genMantelHaenszel(data, member, match = "score", anchor = 1:ncol(data))
```

### Arguments

`data` |
numeric: the data matrix (one row per subject, one column per item). |

`member` |
numeric: the vector of group membership with zero and positive integer entries only. See |

`match` |
specifies the type of matching criterion. Can be either |

`anchor` |
a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See |

### Details

This command computes the generalized Mantel-Haenszel statistic (Somes, 1986) in the specific framework of differential item functioning. It forms the basic command
of `difGMH`

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. They are discarded from sum-score computation.

The vector of group membership, specified with `member`

argument, must hold only zeros and positive integers. The value zero corresponds to the reference group,
and each positive integer value corresponds to one focal group. At least two different positive integers must be supplied.

The matching criterion can be either the test score or any other continuous or discrete variable to be passed in the `genMantelHaenszel`

function. This is specified by the `match`

argument. By default, it takes the value `"score"`

and the test score (i.e. raw score) is computed. The second option is to assign to `match`

a vector of continuous or discrete numeric values, which acts as the matching criterion. Note that for consistency this vector should not belong to the `data`

matrix.

Option `anchor`

sets the items which are considered as anchor items for computing generalized Mantel-Haenszel statistics. Items other than the anchor items and
the tested item are discarded. `anchor`

must hold integer values specifying the column numbers of the corresponding anchor items. It is primarily designed to
perform item purification.

### Value

A vector with the values of the generalized Mantel-Haenszel DIF statistics.

### 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

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

Penfield, R. D. (2001). Assessing differential item functioning among multiple groups: a comparison of three Mantel-Haenszel procedures. *Applied Measurement in Education, 14*, 235-259. doi: 10.1207/S15324818AME1403_3

Somes, G. W. (1986). The generalized Mantel-Haenszel statistic. *The American Statistician, 40*, 106-108. doi: 10.2307/2684866

### See Also

### Examples

```
## Not run:
# Loading of the verbal data
data(verbal)
attach(verbal)
# Creating four groups according to gender (0 or 1) and trait anger
# score ("Low" or "High")
# Reference group: women with low trait anger score (<=20)
group <- rep(0, nrow(verbal))
group[Anger>20 & Gender==0] <- 1
group[Anger<=20 & Gender==1] <- 2
group[Anger>20 & Gender==1] <- 3
# Without continuity correction
genMantelHaenszel(verbal[,1:24], group)
# Removing item 6 from the set of anchor items
genMantelHaenszel(verbal[,1:24], group, anchor = c(1:5, 7:24))
## End(Not run)
```

*difR*version 5.1 Index]