Provides a collection of standard methods to detect differential item functioning among dichotomously scored items. Methods for uniform and non-uniform DIF, based on test-score or IRT methods, for comparing two or more than two groups of respondents, are available (Magis, Beland, Tuerlinckx and De Boeck,A General Framework and an R Package for the Detection of Dichotomous Differential Item Functioning, Behavior Research Methods, 42, 2010, 847-862

```
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* *
* Changes and Developments in the difR Package *
* *
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```

- Changes in difR 5.0 (2018-05-08) -

MAJOR UPDATES

o The SIBTEST method is now available. It is implemented through the 'sibTest()' and 'difSIBTEST()' functions that work similarly to other DIF methods. These functions call the 'SIBTEST()' function from package 'mirt' (Chalmers, 2012).

o Functions 'selectDif()' and 'dichoDif()' were updated accordingly.

o All 'dif...()' functions return now an additional argument called 'p.value' that directly provides the p-values of the selected DIF method. This is to simplify the extraction of the results for e.g., simulation studies. Many thanks to Phil Chalmers (University fo Georgia, Athens, GA; [email protected]) for suggesting this improvement. See other poins below.

o For 'difMH()' function, the $p.value output argument replaces the former $Pval argument (which was returned for exact MH statistic only).

o For 'difStd()' function, the $p.value output argument is not added since the DIF statistic has no known NULL distribution.

o The 'difTID()' function has been thoroughly rewritten in order to call the 'deltaPlot()' function from package 'deltaPlotR' instead, as it is more complete than the former 'difTID()' function.

o Consequently, the 'trItemDiff()' function was removed and functions 'selectDif()' and 'dichoDif()' were updated.

MINOR UPDATES

o DOI numbers were added to the references.

o Some typos were fixed.

- Changes in difR 4.8 (2018-04-28) -

MAJOR UPDATES

o The functions 'mantelHaenszel()', 'breslowDay()', 'genMantelHaenszel()', 'stdPDIF()', 'difMH()', 'difBD()', 'difGMH()', 'difStd()', 'selectDif()', 'selectGenDif()', 'dichoDif()' and 'genDichoDif()' were updated to allow the definition of the matching criterion from an external variable instead of the test score. This is specified through the new 'match' argument.

MINOR UPDATES

o Affiliations and email addresses were updated.

o Some typos were fixed.

- Changes in difR 4.7 (2016-11-22) -

MAJOR UPDATES

o The license for 'difR' package was updated to a GPL license.

o Adjustement for multiple comparisons are now available for all DIF methods, except 'difStd()' (standardized-P-DIF) and 'difTID()' (Transformed Item Difficulties). The argument 'p.adjust.method' was added to specify which adjustment to apply (e.g., "BH" for Benjamini-Hochberg). Adjusted p-values are then returned and DIF identification is based on these adjusted p-values. Note that methods 'difStd()' and 'difTID()' do not return p-values from null statistical distributions and can therefore ot be updated for multiple comparisons. Many thanks to Patricia Martinkova (Czech Academy of Sciences, Prague, Czech Republic; [email protected]) for suggesting this improvement.

o The functions 'selectDif()', 'selectGenDif()', 'dichoDif()' and 'genDichoDif()' were updated accordingly.

o The 'Logistik()' function returns now in addition the matrices 'seM0' and 'seM1' with the standard error values of the parameter estimates in 'parM0' and 'parM1' matrices (with the same format).

o The 'difLogistic()' function returns now in addition the matrices 'logitSe', wth the standard error values of the parameters hold in matrix 'logitPar', as well as matrix 'seM0' from the output of 'Logistik()' function.

o The functions 'Logistik()' and 'difLogistic()' have a new argument 'all.cov' to specify whether all covariance matrices of model parameters should be returned (as lists), for both nested models and all items. Returned arguments are called 'cov.M0' and 'cov.M1'. Default is FALSE so these lists are returned as NULL values.

MINOR UPDATES

o A minor bug was fixed in the 'print.Lord' method. When the 3PL was used with fixed guessing parameter, the 'print.Lord' function was reporting p-values computed with 3 degrees of freedom, while in this case it should be 2 degrees of freedom. Many thanks to Patricia Martinkova (Czech Academy of Sciences, Prague, Czech Republic; [email protected]) for noticing this issue.

o A minor bug was fixed in the 'difMH' method. In case of item purification with asymptotic (not exact) statistics, the DIF detection threshold returned by the function was always the one from the chi-square distrib ution, even when the 'logOR' statistic was used (the computations were however correct).

o The CITATION file was updated.

o Several typos were fixed.

- Changes in difR 4.6 (2015-04-29) -

MAJOR UPDATES

o The 'Logistik' function was rewritten. It now allows to specify a matching criterion that is not the test score (through the 'match' argument). It also permits to specify a continuous group membership variable instead of a binary group membership. This is done by the 'member.type' argument. Finally, the item responses are directly modeled in the logistic regression, not as a two-way table anymore. This is to fix an issue related to the computation of Nagelkerke's R^2 coefficients (which are now returned separately for the two fitted models). Many thanks to Bruno Facon (Department of Psychology, Universite Lille-Nord de France, France) for noticing this issue.

o Similarly, the 'genLogistik' function was rewritten.
It now allows to specify a matching criterion that is
not the test score (through the 'match' argument).
Also, the item responses are directly modeled in the

logistic regression, not as a two-way table anymore.
Nagelkerke's R^2 coefficients are also now returned
separately for the two fitted models.

o The 'difLogReg' function was created as a meta-function for logistic regression DIF analysis. It encompasses all options from 'difLogistic' and 'difGenLogistic' and returns the corresponding output for simplicity of use.

o The 'difLogistic', 'difGenlogistic', 'selectDif', 'selectGenDif', 'dichoDif' and 'genDichoDif' functions were updated according to the previous modifications.

o The 'difMH', 'difStd', 'difBD', 'difTID', 'difLogistic', 'difGMH', 'difGenLogistic', 'difLogReg', 'difLord', 'difRaju' and 'difGenLord' methods now allow specifying a set of anchor items (that are assumed to be DIF-free by the user). The 'anchor' argument was added. If supplied, anchor items are used to compute the test score together with the tested item) and anchor items are not tested for DIF. Item purification is disabled if anchor items are provided.

o The functions 'selectDif', 'selectGenDif', 'dichoDif' and 'genDichoDif' have been updated with the 'anchor' argument.

MINOR UPDATES

o The DESCRIPTION file was updated to meet CRAN policy.

o Several typos were fixed.

- Changes in difR 4.5 (2013-04-07) -

MAJOR UPDATES

o In the 'itemPar2PL', 'itemPar3PL' and 'itemPar3PLconst'

functions, the extraction of the standard errors and
covariances between the item parameters was not
performed accurately from the output of the 'ltm' and
'tpm' functions. Actually, the values were extracted
from the linear parametrization of the model, not from
its IRT form. This was corrected by an appropriate

application of the Delta method. A note was also added
in the 'difR/doc' folder with mathematical details and
notations for the Delta method. Many thanks to Emily
Price (Department of Educational Research and Evaluation,

Ohio University) for noticing this issue, and to Dimitris
Rizopoulos (Erasmus University Rotterdam, The Netherlands)
for providing key information to fix this problem.

MINOR UPDATES

o The authors' affiliations were updated.

o Several typos were fixed.

- Changes in difR 4.4 (2013-01-29) -

MINOR UPDATES

o The 'mantelHaenszel' function was updated to avoid a technical issue that was occuring in extreme cases. When all items but one are flagged as DIF, and item purification process is run, then 'mantelHaenszel' was trying to compute 'rowSums' on a vector and not on a one-column matrix, thus leading to an error. This was fixed. Many thanks to Yung Chih Ou (Department of Educational Psychology and Counseling, National Taiwan Normal University) for noticing this issue.

- Changes in difR 4.3 (2012-06-13) -

MINOR UPDATES

o The computation of the R^2 coefficients in the
'Logistik' function was slightly modified to overcome
a mathematical issue. With large data sets, the null
and model deviances are very large and the ratio of

exponentials of the deviances might return NaN values
and affect the output of the 'difLogistic'. Many thanks
to Marco Pomati (University of Bristol, UK) for
noticing this issue.

o Several typos were fixed.

- Changes in difR 4.2 (2012-04-01) -

MAJOR UPDATES

o The Raju method was improved. Two ways of computing the area between the ICC are available: the "unsigned" one and the "signed" one. See Raju (1990) for further details. Both the 'RajuZ' and the 'difRaju' have now an additional 'signed' logical argument to select which type of area to compute. Many thanks to Dylan Molenaar (Department of Psychology, University of Amsterdam, The Netherlands) for noticing this alternative.

o Because of the previous update, the functions 'difRaju', 'plot.Raj', 'selectDif' and 'dichoDif' were updated.

o The exact Mantel-Haenszel test can now be carried out. The argument 'exact' was added to the 'mantelHaenszel' function. By default, the asymptotic test (Holland and Thayer, 1988) is performed.

o Because of the previous update, the functions 'difMH', 'plot.MH', 'print.MH', 'selectDif' and 'dichoDif' were updated.

MINOR UPDATES

o The difR package was updated to compile under versions 2.14.0 and later of R.

o Several typos were fixed.

- Changes in difR 4.1 (2011-06-22) -

MINOR UPDATE

o The R code used in 'mantelHaenszel' and 'difMH' functions was modified to overcome a technical issue. With some large data sets, the computation of MH DIF statistics was impossible due to integer overflow. The 'mantelHaenszel' function was then returning NA values, 'difMH' was stopping with an error message because of these NAs. The R code was modified to avoid integer overeflow and ensure stable computation of MH DIF statistics. Many thanks to Shih-Ying Yao (University of California - Berkeley) for noticing this issue and helping in solving it.

- Changes in difR 4.0 (2011-03-04) -

MAJOR UPDATES

o An important mistake in the R code has been fixed. Under the 3PL model, Lord's chi-squared statistics were were wrongly computed (see the 'LordChi2' help file for further details). This has now been fixed. Many thanks to J. Patrick Meyer (Curry School of Education, University of Virginia) for having discovered this mistake.

o The non-IRT methods of TID, Mantel-Haenszel, Breslow- Day, standardization and generalized Mantel-Haenszel can now handle data sets with missing values. They must be coded as NA values into the data set. Basically, they are withdrawn from the computation of sum-scores.

o The non-IRT methods of logistic regression and generalized logistic regression can now handle data sets with missing values. They must be coded as NA values into the data set. Basically, they are withdrawn from the computation of sum-scores and the fitting of logistic models.

o The IRT methods of Lord, Raju, LRT and generalized Lord can now handle data sets with missing values, as both 'ltm' and 'lme4' support for missing data. They must be coded as NA values into the data set. They are withdrawn from the fitting of the IRT models.

o The Transformed Item Difficulties (TID) method, also known as Angoff's Delta method, is now available. The function 'trItemDiff' computes the perpendicular distances and the 'difTID' function returns the full output, similarly to other DIF methods.

o An effect size measure has been added for the Lord and Raju methods when the 1PL model is used. It is based on the difference in item difficulties. See the help files of the methods 'difLord' and 'difRaju'.

o The 'itemPar1PL' has a new argument, called 'discr', to fix the common discrimination parameter. By default it is equal to 1, and can be changed to any other value. Alternatively, fixing it to 'NULL' will lead to the estimation of this common parameter (only with the 'ltm' package).

o The 'difLogistic' and 'difGenLogistic' functions return now the fitted parameters of the null model M_0 (see the help file for details on this null model). This is to propose other graphical displays of the item curves (see below).

o The 'plot.Logistic' and 'plot.genLogistic' functions have been updated. The new argument 'itemFit' permits to select whether the item curves are displayed according to the best model (i.e. model M_0 if the item is flagged as DIF and model M_1 otherwise) or the null model (i.e. M_0).

MINOR UPDATES

o The functions 'selectDif' and 'dichoDif' have been updated to allow for the TID method.

o The functions 'itemParEst', 'difLord', 'difRaju', 'difGenLord', 'selectDif', 'selectGenDif', 'dichoDif' and 'genDichoDif' have been updated to incorporate the new 'discr' argument of 'itemPar1PL' function.

o The former argument 'thr' of 'difStd' method has been renamed to 'thrSTD', as there is now an equivalent one for the TID method that is called 'thrTID'.

o The 'plot.Logistic' and 'plot.Lord' functions have a new argument, called 'group.names', to provide the names of the reference and focal group for the legend.

o The 'plot.genLogistic' and 'plot.GenLord' functions have a new argument, called 'ref.name', to provide the name of the reference group for the legend.

o The help files have been checked, typos have been fixed and some descriptions have been rewritten for sake of consistency.

o The 'print.dichoDif' function has been slightly modified: the DIF methods are now printed as a list and not one after each other.

o A minor bug was fixed in the 'print.dichoDif' function: options of the Breslow-Day method were printed even when this method was not requested!

- Changes in difR 3.3 (2010-10-21) -

MAJOR UPDATES

o It is now possible to capture and save the output of each DIF method directly from the 'dif...' functions. The arguments 'save.output' and 'output' control for saving the output (as displayed by the corresponding 'print' function) into a text file, whose name and path are specified within the 'output' argument.

o The functions 'selectDif', 'selectGenDif', 'dichoDif' and 'genDichoDif' have been adapted in order to allow for saving their output too

o Similarly, the plots drawn from the 'plot' functions can be captured into either PDF or JPEG format, by using the newly added 'save.plot' and 'save.options' arguments. They define the name of the figure, the path where it is saved, and the format of the figure.

o In addition, the 'print' functions display a message to specify whether the output was saved (and where the saved file is located) or not, and the 'plot' functions display a message into the R console to specify whether the plot was not captured, the format is incorrect, or the plot was captured and where it was stored.

MINOR UPDATES

o Several help files have been updated to describe the corresponding 'plot' functions.

o Several typos have been fixed.

- Changes in difR 3.2 (2010-10-04) -

MINOR UPDATES

o The reference 'Magis, Beland, Tuerlinckx, and De Boeck (in press)' has been updated as the paper is now published.

o Some typos have been fixed.

- Changes in difR 3.1 (2010-06-22) -

MAJOR UPDATES

o The variance of the log odds-ratio statistic (Philips and Holland, 1987) has been added as output of the 'mantelHaenszel' function.

o The 'difMH' method has a new input argument called 'MHstat'. It specifies which DIF statistic must be considered. Default value 'MHChisq' sets the chi-square statistic, while 'logOR' imposes the log odds-ratio statistic.

o The commands 'print.MH', 'plot.MH', 'selectDif' and 'dichoDif' have been updated according to the changes in the 'difMH' command.

o The 'breslowDay' method has a new input argument called 'BDstat'. It specifies which DIF statistic must be considered. Default value 'BD' sets the Breslow-Day statistic as recommended by Aguerri et al. (2009), while 'trend' imposes the trend test statistic as recommended by Penfield (2003).

o The commands 'print.BD', 'selectDif' and 'dichoDif' have been updated according to the changes in the 'difBD' command.

MINOR UPDATES

o Some typos have been fixed.

o The reference 'Aguerri et al.' in the 'breslowDay' and 'difBD' commands has been updated.

- Changes in difR 3.0 (2010-04-20) -

MAJOR UPDATES

o The Wald statistic can now be used to flag items as DIF with both the logistic and the generalized logistic regression method. The new argument 'criterion' permits to select between 'LRT', the usual likelihood-ratio test, and 'Wald' for the Wald test. For the latter, an appropriate contrast matrix is built up internally.

o The command 'subtestLogistic' has been added to identify DIF items among a subset of groups of examinees, using the output of the 'difGenLogistic' command and the Wald test. Subtests are performed with appropriate contrast matrices built up internally.

o The standardized P-DIF statistics can now be computed with different weights. The default weights are based on the focal group, but other options are weights based on the reference group or on both groups together. The newly added argument 'stdWeight' in the functions 'stdPDIF' and 'difStd'.

o A second measure of effect size has been added for the standardization method. It is a Delta measure, similar to that of the Mantel-Haenszel method, and is described in Dorans (1989, p.228, Eqn. 15).

MINOR UPDATES

o The DESCRIPTION and CITATION files have been updated.

o The help file references have been updated.

o Several typos have been fixed in the help files.

o As a consequence of the first aforementioned major update, the first output argument of the 'Logistik' and 'genLogistik' functions, previously called 'deviance', have been renamed to 'stat'.

o The functions 'selectDif', 'dichoDif', 'selectGenDif' and 'genDichoDif' have been updated to incorporate the different changes of this version of difR.

o The coding of the effect size, which was previously done by means of star symbols (*, ** and ***), has been replaced by capital letters A, B and C for respectively negligible, moderate and large DIF sizes. This is to match the usual ETS conventions, and the change was made within the functions 'difMH', 'difStd', 'difLogistic' and 'difGenLogistic'.

o The TODO file has been added as a list of updates or adds-on for further versions of difR.

o The general 'difR-package' Rd file has been created. It contains a summary of the difR package, with a list of the methods currently implemented and a list of related references.

- Changes in difR 2.2 (2010-01-23) -

MINOR UPDATES

o The system files LICENSE and NEWS have been rewritten for an easier display in Rgui. Several non-ASCII characters have also been removed.

- Changes in difR 2.1 (2010-01-13) -

MINOR UPDATES

o The file CITATION has been created and added to the difR package.

o The display of the output of Mantel-Haenszel, standardization, logistic regression and generalized logistic regression have been slightly modified: the codes for the effect sizes are now returned as "Effect size codes" and not "Signif. codes" as in the previous version of difR.

o Several issues regarding non-ASCII characters in the help files have been fixed.

- Changes in difR 2.0 (2009-12-18) -

MAJOR UPDATES

o The logistic regression method has been improved. In addition to the deviance statistics, the function 'Logistik' also returns the fitted parameters of the two nested models which are compared by means of the likelihood-ratio test. Moreover, the argument 'type' has been added to test either nonuniform ('type="nudif"'), uniform ('type="udif"') or both DIF effects simultaneously ('type="both"'). The 'difLogistic' function has been updated acordingly, and returns the matrix with the fitted parameters of the best model for each item.

o The 'plot.Logistic' function has been improved to allow for plotting the logistic curves of any selected item according to the best model retained in the 'difLogistic' function.

o The 'plot.Lord' function has been improved to allow for plotting the item characteristic curves of any selected item, according to the model fitted and the returned item parameter estimates by the 'difLord' function.

o The 'plot.GenLord' function has been improved to allow for plotting the item characteristic curves of any selected item, according to the model fitted and the returned item parameter estimates by the 'difGenLord' function.

o The generalized logistic regression method is now available. It extends the logistic regression to more than one focal group, by an appropriate extension of the logistic models and the comparison of model parameters. The functions 'genLogistik' and 'difGenlogistic' are the corresponding versions of 'Logistik' and 'difLogistic' for this generalized method.

o Generalized versions of the functions 'selectDif' and 'dichoDif' have been developed for comparing the results of the generalized tests that are currently available (generalized Mantel-Haenszel, generalized Lord's chi-square test and generalized logistic regression). These are the 'genSelectDif' and 'genDichoDif' functions. They operate similarly to their "non-generalized" versions.

o Some measures of effect size are now available. For Mantel-Haenszel method, the effect size is the estimated common odds ratio, up to a transformation, to get the Delta measure on the ETS delta scale. For the standardization method, the standardized P-DIF statistic is used as the measure of effect size and the classification proposed by Dorans, Schmitt and Bleistein (1992) is adopted. For logistic regression and generalized logistic regression, the effect size is the difference in nagelkerke's R^2 coefficients between the two tested models. Both classification scales of Zumbo and Thomas (1997) and Jodoign and Gierl (2001) are available. These measures of effect sizes are displayed by the 'print' functions of the different methods.

MINOR UPDATES

o The functions 'selectDif' and 'dichoDif' have been updated to fix a minor bug occuring when Lord or Raju method was requested: the arguments 'engine', 'irtParam' and 'same.scale' were not passed correctly to thes functions.

o The examples taking a long time to run have been fixed using the 'Not run' approach.

o A minor bug was fixed in the Examples section of the 'mantelhaenszel' function: the definition of the data and group variable were incorrect.

o The significance code for standardization method was corrected in the 'difStd' function.

o The description of the package (in file DESCRIPTION) has been slightly modified.

o The help files of the commands 'breslowDay' and 'difBD' have been updated to mention that the currently implemented Breslow-Day statistic is the one given by Aguerri et al. (in press) and NOT the statistic for the test of trend in odds ratio heterogeneity (Penfield, 2003).

- Changes in difR 1.1 (2009-10-27) -

MINOR UPDATES

o The output of 'itemPar2PL' function was corrected to fix a bug. The parameter estimates of the item difficulties were actually not returned as item difficulties (in the IRT sense) but as additive intercept parameters as described in the help file of the 'ltm' function of the eponymous package. Version 1.1 of difR was corrected to return the correct item difficulty estimates. Note that functions 'itemPar1PL', 'itemPar3PL' and 'itemPar3PLconst' were not affected by this bug.

o The listing of the authors was corrected in the reference manual to fix a printing mistake.

o Several R codes in the Example sections have been preceded by the '#' symbol, so that they are not executed when copy-pasting the full R code from these sections. However, the R code itself remains functioning but it was not executed during the building of the difR package version 1.1. Anyone interested in seeing how the command works has just to copy-paste the R code without the '#' symbol. This is mentioned in the help files by the '(remove #)' message.