dichoDif {difR}R Documentation

Comparaison of DIF detection methods

Description

This function compares the specified DIF detection methods with respect to the detected items.

Usage

 dichoDif(Data, group, focal.name, method, alpha=0.05, 
 correct=TRUE, thr=0.1, model="2PL", c=NULL, irtParam=NULL, 
 same.scale=TRUE, purify=FALSE, nrIter=10)
 ## S3 method for class 'dichoDif':
 print(x, ...)
 

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.
method character vector specifying the different methods to be compared. See Details.
alpha numeric: significance level (default is 0.05).
correct logical: should the Mantel-Haenszel continuity correction be used? (default is TRUE).
thr numeric: the threshold (cut-score) for standardized P-DIF statistic (default is 0.10).
model character: the IRT model to be fitted (either "1PL", "2PL" or "3PL"). Default is "2PL".
c optional numeric value or vector giving the values of the constrained pseudo-guessing parameters. See Details.
irtParam matrix with 2J rows (where J is the number of items) and at most 9 columns containing item parameters estimates. See Details.
same.scale logical: are the item parameters of the irtParam matrix on the same scale? (default is "TRUE"). See Details.
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.
x result from a dichoDif class object.
... other generic parameters for the print function.

Details

dichoDif is a generic function which calls one or several DIF detection methods and summarize their output. The possible methods are: "MH" for mantel-Haenszel (Holland and Thayer, 1988), "Std" for standardization (Dorans and Kullick, 1986), "Logistic" for logistic regression (Swaminathan and Rogers, 1990), "BD" for Breslow-Day method (Penfield, 2003), "Lord" for Lord's chi-square test (Lord, 1980), "Raju" for Raju's area method (Raju, 1990), and "LRT" for likelihood-ratio test method (Thissen, Steinberg and Wainer, 1988).

If method has a single component, the output of dichoDif is exactly the one provided by the method itself. Otherwise, the main output is a matrix with one row per item and one column per method. For each specified method and related arguments, items detected as DIF and non-DIF are respectively encoded as "DIF" and "NoDIF". When printing the output an additional column is added, counting the number of times each item was detected as functioning differently (Note: this is just an informative summary, since the methods are obviously not independent for the detection of DIF items).

The Data is a matrix whose rows correspond to the subjects and columns to the items. Missing values are not allowed.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.

For Lord and Raju methods, one can specify either the IRT model to be fitted (by means of model and c arguments), or the item parameter estimates with arguments irtParam and same.scale. See difLord and difRaju for further details.

The threshold for detecting DIF items depends on the method. For standardization it has to be fully specified (through the thr argument), while for the other methods it is depending on the significance level set by alpha.

Option correct specifies whether the continuity correction has to be applied to Mantel-Haenszel statistic (see difMH).

Item purification can be requested by specifying purify option to TRUE. Recall that item purification process is slightly different for IRT and for non-IRT based methods. See the corresponding methods for further information.

Value

Either the output of one of the DIF detection methods, or a list of class "dichoDif" with the following arguments:

DIF a character matrix with one row per item and whose columns refer to the different specified detection methods. See Details.
alpha the significance level alpha.
thr the value of thr option.
model the value of model option.
c the value of c option.
irtParam the value of irtParam option.
same.scale the value of same.scale option.
purification the value of purify option.
nrPur an integer vector (of length equal to the number of methods) with the number of iterations in the purification process. Returned only if purify is TRUE.
convergence a logical vector (of length equal to the number of methods) indicating whether the iterative purification process converged. Returned only if purify is TRUE.

Author(s)

Sebastien Beland
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
sebastien.beland.1@hotmail.com
David Magis
Research Group of Quantitative Psychology and Individual Differences
Katholieke Universiteit Leuven
David.Magis@psy.kuleuven.be, http://ppw.kuleuven.be/okp/home/
Gilles Raiche
Centre sur les Applications des Modeles de Reponses aux Items (CAMRI)
Universite du Quebec a Montreal
raiche.gilles@uqam.ca, http://www.er.uqam.ca/nobel/r17165/

References

Dorans, N. J. and Kullick, E. (1986). Demonstrating the utility of the standardization approach to assessing unexpected differential item performance on the Scholastic Aptitude Test. Journal of Educational Measurement, 23, 355-368.

Holland, P. W. and Thayer, D. T. (1988). Differential item performance and the Mantel-Haenszel procedure. In H. Wainer and H. I. Braun (Dirs.), Test validity. Hillsdale, New Jersey: Lawrence Erlbaum Associates.

Lord, F. (1980). Applications of item response theory to practical testing problems. Hillsdale, NJ: Lawrence Erlbaum Associates.

Penfield, R.D. (2003). Application of the Breslow-Day test of trend in odds ratio heterogeneity to the detection of nonuniform DIF. Alberta Journal of Educational Research, 49, 231-243.

Raju, N. S. (1990). Determining the significance of estimated signed and unsigned areas between two item response functions. Applied Psychological Measurement, 14, 197-207.

Swaminathan, H. and Rogers, H. J. (1990). Detecting differential item functioning using logistic regression procedures. Journal of Educational Measurement, 27, 361-370.

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

difMH, difStd, difBD, difLogistic, difLord, difRaju, difLRT

Examples

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

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

# Comparing Mantel-Haenszel, standardization and logistic regression
# Standardization threshold of 0.08, no continutiy correction, 
# with item purification (remove #)

# dichoDif(verbal, group=25, focal.name=1, method=c("MH","Std","Logistic"),
# correct=FALSE, thr=0.08, purify=TRUE)

# Comparing Lord and Raju results with 2PL model and
# with item purification (remove #)

# dichoDif(verbal, group=25, focal.name=1, method=c("Lord","Raju"),
# model="2PL", purify=TRUE)

[Package difR version 1.1 Index]