difSIBTEST: SIBTEST and Crossing-SIBTEST DIF method

Description

Performs DIF detection using SIBTEST (Shealy & Stout, 1993) or the modified Crossing-SIBTEST method (Chalmers, 2018).

Usage

difSIBTEST(
  Data,
  group,
  focal.name,
  type = "udif",
  anchor = NULL,
  alpha = 0.05,
  purify = FALSE,
  nrIter = 10,
  p.adjust.method = NULL,
  puriadjType = "simple",
  save.output = FALSE,
  output = c("out", "default")
)
# S3 method for SIBTEST
plot(
  x,
  pch = 8,
  number = TRUE,
  col = "red",
  save.plot = FALSE,
  save.options = c("plot", "default", "pdf"),
  ...
)

Value

A list of class "SIBTEST" with the following arguments:

Beta: the values of the SIBTEST Beta values.
SE: the standard errors of the Beta values.
X2: the values of the SIBTEST or Crossing-SITBTEST chi-square statistics.
df: the degrees of freedom for X2 statistics.
p.value: the p-values for the SIBTEST or Crossing-SIBTEST statistics.
type: the value of the type argument.
alpha: the value of alpha argument.
DIFitems: either the column indicators of the items which were detected as DIF items, or "No DIF item detected".
p.adjust.method: the value of the p.adjust.method argument.
adjusted.p: either NULL or the vector of adjusted p-values for multiple comparisons.
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.
puriadjType: the value of puriadjType option. Returned only when purify is TRUE.
names: the names of the items or NULL if the items have no name.
anchor.names: the value of the anchor argument.
save.output: the value of the save.output argument.
output: the value of the output argument.

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.
type: character: the type of DIF effect to test. Possible values are "udif" (default) for uniform DIF using SIBTEST, or "nudif" for nonuniform DIF using Crossing-SIBTEST (CSIBTEST).
anchor: either NULL (default) or a vector of item names (or identifiers) to specify the anchor items. See Details.
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 NULL (default) or the acronym of the method for p-value adjustment for multiple comparisons. See Details.
puriadjType: character: type of combination of the item purification and the method for p-value adjustment for multiple comparisons. Either "simple" for the item purification followed by the selected p-adjustment method (default) or "combined" for the p-adjustment method applied in each iteration of item purification. For details, see Hladká, Martinková, and Magis (2024). Argument is ignored when purify is FALSE or p.adjust.method is NULL.
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 "SIBTEST" 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.

Author

David Magis
Data science consultant at IQVIA Belux
Brussels, Belgium
Adela Hladka (nee Drabinova)
Institute of Computer Science of the Czech Academy of Sciences
hladka@cs.cas.cz

Details

The SIBTEST method (Shealy & Stout, 1993) allows for detecting uniform differential item functioning without requiring an item response model approach. Its modified version, the Crossing-SIBTEST (Chalmers, 2018; Li & Stout, 1996), focuses on nonuniform DIF instead. This function provides a wrapper to the SIBTEST function from the mirt package (Chalmers, 2012) to fit within the difR framework (Magis et al., 2010). Therefore, if you are using this function for publication purposes please cite Chalmers (2018; 2012) and Magis et al. (2010).

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).

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 type of DIF effect, uniform through SIBTEST or nonuniform through Crossing-SIBTEST, is determined by the type argument. By default it is "udif" for uniform DIF, and may take the value "nudif" for nonuniform DIF.

The threshold (or cut-score) for classifying items as DIF is computed as the quantile of the chi-square distribution with lower-tail probability of one minus alpha and with one degree of freedom. Note that the degrees of freedom are also returned by the df argument.

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 & 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 difSIBTEST, as displayed by the print.SIBTEST 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.SIBTEST 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. Note that no plot is returned for exact inference.

References

Chalmers, R. P. (2012). mirt: A Multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1--29, tools:::Rd_expr_doi("10.18637/jss.v048.i06")

Chalmers, R. P. (2018). Improving the Crossing-SIBTEST statistic for detecting non-uniform DIF. Psychometrika, 83(2), 376--386, tools:::Rd_expr_doi("10.1007/s11336-017-9583-8")

Hladká, A., Martinková, P., and Magis, D. (2023). Combining item purification and multiple comparison adjustment methods in detection of differential item functioning. Multivariate Behavioral Research, 59(1), 46--61, tools:::Rd_expr_doi("10.1080/00273171.2023.2205393")

Kim, J., and Oshima, T. C. (2013). Effect of multiple testing adjustment in differential item functioning detection. Educational and Psychological Measurement, 73, 458--470, tools:::Rd_expr_doi("10.1177/0013164412467033")

Li, H.-H., and Stout, W. (1996). A new procedure for detection of crossing DIF. Psychometrika, 61, 647--677, tools:::Rd_expr_doi("10.1007/BF02294041")

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, tools:::Rd_expr_doi("10.3758/BRM.42.3.847")

Shealy, R. and Stout, W. (1993). A model-based standardization approach that separates true bias/DIF from group ability differences and detect test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159--194, tools:::Rd_expr_doi("10.1007/BF02294572")

Examples

Run this code


if (FALSE) {

 # 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
 r <- difSIBTEST(verbal, group = 25, focal.name = 1)
 difSIBTEST(verbal, group = "Gender", focal.name = 1)
 difSIBTEST(verbal[, 1:24], group = verbal[, 25], focal.name = 1)

 # Test for nonuniform DIF
 difSIBTEST(verbal, group = 25, focal.name = 1, type = "nudif")

 # Multiple comparisons adjustment using Benjamini-Hochberg method
 difSIBTEST(verbal, group = 25, focal.name = 1, p.adjust.method = "BH")

 # With item purification
 difSIBTEST(verbal, group = 25, focal.name = 1, purify = TRUE)
 r2 <- difSIBTEST(verbal, group = 25, focal.name = 1, purify = TRUE, nrIter = 5)

 # With combination of item purification and multiple comparisons adjustment
 difSIBTEST(verbal, group = 25, focal.name = 1, purify = TRUE,
            p.adjust.method = "BH", puriadjType = "simple")
 difSIBTEST(verbal, group = 25, focal.name = 1, purify = TRUE,
            p.adjust.method = "BH", puriadjType = "combined")

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

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

 # Graphical devices
 plot(r)
 plot(r2)

 # 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"))
}

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