difGMH {difR} | R Documentation |
Generalized Mantel-Haenszel DIF method
Description
Performs DIF detection among multiple groups using the generalized Mantel-Haenszel method.
Usage
difGMH(Data, group, focal.names, anchor = NULL, match = "score", alpha = 0.05,
purify = FALSE, nrIter = 10, p.adjust.method = NULL, save.output = FALSE,
output = c("out", "default"))
## S3 method for class 'GMH'
print(x, ...)
## S3 method for class 'GMH'
plot(x, pch = 8, number = TRUE, col = "red", save.plot = FALSE,
save.options = c("plot", "default", "pdf"), ...)
Arguments
Data |
numeric: either the data matrix only, or the data matrix plus the vector of group membership. See Details. |
group |
numeric or character: either the vector of group membership or the column indicator (within |
focal.names |
numeric or character vector indicating the levels of |
anchor |
either |
match |
specifies the type of matching criterion. Can be either |
alpha |
numeric: significance level (default is 0.05). |
purify |
logical: should the method be used iteratively to purify the set of anchor items? (default is FALSE). |
nrIter |
numeric: the maximal number of iterations in the item purification process (default is 10). |
p.adjust.method |
either |
save.output |
logical: should the output be saved into a text file? (Default is |
output |
character: a vector of two components. The first component is the name of the output file, the second component is either the file path or
|
x |
the result from a |
pch , col |
type of usual |
number |
logical: should the item number identification be printed (default is |
save.plot |
logical: should the plot be saved into a separate file? (default is |
save.options |
character: a vector of three components. The first component is the name of the output file, the second component is either the file path or
|
... |
other generic parameters for the |
Details
The generalized Mantel-Haenszel statistic (Somes, 1986) can be used to detect uniform differential item functioning among multiple groups, without requiring an item response model approach (Penfield, 2001).
The Data
is a matrix whose rows correspond to the subjects and columns to the items. In addition, Data
can hold the vector of group membership.
If so, group
indicates the column of Data
which corresponds to the group membership, either by specifying its name or by giving the column number.
Otherwise, group
must be a vector of same length as nrow(Data)
.
Missing values are allowed for item responses (not for group membership) but must be coded as NA
values. They are discarded from sum-score computation.
The vector of group membership must hold at least three value, either as numeric or character. The focal groups are defined by the values of the argument
focal.names
. If there is a unique focal group, then difGMH
returns the output of difMH
(without continuity correction).
The threshold (or cut-score) for classifying items as DIF is computed as the quantile of the chi-squared distribution with lower-tail
probability of one minus alpha
and with as many degrees of freedom as the number of focal groups.
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.
Item purification can be performed by setting purify
to TRUE
. Purification works as follows: if at least one item detected as functioning
differently at the first step of the process, then the data set of the next step consists in all items that are currently anchor (DIF free) items, plus the
tested item (if necessary). The process stops when either two successive applications of the method yield the same classifications of the items (Clauser and Mazor,
1998), or when nrIter
iterations are run without obtaining two successive identical classifications. In the latter case a warning message is printed.
Adjustment for multiple comparisons is possible with the argument p.adjust.method
. The latter must be an acronym of one of the available adjustment methods of the p.adjust
function. According to Kim and Oshima (2013), Holm and Benjamini-Hochberg adjustments (set respectively by "Holm"
and "BH"
) perform best for DIF purposes. See p.adjust
function for further details. Note that item purification is performed on original statistics and p-values; in case of adjustment for multiple comparisons this is performed after item purification.
A pre-specified set of anchor items can be provided through the anchor
argument. It must be a vector of either item names (which must match exactly the column names of Data
argument) or integer values (specifying the column numbers for item identification). In case anchor items are provided, they are used to compute the test score (matching criterion), including also the tested item. None of the anchor items are tested for DIF: the output separates anchor items and tested items and DIF results are returned only for the latter. Note also that item purification is not activated when anchor items are provided (even if purify
is set to TRUE
). By default it is NULL
so that no anchor item is specified.
The output of the difGMH
, as displayed by the print.GMH
function, can be stored in a text file provided that save.output
is set to TRUE
(the default value FALSE
does not execute the storage). In this case, the name of the text file must be given as a character string into the first component
of the output
argument (default name is "out"
), and the path for saving the text file can be given through the second component of output
. The
default value is "default"
, meaning that the file will be saved in the current working directory. Any other path can be specified as a character string: see
the Examples section for an illustration.
The plot.GMH
function displays the DIF statistics in a plot, with each item on the X axis. The type of point and the colour are fixed by the usual pch
and col
arguments. Option number
permits to display the item numbers instead. Also, the plot can be stored in a figure file, either in PDF or JPEG
format. Fixing save.plot
to TRUE
allows this process. The figure is defined through the components of save.options
. The first two components
perform similarly as those of the output
argument. The third component is the figure format, with allowed values "pdf"
(default) for PDF file and
"jpeg"
for JPEG file.
Value
A list of class "GMH" with the following arguments:
GMH |
the values of the generalized Mantel-Haenszel statistics. |
p.value |
the vector of p-values for the generalized Mantel-Haenszel statistics. |
alpha |
the value of |
thr |
the threshold (cut-score) for DIF detection. |
DIFitems |
either the items which were detected as DIF items, or "No DIF item detected". |
match |
a character string, either |
p.adjust.method |
the value of the |
adjusted.p |
either |
purification |
the value of |
nrPur |
the number of iterations in the item purification process. Returned only if |
difPur |
a binary matrix with one row per iteration in the item purification process and one column per item. Zeros and ones in the i-th
row refer to items which were classified respectively as non-DIF and DIF items at the (i-1)-th step. The first row corresponds to the initial
classification of the items. Returned only if |
convergence |
logical indicating whether the iterative item purification process stopped before the maximal number |
names |
the names of the items. |
anchor.names |
the value of the |
focal.names |
the value of |
save.output |
the value of the |
output |
the value of the |
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
Clauser, B. E. and Mazor, K. M. (1998). Using statistical procedures to identify differential item functioning test items. Educational Measurement: Issues and Practice, 17, 31-44.
Kim, J., and Oshima, T. C. (2013). Effect of multiple testing adjustment in differential item functioning detection. Educational and Psychological Measurement, 73, 458–470. doi: 10.1177/0013164412467033
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 ("Man" or "Woman") and
# trait anger score ("Low" or "High")
group <- rep("WomanLow",nrow(verbal))
group[Anger>20 & Gender==0] <- "WomanHigh"
group[Anger<=20 & Gender==1] <- "ManLow"
group[Anger>20 & Gender==1] <- "ManHigh"
# New data set
Verbal <- cbind(verbal[,1:24], group)
# Reference group: "WomanLow"
names <- c("WomanHigh", "ManLow", "ManHigh")
# Three equivalent settings of the data matrix and the group membership
difGMH(Verbal, group = 25, focal.names = names)
difGMH(Verbal, group = "group", focal.name = names)
difGMH(Verbal[,1:24], group = Verbal[,25], focal.names = names)
# Multiple comparisons adjustment using Benjamini-Hochberg method
difGMH(Verbal, group = 25, focal.names = names, p.adjust.method = "BH")
# With item purification
difGMH(Verbal, group = 25, focal.names = names, purify = TRUE)
difGMH(Verbal, group = 25, focal.names = names, purify = TRUE, nrIter = 5)
# With items 1 to 5 set as anchor items
difMH(Verbal, group = 25, focal.name = names, anchor = 1:5)
difMH(Verbal, group = 25, focal.name = names, anchor = 1:5, purify = TRUE)
# Saving the output into the "GMHresults.txt" file (and default path)
r <- difGMH(Verbal, group = 25, focal.name = names, save.output = TRUE,
output = c("GMHresults","default"))
# Graphical devices
plot(r)
# Plotting results and saving it in a PDF figure
plot(r, save.plot = TRUE, save.options = c("plot", "default", "pdf"))
# Changing the path, JPEG figure
path <- "c:/Program Files/"
plot(r, save.plot = TRUE, save.options = c("plot", path, "jpeg"))
## End(Not run)