difLogistic: Logistic regression DIF method

In difR: Collection of Methods to Detect Dichotomous Differential Item Functioning (DIF)

Description

Performs DIF detection using logistic regression method.

Usage

difLogistic(Data, group, focal.name, anchor = NULL, member.type = "group", 
 	match = "score", type = "both", criterion = "LRT", alpha = 0.05, 
 	all.cov = FALSE, purify = FALSE, nrIter = 10, p.adjust.method = NULL, 
 	save.output = FALSE, output = c("out", "default"))
## S3 method for class 'Logistic'
print(x, ...)
## S3 method for class 'Logistic'
plot(x, plot="lrStat", item = 1, itemFit = "best", pch = 8, number = TRUE,
 	col = "red", colIC = rep("black", 2), ltyIC = c(1, 2), save.plot = FALSE,
 	save.options = c("plot", "default", "pdf"), group.names = NULL, ...)
 

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. Ignored if member.type is not "group".
anchor	either NULL (default) or a vector of item names (or identifiers) to specify the anchor items. Ignored if match is not "score". See Details.
member.type	character: either "group" (default) to specify that group membership is made of two groups, or "cont" to indicate that group membership is based on a continuous criterion. 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.
type	a character string specifying which DIF effects must be tested. Possible values are "both" (default), "udif" and "nudif". See Details.
criterion	a character string specifying which DIF statistic is computed. Possible values are "LRT" (default) or "Wald". See Details.
alpha	numeric: significance level (default is 0.05).
all.cov	logical: should all covariance matrices of model parameter estimates be returned (as lists) for both nested models and all items? (default is FALSE.
purify	logical: should the method be used iteratively to purify the set of anchor items? (default is FALSE). Ignored if match is not "score".
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.
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 Logistik class object.
plot	character: the type of plot, either "lrStat" (default) or "itemCurve". See Details.
item	numeric or character: either the number or the name of the item for which logistic curves are plotted. Used only when plot="itemCurve".
itemFit	character: the model to be selected for drawing the item curves. Possible values are "best" (default) for drawing from the best of the two models, and "null" for using fitted parameters of the null model M_0. Not used if "plot" is "lrStat". See Details.
pch, col	type of usual pch and col graphical options.
number	logical: should the item number identification be printed (default is TRUE).
colIC, ltyIC	vectors of two elements of the usual col and lty arguments for logistic curves. Used only when plot="itemCurve".
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.
group.names	either NULL (default) or a vector of two character strings giving the names of the reference group and the focal group (in this order) for display in the legend. Ignored if plot is "lrStat".
...	other generic parameters for the plot or the print functions.

Details

The logistic regression method (Swaminathan and Rogers, 1990) allows for detecting both uniform and non-uniform differential item functioning without requiring an item response model approach. It consists in fitting a logistic model with the matching criterion, the group membership and an interaction between both as covariates. The statistical significance of the parameters related to group membership and the group-score interaction is then evaluated by means of either the likelihood-ratio test or the Wald test. The argument type permits to test either both uniform and nonuniform effects simultaneously (type="both"), only uniform DIF effect (type="udif") or only nonuniform DIF effect (type="nudif"). The argument criterion permits to select either the likelihood ratio test (criterion=="LRT") or the Wald test (criterion=="Wald"). See Logistik for further details.

The group membership can be either a vector of two distinct values, one for the reference group and one for the focal group, or a continuous or discrete variable that acts as the "group" membership variable. In the former case, the member.type argument is set to "group" and the focal.name defines which value in the group variable stands for the focal group. In the latter case, member.type is set to "cont", focal.name is ignored and each value of the group represents one "group" of data (that is, the DIF effects are investigated among participants relying on different values of some discrete or continuous trait). See Logistik for further details.

The matching criterion can be either the test score or any other continuous or discrete variable to be passed in the Logistik 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 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 the fitting of the logistic models (see glm for further details).

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 one (if type="udif" or type="nudif") or two (if type="both") degrees of freedom.

Item purification can be performed by setting purify to TRUE. Purification works as follows: if at least one item is 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. Note that purification is possible only if the test score is considered as the matching criterion. Thus, purify is ignored when match is not "score".

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. By default it is NULL so that no anchor item is specified. Note also that item purification is not activated when anchor items are provided (even if purify is set to TRUE). Moreover, if the match argument is not set to "score", anchor items will not be taken into account even if anchor is not NULL.

The measures of effect size are provided by the difference Δ R^2 between the R^2 coefficients of the two nested models (Nagelkerke, 1991; Gomez-Benito, Dolores Hidalgo and Padilla, 2009). The effect sizes are classified as "negligible", "moderate" or "large". Two scales are available, one from Zumbo and Thomas (1997) and one from Jodoin and Gierl (2001). The output displays the Δ R^2 measures, together with the two classifications.

The output of the difLogistic, as displayed by the print.Logistic 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.

Two types of plots are available. The first one is obtained by setting plot="lrStat" and it is the default option. The likelihood ratio statistics are displayed on the Y axis, for each item. The detection threshold is displayed by a horizontal line, and items flagged as DIF are printed with the color defined by argument col. By default, items are spotted with their number identification (number=TRUE); otherwise they are simply drawn as dots whose form is given by the option pch.

The other type of plot is obtained by setting plot="itemCurve". In this case, the fitted logistic curves are displayed for one specific item set by the argument item. The latter argument can hold either the name of the item or its number identification. If the argument itemFit takes the value "best", the curves are drawn according to the output of the best model among M_0 and M_1. That is, two curves are drawn if the item is flagged as DIF, and only one if the item is flagged as non-DIF. If itemFit takes the value "null", then the two curves are drawn from the fitted parameters of the null model M_0. See Logistik for further details on the models. The colors and types of traits for these curves are defined by means of the arguments colIC and ltyIC respectively. These are set as vectors of length 2, the first element for the reference group and the second for the focal group. Finally, the argument group.names permits to display the names of the reference and focal groups (instead of "Reference" and "Focal") in the legend.

Both types of plots 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 "Logistic" with the following arguments:

Logistik	the values of the logistic regression statistics.
p.value	the vector of p-values for the logistic regression statistics.
logitPar	a matrix with one row per item and four columns, holding the fitted parameters of the best model (among the two tested models) for each item.
logitSe	a matrix with one row per item and four columns, holding the standard errors of the fitted parameters of the best model (among the two tested models) for each item.
parM0	the matrix of fitted parameters of the null model M_0, as returned by the Logistik command.
seM0	the matrix of standard error of fitted parameters of the null model M_0, as returned by the Logistik command.
cov.M0	either NULL (if all.cov argument is FALSE) or a list of covariance matrices of parameter estimates of the "full" model (M_0) for each item (if all.cov argument is TRUE).
cov.M1	either NULL (if all.cov argument is FALSE) or a list of covariance matrices of parameter estimates of the "reduced" model (M_1) for each item (if all.cov argument is TRUE).
deltaR2	the differences in Nagelkerke's R^2 coefficients. See Details.
alpha	the value of alpha argument.
thr	the threshold (cut-score) for DIF detection.
DIFitems	either the column indicators for the items which were detected as DIF items, or "No DIF item detected".
member.type	the value of the member.type argument.
match	a character string, either "score" or "matching variable" depending on the match argument.
type	the value of type argument.
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 of nrItem allowed iterations. Returned only if purify is TRUE.
names	the names of the items.
anchor.names	the value of the anchor argument.
criterion	the value of the criterion 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.

Finch, W.H. and French, B. (2007). Detection of crossing differential item functioning: a comparison of four methods. Educational and Psychological Measurement, 67, 565-582. doi: 10.1177/0013164406296975

Gomez-Benito, J., Dolores Hidalgo, M. and Padilla, J.-L. (2009). Efficacy of effect size measures in logistic regression: an application for detecting DIF. Methodology, 5, 18-25. doi: 10.1027/1614-2241.5.1.18

Hidalgo, M. D. and Lopez-Pina, J.A. (2004). Differential item functioning detection and effect size: a comparison between logistic regression and Mantel-Haenszel procedures. Educational and Psychological Measurement, 64, 903-915. doi: 10.1177/0013164403261769

Jodoin, M. G. and Gierl, M. J. (2001). Evaluating Type I error and power rates using an effect size measure with logistic regression procedure for DIF detection. Applied Measurement in Education, 14, 329-349. doi: 10.1207/S15324818AME1404_2

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

Nagelkerke, N. J. D. (1991). A note on a general definition of the coefficient of determination. Biometrika, 78, 691-692. doi: 10.1093/biomet/78.3.691

Swaminathan, H. and Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27, 361-370. doi: 10.1111/j.1745-3984.1990.tb00754.x

Zumbo, B.D. (1999). A handbook on the theory and methods of differential item functioning (DIF): logistic regression modelling as a unitary framework for binary and Likert-type (ordinal) item scores. Ottawa, ON: Directorate of Human Resources Research and Evaluation, Department of National Defense.

Zumbo, B. D. and Thomas, D. R. (1997). A measure of effect size for a model-based approach for studying DIF. Prince George, Canada: University of Northern British Columbia, Edgeworth Laboratory for Quantitative Behavioral Science.

See Also

Logistik, dichoDif

Examples

## Not run: 

 # Loading of the verbal data
 data(verbal)

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

 # Testing both DIF effects simultaneously
 # Three equivalent settings of the data matrix and the group membership
 r <- difLogistic(verbal, group=25, focal.name = 1)
 difLogistic(verbal, group = "Gender", focal.name = 1)
 difLogistic(verbal[,1:24], group = verbal[,25], focal.name = 1)

 # Returning all covariance matrices of model parameters
 difLogistic(verbal, group=25, focal.name = 1, all.cov = TRUE)

 # Testing both DIF effects with the Wald test
 r2 <- difLogistic(verbal, group = 25, focal.name = 1, criterion = "Wald")

 # Testing nonuniform DIF effect
 difLogistic(verbal, group = 25, focal.name = 1, type = "nudif")

 # Testing uniform DIF effect
 difLogistic(verbal, group = 25, focal.name = 1, type = "udif")

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

 # With item purification
 difLogistic(verbal, group = "Gender", focal.name = 1, purify = TRUE)
 difLogistic(verbal, group = "Gender", focal.name = 1, purify = TRUE, nrIter = 5)

 # With items 1 to 5 set as anchor items
 difLogistic(verbal, group = 25, focal.name = 1, anchor = 1:5)

 # Using anger trait score as the matching criterion
 difLogistic(verbal,group = 25, focal.name = 1,match = anger)

 # Using trait anger score as the group variable (i.e. testing
 # for DIF with respect to trait anger score)
 difLogistic(verbal[,1:24],group = anger,member.type = "cont")

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

 # Graphical devices
 plot(r)
 plot(r2)
 plot(r, plot = "itemCurve", item = 1)
 plot(r, plot = "itemCurve", item = 1, itemFit = "null")
 plot(r, plot = "itemCurve", item = 6)
 plot(r, plot = "itemCurve", item = 6, itemFit = "null")

 # 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)
 

difR documentation built on July 2, 2020, 3:34 a.m.