Package 'deltaPlotR'

Adjusting the proportions of correct responses for extreme cases

Description

This command modifies the proportions of correct responses when these equal either zero or one, for compatibility with the Delta plot.

Usage

adjustExtreme(data = NULL, group = NULL, focal.name = NULL, prop, 
 method = "constraint", const.range = c(0.001, 0.999), nrAdd = 1)

Arguments

data	numeric: the data matrix: one row per subject, one column per item, with possible entries 0, 1 or NA. Default value is NULL.
group	numeric or character: a vector of the same length as nrow(data) with two different values, one for the reference group, one for the focal group. Values can be either numeric or character. Default value is NULL.
focal.name	numeric or character: the value used in the group vector to refer to the focal group. Default value is NULL.
prop	numeric: a matrix with one row per item and two columns. The first column holds the percentage of correct responses for each item in the reference group, and the second column holds the same percentages but for the focal group.
method	character: the method used to modify the extreme proportions. Possible values are "constraint" (default) or "add". See Details.
const.range	numeric: a vector of two constraining proportions. Default values are 0.001 and 0.999. Ignored if method is "add".
nrAdd	integer: the number of successes and the number of failures to add to the data in order to adjust the proportions. Default value is 1. Ignored if method is "constraint".

Details

The Delta plot method requires the computation of the proportions o correct responses per item and per group. However, these proportions must be stricly greater than zero and smaller than one, since they are transformed onto z-scores. Thus, extreme proportions must be adjusted for proper use of the Delta plot.

Two approaches are currently implemented and set to adjustExtreme by the method argument.

The first method is the constraint method and is set by method="constraint". It simply consists in constraining the proportions within a specified range of values in (0,1). This restricted range of values is set by the const.range argument and takes the default value c(0.001, 0.999).

The second method is the so-called add method and is specified by method="add". It consists in rabitrarily adding some successes and the same number of failures to the data, in order to get a modified proportion of successes. This number of extra successes is set by the nrAdd argument, with default value one. In sum, by default one success one failure is added to the item responses, so that the newly computed proportion of successes is not extreme anymore, yet close to the original value. This default values refers to the so-called Laplace rule (see e.g. Jaynes, 2003).

The input arguments are: the data matrix of item responses (ith possible entries 0, 1 and NA for missing data), the vector of group memebership and the numeric (or character) value coding for the focal group. By default they take the NULL value so they can be left unassigned, but then only the "constraint" method can be applied. In any case, the matrix of proportions of correct responses per item and per group of respondents must be specified through the prop argument.

Value

A list with the following arguments:

adj.prop	the restricted proportions, in the same format as the input prop matrix.
method	the value of the methodargument or "constraint" if the latter was applied by lack of data.
range	the value of the const.range argument.
nrAdd	the value of the nrAdd argument.

Author(s)

David Magis
Post-doc Fellow of the National Funds for Scientific Research (FNRS, Belgium)
University of Liege
[email protected], http://ppw.kuleuven.be/okp/home/
Bruno Facon
Professor, Department of Psychology
Universite Lille-Nord de France
[email protected],

References

Angoff, W. H. and Ford, S. F. (1973). Item-race interaction on a test of scholastic aptitude. Journal of Educational Measurement, 10, 95-106.

Jaynes, E.T. (2003). Probability theory: The logic of science. Cambridge, UK: Cambridge University Press.

Magis, D., and Facon, B. (2012). Angoff's Delta method revisited: improving the DIF detection under small samples. British Journal of Mathematical and Statistical Psychology, 65, 302-321.

Magis, D. and Facon, B. (2014). deltaPlotR: An R Package for Differential Item Functioning Analysis with Angoff's Delta Plot. Journal of Statistical Software, Code Snippets, 59(1), 1-19. URL http://www.jstatsoft.org/v59/c01/

See Also

deltaPlot

Examples

# Loading of the verbal data
 data(verbal)
 attach(verbal)

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

 # Computing the proportions of correct answers per group
 prop <- matrix(NA, 24, 2)
 for (i in 1:24){
  prop[i,1] <- mean(verbal[verbal[,25]==0,i], na.rm=TRUE)
  prop[i,2] <- mean(verbal[verbal[,25]==1,i], na.rm=TRUE)
 }

 # "constraint" method
 adjustExtreme(data=verbal[,1:24], group=verbal[,25], focal.name=1, prop=prop)

 # "constraint" method with differently specified range
 adjustExtreme(data=verbal[,1:24], group=verbal[,25], focal.name=1, prop=prop,
  const.range=c(0.01,0.99))

 # "add" method
 adjustExtreme(data=verbal[,1:24], group=verbal[,25], focal.name=1, prop=prop,
  method="add")

 # "add" method with different number of successes added
 adjustExtreme(data=verbal[,1:24], group=verbal[,25], focal.name=1, prop=prop,
  method="add", nrAdd=2)

 # "constraint" method because of lack of provided data
 adjustExtreme(prop=prop)

---

Delta Plot method for dichotomous DIF

Description

This command computes the Delta plot statistics for dichotomous differential item functioning, with all associated output (Delta points, perpendicular distances). The modified Delta plot is also available, as well as several item purification techniques.

Usage

deltaPlot(data, type = "response", group, focal.name, thr = "norm", 
 purify = FALSE, purType = "IPP1", maxIter = 10, alpha =0.05, 
 extreme = "constraint", const.range = c(0.001, 0.999), nrAdd = 1, 
 save.output = FALSE,output = c("out", "default"))
## S3 method for class 'deltaPlot'
print(x, only.final = TRUE, ...)

Arguments

data	numeric: either (a) the data matrix with item responses and group membership, (b) the two-column matrix of proportions of correct responses per item and per group, or (c) the two-column matrix of Delta scores. See Details.
type	character: the type of data argument. Possible values are "response" (default), "prop" and "delta". See Details.
group	integer or character: a single value for locating the group membership column in the data argument. Ignored if type is not "response". See Details.
focal.name	numeric or character: the value used in the group membership column to refer to the focal group. Ignored if type is not "response". See Details.
thr	numeric or character: the threshold for flagging items as DIF. Can be a positive numeric value or "norm". See Details.
purify	logical: should item purification be performed? (Default is codeFALSE). See Details.
purType	character: the type of purification process to be run. Possible values are "IPP1" (default), "IPP2" and "IPP3". Ignored if purify is FALSE. See Details.
maxIter	integer: the maximum number of iteration in the purification process (default is 10). Ignored if purify is FALSE.
alpha	numeric: the significance level for calculating the detection threshold (default is 0.05). Ignored if thr is numeric.
extreme	character: the method used to modify the extreme proportions. Possible values are "constraint" (default) or "add". See Details.
const.range	numeric: a vector of two constraining proportions. Default values are 0.001 and 0.999. Ignored if extreme is "add".
nrAdd	integer: the number of successes and the number of failures to add to the data in order to adjust the proportions. Default value is 1. Ignored if extreme is "constraint".
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 ("out" by default), the second component is either the file path or "default" (default value). See Details.
x	an object of class "deltaPlot", typically the output of the deltaPlot function.
only.final	logical: should only the first and last steps of the purification process be printed? (default is TRUE. If FALSE all perpendicular distances, parameters of the major axis, and detection thresholds are printed additionally. Ignored if purify is FALSE.
...	other generic parameters for the plot or the print functions.

Details

Angoff's Delta plot (Angoff and Ford, 1973) is a straightforward test-score method to detect DIF among dichotomously scored items. Proportions of correct responses are computed first per item and per group of respondents, and are successively transformed onto z-scores and then onto $\Delta$ scores. The pairs of $\Delta$ scores can be displayed onto a scatter plot, called the Delta plot, and the majr axis of the ellipsoid of Delta points is derived. Eventually, items whose perpendicular distance (from the major axis) is too large are flagged as DIF. See Angoff and Ford (1973) for further details.

The data must be passed through the argument data and can be of three types. Each type is defined by the type argument and can take three values: "response", "prop" and "delta".

• If type is "response", the input data consist in a matrix with one row per respondent and $J+1$ columns, where $J$ is the number of items. In the colmuns coding for the items, only possible entries are 0 (for incorrect responses), 1 (for corect responses) and NA (for missing values). The extra column is used to define group membership: all respondents of the reference group take the same value (either numeric or character), and all respondents in the focal group take the same (numeric or character) value but different from the reference group. Note that the group membership column can be located anywhere in the data set (not especially in first or last position).

• If type is "prop", the input data consist in a two-column matrix with one row per item. Each row contains the proportions of correct responses, respectively in the reference group (first column) and in the focal group (second column).

• If type is "delta", the input data consist in a two-column matrix that is similar to that provided with the "prop" type of input, but with the Delta scores provided instead of the proportions of correct responses.

If the type of input is either "prop" or "delta", not anymore input information is required and the arguments group and focal.bname are ignored. Otherwise, the group membership column in the data matrix is specified by giving to argument group either the column number (1 for first column, etc.) or the column name (provided the data matrix has argument names). Moreover, the focal group is specified by giving to the argument focal.name the value that was used in the group membership column to code for the focal group.

If the input type is not "delta", then extreme proportions of correct responses (either provided when type is "prop" or computed from the data if type is "response") are adjusted by specifying the arguments extreme, const.range and nrAdd with appropriate values. See the adjustExtreme function for further details (note that the cuyrrent extreme argument corresponds to the method argument in this function).

The threshold for flaging items as DIF can be of two types and is specified by the thr argument.

1. It can be fixed to some arbitrary positive value by the user, for instance 1.5 (Angoff and Ford, 1973). In this case, thr takes the required numeric threshold value.

2. Alternatively, it can be derived from the bivariate normal approximation of the Delta points (Magis and Facon, 2012). In this case, thr must be given the character value "norm" (which is the default value). This threshold equals

   $\Phi^{-1}(1-\alpha/2) \; \sqrt{\frac{b^2\,{s_0}^2-2\,b\,s_{01}+{s_1}^2}{b^2+1}}$

   where $\Phi$ is the density of the standard normal distribution, $\alpha$ is the significance level (set by the argument alpha with default value 0.05), $b$ is the slope parameter of the major axis, $s_0$ and $s_1$ are the sample standard deviations of the Delta scores in the reference group and the focal group, respecively, and $s_{01}$ is the sample covariance of the Delta scores (see Magis and Facon, 2012, for further details).

Item purification can be performed by setting the argument purify to TRUE (by default it is FALSE so no purification is performed). The item purification process (IPP) starts when at least one item was flagged as DIF after the first run of the Delta plot, and proceeds as follows.

1. The intercept and slope parameters of the major axis are re-calculated by removing all DIF that are currently flagged as DIF. This yields updated values $a^*$, $b^*$, $s_0^*$, $s_1^*$ and $s_{01}^*$ of the intercept and slope parameters, sample stanbdard deviations and sample covariance of the Delta scores.

2. Perpendicular distances (for all items) are updated with respect to the updated major axis.

3. Detection threshold is also updated. Three possible updates are possible: see below.

4. All items are now tested for the presence of DIF, given the updated perpendicular distances and major axis.

5. If the set of items flagged as DIF is the same as the one from the previous loop, stop the process. Otherwise go back to step 1.

Unlike traditional DIF methods, the detection threshold may also be updated since it depends on the sample estimates (when the normal approximation is considered). Three approaches are currently implemented and are specified by the purType argument.

1. Method 1 (purType=="IPP1"): the same threshold is used throughout the purification process, it is not iteratively updated. The threshold is the one obtained after the first run of the Delta plot.

2. Method 2 (purType=="IPP2"): only the slope parameter is updated in the threshold formula. By this way, one keeps the full data structure (i.e. neither the sample variances nor the sample covariance of the Delta scores are modified) but only the slope parameter is adjusted to lessen the impact of DIF items.

3. Method 3 (purType=="IPP3"): all adjusted parameters are plugged in the threshold formula. This approach completely discards the effect of items flagged as DIF from the computation of the threshold.

See Magis and Facon (2013) for further details. Note that purification can also be performed with fixed threshold (i.e. specified by the user), but then only IPP1 process is performed.

In order to avoid possible infinite loops in the purification process, a maximal number of iterations must be specified through the argument maxIter. The default maximal number of iterations is 10.

The output contains all input information, the Delta scores and perpendicular distances, the parameter of the major axis and the items flagged as DIF (if none, a character sentence is returned). In addition, the detection threshold and the type of threshold (fixed or normal approximation) is provided.

If item purification was run, several additional elements are returned: the number of iterations, a logical indicator whether the convergence was reached (or not, meaning that the process stopped because of reaching the maximal number of allowed iterations), a matrix with indicators of which items were flagged as DIF at each iteration, and the type of item purification process. Moreover, perpendicular distances are returned in a matrix format (one column per iteration), as well as successive major axis parameters (one row per iteration) and successive thresholds (as a vector).

The output is managed and printed in a more user-friendly way. When item purification is performed, only the first and last steps are displayed. Specifying the argument only.final to FALSE prints in addition all intermediate steps of the process (successive perpendicular distances, parameters of the major axis, and detection thresholds).

The output can be saved into na text file by specifying the argument save.output to TRUE (by default the output is not captured). If so, the argument output can be specified as a vector of two character values. The first one gives the desired name of the text file, and the second one specifies the directory where the file will be saved (full path is required but without the final "/" symbol, see Examples below). By default, the output will be saved in the current working directory as "out.txt" file.

Value

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

Props	the matrix of proportions of correct responses, or NA if type is "delta".
adjProps	the restricted proportions, in the same format as the output Props matrix, or NA if type is "delta".
Deltas	the matrix of Delta scores.
Dist	a matrix with perpendicular distances, one row per item and one column per run of the Delta plot. If purify is FALSE, only a single column is returned.
axis.par	a matrix with two columns, holding respectively the intercepts and the slope parameters of the major axis. Each row refers to one step of the purification process. If purify is FALSE, only a single row is returned.
nrIter	the number of iterations invloved in the purification process. Returned only if purify is TRUE.
maxIter	the value of the maxIter argument. Returned only if purify is TRUE.
convergence	a logical value indicating whether convergence was reached in the purification process. Returned only if purify is TRUE.
difPur	a matrix with one column per item and one row per iteration in the purification process, holding zeros and ones to indicate which items were flagged as DIF or not at each step of the process. Returned only if purify is TRUE.
thr	a vector of successive threshold values used during the purification process. If purify is FALSE, a single value is returned.
rule	a character value indicating whether the threshold was "fixed" by the user (i.e. by setting thr to a numeric value) or whether it was computed by normal approximation (i.e. by setting thr to "norm").
purType	the value of the purType argument. Returned only if purify is TRUE.
DIFitems	either "No DIF item detected" or an integer vector with the items that were flagged as DIF.
adjust.extreme	the value of the extreme argument.
const.range	the value of the const.range argument.
nrAdd	the value of the nrAdd argument.
purify	the value of the purify argument.
alpha	the value of the alpha argument.
save.output	the value of the save.output argument.
output	the value of the output argument.

Author(s)

David Magis
Post-doc Fellow of the National Funds for Scientific Research (FNRS, Belgium)
University of Liege
[email protected], http://ppw.kuleuven.be/okp/home/
Bruno Facon
Professor, Department of Psychology
Universite Lille-Nord de France
[email protected],

References

Angoff, W. H. and Ford, S. F. (1973). Item-race interaction on a test of scholastic aptitude. Journal of Educational Measurement, 10, 95-106.

Magis, D., and Facon, B. (2012). Angoff's Delta method revisited: improving the DIF detection under small samples. British Journal of Mathematical and Statistical Psychology, 65, 302-321.

Magis, D., and Facon, B. (2013). Item purification does not always improve DIF detection: a counter-example with Angoff's Delta plot. Educational and Psychological Measurement, 73, 293-311.

Magis, D. and Facon, B. (2014). deltaPlotR: An R Package for Differential Item Functioning Analysis with Angoff's Delta Plot. Journal of Statistical Software, Code Snippets, 59(1), 1-19. URL http://www.jstatsoft.org/v59/c01/

See Also

adjustExtreme

Examples

# Loading of the verbal data
 data(verbal)
 attach(verbal)

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

 # Basic Delta plot, threshold 1.5, no item purification
 res <- deltaPlot(data=verbal, type="response", group=25, focal.name=1, purify=FALSE, 
                  thr=1.5)

 # Equivalent writing
 res <- deltaPlot(data=verbal, type="response", group="Gender", focal.name=1, 
                  purify=FALSE, thr=1.5)

 # Using proportions of correct responses as input
 dataRef <- verbal[verbal[,25]==0,1:24]
 dataFoc <- verbal[verbal[,25]==1,1:24]
 p0 <- colMeans(dataRef)
 p1 <- colMeans(dataFoc)
 res.1 <- deltaPlot(data=cbind(p0,p1), type="prop", purify=FALSE, thr=1.5)

 # Using Delta values as input
 Delta <- 4*qnorm(1-cbind(p0,p1))+13
 res.2 <- deltaPlot(data=Delta, type="delta", purify=FALSE, thr=1.5)

 # 'norm' threshold
 res <- deltaPlot(data=verbal, type="response", group="Gender", focal.name=1, 
                  purify=FALSE, thr="norm")

 # Keeping the first 10 items to exhibit DIF
 data <- verbal[,c(1:10,25)]
 deltaPlot(data=data, type="response", group=11, focal.name=1, purify=FALSE, thr="norm")
   # Item 8 is flagged as DIF

 # Item purification with the three processes
 res0 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=TRUE, 
           thr=1.5, purType="IPP1") 
 res0 # No DIF item detected

 res1 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=TRUE, 
           thr="norm", purType="IPP1") 
 res1 # Item 8 flagged as DIF after 2 iterations

 res2 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=TRUE, 
           thr="norm", purType="IPP2") 
 res2 # Item 8 flagged as DIF after 2 iterations

 res3 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=TRUE, 
           thr="norm", purType="IPP3") 
 res3 # Items 6, 7 and 8 flagged as DIF after 4 iterations

 # Printing the full results of item purification
 print(res, only.final=FALSE)
 print(res0, only.final=FALSE)
 print(res1, only.final=FALSE)
 print(res2, only.final=FALSE)
 print(res3, only.final=FALSE)

---

Plot of the Deltas points from the Delta Plot method

Description

This command plots the output of the deltaPlot function as a diagonal plot of Deltas points. Several graphical options are available.

Usage

diagPlot(x, pch = 2, pch.mult = 17, axis.draw = TRUE, thr.draw = FALSE, 
 dif.draw = c(1,3), print.corr = FALSE, xlim = NULL, ylim = NULL, xlab = NULL, 
 ylab = NULL,main = NULL, save.plot = FALSE, 
 save.options = c("plot", "default", "pdf"))

Arguments

x	an object of class "deltaPlot", typically the output of the deltaPlot function.
pch	integer: the usual point character type for point display. Default value is 2, that is, Delta points are drawn as empty triangles.
pch.mult	integer: the typoe of point to be used for superposing onto Delta points that correspond to several items. Default value is 17, that is, full black traingles are drawn onto existing Delta plots wherein multiple items are located.
axis.draw	Logical: should the major axis be drawn? (default is TRUE). If so, it will be drawn as a solid line.
thr.draw	logical: should the upper and lower bounds for DIF detection be drawn? (default is FALSE). If TRUE, they will be drawn as dashed lines.
dif.draw	numeric: a vector of two integer values to specify how the DIF items should be displayed. The first component of dif.draw is the type of point (i.e. the usual pch argument) and the second component determlines the point size (i.e. the usual cex argument). Default values are 1 and 3, meaning that empty circles of three time the usual size are drawn around the Delta points of items flagged as DIF.
print.corr	Logical: should the sample correlation of Delta scores be printed? (default is FALSE). If TRUE, it is printed in upper-left corner of the plot.
xlim, ylim, xlab, ylab, main	either the usual plot arguments xlim, ylim, xlab, ylab and main, or NULL (default value for all arguments). If NULL, the X and Y axis limits are computed from the range of Delta scores, the X and Y axis labels are "Reference group" and "Focal group" respectively, and no main title is produced.
save.plot	logical: should the plot be saved in an external figure? (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 (without final "/" symbol) or "default" (default), and the third component is the file extension, either "pdf" (default) or "jpeg". Ignored if save.plot is FALSE.

Details

The results of the Delta plot method can be graphically displayed using this function. Basically the Delta plot displays the items in a scatter plot by means of their Delta points, and the major axis is drawn. Several options permit to enhance this basic plot.

The input data x must be a list of class deltaPlot, so typically the output of the deltaPlot function. All other argumpents are rather standard and for optimization of the graphical display.

The type of point is defined by the cex argument. It takes the default value 2, which means that items are displayed with empty triangles. If several items are located on exactly the same Delta point, the pch.mult argument defines the type of point to display bover the existing point. The default value is 17, that is, a full black triangle. In this way, multiple items located at a single Delta point can easily be located on the plot.

Two types of axes can be draw: the major axis and the upper and lower bounds for DIF detection. The major axis is drawn by default, while the upper and lower bounds are not. The major axis can be withdrawn by setting the argument axis.draw to FALSE, and the bounds can be displayed by setting the argument thr.draw to TRUE. The major axis is always drawn by a solid line, the bounds by dashed lines.

Items flagged as DIF are also clearly identified on the plot. The argument dif.draw defines both the type of point and the size of the point to draw over the existing Delta points (for items flagged as DIF only). The defaulkt value is c(1,3), meaning that empty circles three times larger than usual are drawn.

The sample correlation between the Delta scores can also be printed, in the upper-left corner of the plot. To do this, the argument print.corr must be set to TRUE.

Finally, the function will automatically determines the X and Y axis limits and specifies default labels for X and Y axes and the main title. These can also be specified by the user, using the usual xlim, ylim, xlab, ylab and main arguments.

The plot can be saved in an external file, either as PDF or JPEG format. First, the argument save.plot must be set to TRUE (default is FALSE). Then, the name of the figure, its location and format are specified through the argument save.options, all as character strings. See the Examples section for further information and a practical example.

Author(s)

David Magis
Post-doc Fellow of the National Funds for Scientific Research (FNRS, Belgium)
University of Liege
[email protected], http://ppw.kuleuven.be/okp/home/
Bruno Facon
Professor, Department of Psychology
Universite Lille-Nord de France
[email protected],

References

Angoff, W. H. and Ford, S. F. (1973). Item-race interaction on a test of scholastic aptitude. Journal of Educational Measurement, 10, 95-106.

Magis, D., and Facon, B. (2012). Angoff's Delta method revisited: improving the DIF detection under small samples. British Journal of Mathematical and Statistical Psychology, 65, 302-321.

Magis, D., and Facon, B. (2013). Item purification does not always improve DIF detection: a counter-example with Angoff's Delta plot. Educational and Psychological Measurement, 73, 293-311.

Magis, D. and Facon, B. (2014). deltaPlotR: An R Package for Differential Item Functioning Analysis with Angoff's Delta Plot. Journal of Statistical Software, Code Snippets, 59(1), 1-19. URL http://www.jstatsoft.org/v59/c01/

See Also

deltaPlot

Examples

# Loading of the verbal data
 data(verbal)
 attach(verbal)

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

 # Basic Delta plot, threshold 1.5, no item purification
 res <- deltaPlot(data=verbal, type="response", group=25, focal.name=1, purify=FALSE, 
                  thr=1.5)

 # Keeping the first 10 items to exhibit DIF
 data <- verbal[,c(1:10,25)]
 res0 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=FALSE,
  thr="norm")
 res0 # Item 8 is flagged as DIF

 res1 <- deltaPlot(data=data, type="response", group=11, focal.name=1, purify=TRUE, 
           thr="norm", purType="IPP3") 
 res1 # Items 6, 7 and 8 flagged as DIF after 4 iterations

 # Delta plot, default options
 diagPlot(res)
 diagPlot(res0)
 diagPlot(res1)

 # Drawing upper and lower bounds and removing the major axis
 diagPlot(res, axis.draw=FALSE, thr.draw=TRUE)
 diagPlot(res1, axis.draw=FALSE, thr.draw=TRUE)

 # Modifying the type of points for all and for DIF items
 diagPlot(res, pch=3, dif.draw=c(2,4))
 diagPlot(res1, pch=3, dif.draw=c(2,4))

 # Printing the correlation and modifying the axis limits
 diagPlot(res, xlim=c(9,20), ylim=c(9,20), print.corr=TRUE)
 diagPlot(res1, xlim=c(9,17), print.corr=TRUE)

 # Saving the plots as PDF and JPEG files, default folder, specific names
 diagPlot(res, save.plot=TRUE, save.options=c("res","default","pdf"))
 diagPlot(res1, save.plot=TRUE, save.options=c("res1","default","jpeg"))

 # Modifying the results to make two items be located on the same place
 res2<-res1
 res2$Deltas[9,]<-res2$Deltas[3,]
 diagPlot(res2)

---

Verbal Aggression Data Set

Description

The Verbal Aggression data set comes from Vansteelandt (2000) and is made of the responses of 316 subjects (243 women and 73 men) to a questionnaire of 24 items, about verbal aggression. All items describe a frustrating situation together with a verbal agression response. A correct answer responses is coded as 0 and 1, a value of one meaning that the subject would (want to) respond to the frustrating situation in an aggressive way. In addition, the Trait Anger score (Spielberger, 1988) was computed for each subject.

Format

The verbal matrix consists of 316 rows (one per subject) and 26 columns.

The first 24 columns hold the responses to the dichotomously scored items. The 25th column holds the trait anger score for each subject. The 26th column is vector of the group membership; values 0 and 1 refer to women and men, respectively.

Each item name starts with S followed by a value between 1 and 4, referring to one of the situations below:

S1: A bus fails to stop for me.

S2: I miss a train because a clerk gave me faulty information.

S3: The grocery store closes just as I am about to enter.

S4: The operator disconnects me when I had used up my last 10 cents for a call.

The second part of the name is either Want or Do, and indicates whether the subject wanted to respond to the situation or actually did respond.

The third part of the name is one of the possible aggressive responses, either Curse, Scold or Shout.

For example, item S1WantShout refers to the sentence: "a bus fails to stop for me. I want to shout". The corresponding item response is 1 if the subject agrees with that sentence, and 0 if not.

Note

This data set was originally included in the difR package (Magis, Beland and Raiche, 2012). It is reproduced here for illustrative purposes.

Source

The Verbal agression data set is taken originally from Vansteelandt (2000) and has been used as an illustrative example in De Boeck (2008), De Boeck and Wilson (2004) and Smits, De Boeck and Vansteelandt (2004), among others. The following URL http://bear.soe.berkely.edu/EIRM/ permits to get access to the full data set.

References

De Boeck, P. (2008). Random item IRT models. Psychometrika, 73, 533-559.

De Boeck, P. and Wilson, M. (2004). Explanatory item response models: a generalized linear and nonlinear approach. New-York: Springer.

Magis, D., Beland, S. and Raiche, G. (2012). difR: Collection of methods to detect dichotomous differential item functioning (DIF) in psychometrics. R package version 4.2.

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.

Smits, D., De Boeck, P. and Vansteelandt, K. (2004). The inhibition of verbal aggressive behavior. European Journal of Personality, 18, 537-555.

Spielberger, C.D. (1988). State-trait anger expression inventory research edition. Professional manual. Odessa, FL: Psychological Assessment Resources.

Vansteelandt, K. (2000). Formal models for contextualized personality psychology. Unpublished doctoral dissertation, K.U. Leuven, Belgium.

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