difStd {difR}

Standardization DIF method

Description

Performs DIF detection using standardization method.

Usage

difStd(Data, group, focal.name, anchor = NULL, match = "score", 
  	stdWeight = "focal", thrSTD = 0.1, purify = FALSE, nrIter = 10, 
  	save.output = FALSE, output = c("out", "default"))
## S3 method for class 'PDIF'
print(x, ...)
## S3 method for class 'PDIF'
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 data) of group membership. See Details.

focal.name

numeric or character indicating the level of group which corresponds to the focal group.

anchor

either NULL (default) or a vector of item names (or identifiers) to specify the anchor items. 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.

stdWeight

character: the type of weights used for the standardized P-DIF statistic. Possible values are "focal" (default), "reference" and "total". See Details.

thrSTD

numeric: the threshold (cut-score) for standardized P-DIF statistic (default is 0.10).

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).

save.output

logical: should the output be saved into a text file? (Default is FALSE).

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 "default" (default value). See Details.

x

the result from a PDIF class object.

pch, col

type of usual pch and col graphical options.

number

logical: should the item number identification be printed (default is TRUE).

save.plot

logical: should the plot be saved into a separate file? (default is FALSE).

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 "default" (default value), and the third component is the file extension, either "pdf" (default) or "jpeg". See Details.

...

other generic parameters for the plot or the print functions.

Details

The method of standardization (Dorans and Kulick, 1986) allows for detecting uniform differential item functioning without requiring an item response model approach.

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 only two different values, either as numeric or character. The focal group is defined by the value of the argument focal.name.

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

The threshold (or cut-score) for classifying items as DIF has to be set by the user by the argument thrSTD. Default value is 0.10 but Dorans (1989) also recommends value 0.05. For this reason it is not possible to provide asymptotic p-values.

The weights for computing the standardized P-DIF statistics are defined through the argument stdWeight, with possible values "focal" (default value), "reference" and "total". See stdPDIF for further details.

In addition, two types of effect sizes are displayed. The first one is obtained from the standardized P-DIF statistic itself. According to Dorans, Schmitt and Bleistein (1992), the effect size of an item is classified as negligible if |St-P-DIF| \leq 0.05, moderate if 0.05 \leq |St-P-DIF| \leq 0.10, and large if if |St-P-DIF| \geq 0.10. The second one is based on the transformation to the ETS Delta Scale (Holland and Thayer, 1985) of the standardized 'alpha' values (Dorans, 1989; Holland, 1985). The values of the effect sizes, together with the Dorans, Schmitt and Bleistein (DSB) and the ETS Delta scale (ETS) classification, are printed with the output.

Item purification can be performed by setting purify to TRUE. Purification works as follows: if at least one item was detected as functioning differently at some 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.

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 difStd, as displayed by the print.PDIF 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.PDIF function displays the DIF statistics in a plot, with each item on the X axis. The type of point and the color 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 "PDIF" with the following arguments:

PDIF

the values of the standardized P-DIF statistics.

stdAlpha

the values of the standardized alpha values (for effect sizes computation).

alpha

the value of alpha argument.

thr

the value of the thrSTD argument.

DIFitems

either the column indicators of the items which were detected as DIF items, or "No DIF item detected".

match

a character string, either "score" or "matching variable" depending on the match argument.

purification

the value of purify option.

nrPur

the number of iterations in the item purification process. Returned only if purify is TRUE.

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 purify is TRUE.

convergence

logical indicating whether the iterative item purification process stopped before the maximal number nrIter of allowed iterations. Returned only if purify is TRUE.

names

the names of the items.

anchor.names

the value of the anchor argument.

stdWeight

the value of the stdWeight argument.

save.output

the value of the save.output argument.

output

the value of the output argument.

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

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.

Dorans, N. J. (1989). Two new approaches to assessing differential item functioning. Standardization and the Mantel-Haenszel method. Applied Measurement in Education, 2, 217-233. doi: 10.1207/s15324818ame0203_3

Dorans, N. J. and Kulick, E. (1986). Demonstrating the utility of the standardization approach to assessing unexpected differential item performance on the Scholastic Aptitude Test. Journal of Educational Measurement, 23, 355-368. doi: 10.1111/j.1745-3984.1986.tb00255.x

Dorans, N. J., Schmitt, A. P. and Bleistein, C. A. (1992). The standardization approach to assessing comprehensive differential item functioning. Journal of Educational Measurement, 29, 309-319. doi: 10.1111/j.1745-3984.1992.tb00379.x

Holland, P. W. (1985, October). On the study of differential item performance without IRT. Paper presented at the meeting of Military Testing Association, San Diego (CA).

Holland, P. W. and Thayer, D. T. (1985). An alternative definition of the ETS delta scale of item difficulty. Research Report RR-85-43. Princeton, NJ: Educational Testing Service.

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

See Also

stdPDIF, dichoDif

Examples

## Not run: 

 # Loading of the verbal data
 data(verbal)

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

 # Three equivalent settings of the data matrix and the group membership
 difStd(verbal, group = 25, focal.name = 1)
 difStd(verbal, group = "Gender", focal.name = 1)
 difStd(verbal[,1:24], group = verbal[,25], focal.name = 1)

 # With other weights
 difStd(verbal, group = "Gender", focal.name = 1, stdWeight = "reference")
 difStd(verbal, group = "Gender", focal.name = 1, stdWeight = "total")
 
 # With item purification
 difStd(verbal, group = "Gender", focal.name = 1, purify = TRUE)
 difStd(verbal, group = "Gender", focal.name = 1, purify = TRUE, nrIter = 5)

 # With items 1 to 5 set as anchor items
 difStd(verbal, group = "Gender", focal.name = 1, anchor = 1:5)
 difStd(verbal, group = "Gender", focal.name = 1, anchor = 1:5, purify = TRUE)


 # With detection threshold of 0.05
 difStd(verbal, group = "Gender", focal.name = 1, thrSTD = 0.05)

 # Saving the output into the "STDresults.txt" file (and default path)
 r <- difStd(verbal, group = 25, focal.name = 1, save.output  =  TRUE, 
            output = c("STDresults","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)