genMantelHaenszel {difR}

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 Details.

match

specifies the type of matching criterion. Can be either "score" (default) to compute the test score, or any continuous or discrete variable with the same length as the number of rows of data. See Details.

anchor

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

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
[e-mail], http://www.cdame.uqam.ca/
David Magis
Department of Psychology, University of Liege
Research Group of Quantitative Psychology and Individual Differences, KU Leuven
[e-mail], 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
[e-mail], 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

difGMH

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)