difR (version 5.1)

difLRT: Likelihood-Ratio Test DIF method

Description

Performs DIF detection using Likelihood Ratio Test (LRT) method.

Usage

difLRT(Data, group, focal.name, alpha = 0.05, purify = FALSE, nrIter = 10, 
 	p.adjust.method = NULL, save.output = FALSE, output = c("out", "default")) 
# S3 method for LRT
print(x, ...)
# S3 method for LRT
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.

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.

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 LRT 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.

Value

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

LRT

the values of the likelihood-ratio statistics.

p.value

the vector of p-values for the likelihood-ratio statistics.

alpha

the value of alpha argument.

thr

the threshold (cut-score) for DIF detection.

DIFitems

either 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.

convergence

logical indicating whether the iterative item purification process stopped before the maximal number of allowed iterations (10 by default). Returned only if purify is TRUE.

names

the names of the items.

save.output

the value of the save.output argument.

output

the value of the output argument.

Details

The likelihood-ratio test method (Thissen, Steinberg and Wainer, 1988) allows for detecting uniform differential item functioning by fitting a closed-form Rasch model and by testing for extra interactions between group membership and item response. Currently only the Rasch model can be used, so only uniform DIF can be detected. Moreover, items are tested one by one and the other items act as anchor items.

The Data is a matrix whose rows correspond to the subjects and columns to the items. Missing values are allowed but must be coded as NA values. 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 function glmer from package lme4 (Bates and Maechler, 2009) is used to fit the closed-form Rasch model. More precisely, the probability that response \(Y_{ijg}\) of subject i from group g (focal or reference) to item j is modeled as

$$logit (Pr(Y_{ijg}=1) = \theta_{ig} + \gamma_g - \beta_j$$

where \(\theta_i\) is subject's ability, \(\beta_j\) is the item difficulty and \(\gamma_g\) is the difference mean ability level between the focal and the reference groups. Subject abilities are treated as random effects, while item difficulties and \(\gamma_g\) are treated as fixed effects. Each item is tested by incorporating an interaction term, \(\delta_{gj}\), and by testing its statistical significance using the traditional likelihood-ratio test.

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 one degree of freedom.

Item purification can be performed by setting purify to TRUE. In this case, items detected as DIF are iteratively removed from the set of tested items, and the procedure is repeated (using the remaining items) until no additional item is identified as functioning differently. The process stops when either there is no new item detected as DIF, or when nrIter iterations are run and new DIF items are nevertheless detected. 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.

The output of the difLRT, as displayed by the print.LRT 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.LRT 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.

References

Bates, D. and Maechler, M. (2009). lme4: Linear mixed-effects models using S4 classes. R package version 0.999375-31. http://CRAN.R-project.org/package=lme4

Kim, J., and Oshima, T. C. (2013). Effect of multiple testing adjustment in differential item functioning detection. Educational and Psychological Measurement, 73, 458--470. 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. 10.3758/BRM.42.3.847

Thissen, D., Steinberg, L. and Wainer, H. (1988). Use of item response theory in the study of group difference in trace lines. In H. Wainer and H. Braun (Eds.), Test validity. Hillsdale, NJ: Lawrence Erlbaum Associates.

See Also

LRT, dichoDif

Examples

# NOT RUN {
 # Loading of the verbal data
 data(verbal)
 attach(verbal)

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

 # Keeping the first 5 items and the first 50 subjects
 # (this is an artificial simplification to reduce the computational time)
 verbal <- verbal[1:50, c(1:5, 25)]

 # Three equivalent settings of the data matrix and the group membership
 r <- difLRT(verbal, group = 6, focal.name = 1)
 difLRT(verbal, group = "Gender", focal.name = 1)
 difLRT(verbal[,1:5], group = verbal[,6], focal.name = 1)

 # Multiple comparisons adjustment using Benjamini-Hochberg method
 difLRT(verbal, group = 6, focal.name = 1, p.adjust.method = "BH")

 # With item purification
 difLRT(verbal, group = 6, focal.name = 1, purify = TRUE)

 # Saving the output into the "LRTresults.txt" file (and default path)
 r <- difLRT(verbal, group = 6, focal.name = 1, save.output = TRUE, 
            output = c("LRTresults", "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"))

 # WARNING: do not trust the results above since they are based on a selected 
 # subset of the verbal data set!
 
# }
# NOT RUN {
 
# }