breslowDay: Breslow-Day DIF statistic

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

Description

Computes Breslow-Day statistics for DIF detection.

Usage

breslowDay(data, member, match = "score", anchor = 1:ncol(data), 
     BDstat = "BD")
 

Arguments

data	numeric: the data matrix (one row per subject, one column per item).
member	numeric: the vector of group membership with zero and one entries only. 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.
anchor	a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See Details.
BDstat	character specifying the DIF statistic to be used. Possible values are "BD" (default) and "trend". See Details.

Details

breslowDay computes one of the Breslow-Day statistics (1980) in the specific framework of differential item functioning. It forms the basic command of difBD and is specifically designed for this call.

The data are supplied by the data argument, with one row per subject and one column per item. Missing values are allowed but must be coded as NA values. They are discarded from sum-score computation.

The vector of group membership, specified by the member argument, must hold only zeros and ones, a value of zero corresponding to the reference group and a value of one to the focal group.

The matching criterion can be either the test score or any other continuous or discrete variable to be passed in the breslowDay 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.

Option anchor sets the items which are considered as anchor items for computing Breslow-Day DIF statistics. Items other than the anchor items and the tested item are discarded. anchor must hold integer values specifying the column numbers of the corresponding anchor items. It is primarily designed to perform item purification.

Two test statistics are available: the usual Breslow-Day statistic for testing homogeneous association (Aguerri, Galibert, Attorresi and Maranon, 2009) and the trend test statistic for assessing some monotonic trend in the odss ratios (Penfield, 2003). The DIF statistic is supplied by the BDstat argument, with values "BD" (default) for the usual statistic and "trend" for the trend test statistic.

Value

A list with three arguments:

res	A matrix with one row per item and three columns: the first one contains the Breslow-Day statistic values, the second column indicates the degrees of freedom, and the last column displays the asymptotic p-values.
BDstat	the value of the BDstat argument.
match	a character string, either "score" or "matching variable" depending on the match 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

Aguerri, M.E., Galibert, M.S., Attorresi, H.F. and Maranon, P.P. (2009). Erroneous detection of nonuniform DIF using the Breslow-Day test in a short test. Quality and Quantity, 43, 35-44. doi: 10.1007/s11135-007-9130-2

Breslow, N.E. and Day, N.E. (1980). Statistical methods in cancer research, vol. I: The analysis of case-control studies. Scientific Publication No 32. International Agency for Research on Cancer, Lyon, France.

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

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.

See Also

difBD, dichoDif

Examples

## Not run: 

 # Loading of the verbal data
 data(verbal)

 # With all items as anchor items
 breslowDay(verbal[,1:24], verbal[,26])

 # With all items as anchor items and trend
 # test statistic
 breslowDay(verbal[,1:24], verbal[,26], BDstat = "trend")

 # Removing item 3 from the set of anchor items
 breslowDay(verbal[,1:24], verbal[,26], anchor = c(1:5, 7:24))

## End(Not run)

Example output

$res
         [,1] [,2]   [,3]
 [1,]  9.6257   13 0.7242
 [2,] 15.8210   16 0.4655
 [3,] 17.8526   15 0.2705
 [4,]  3.4587   11 0.9832
 [5,] 18.0873   14 0.2028
 [6,] 17.3823   16 0.3613
 [7,] 18.4747   16 0.2968
 [8,]  8.4961   15 0.9024
 [9,]  9.9836   18 0.9324
[10,] 11.8175   15 0.6928
[11,] 31.7499   16 0.0108
[12,]  8.2418   16 0.9413
[13,] 15.2799   14 0.3593
[14,]  4.8176   12 0.9638
[15,] 10.3749   16 0.8463
[16,] 13.8145   15 0.5396
[17,] 13.6044   14 0.4796
[18,] 23.8261   16 0.0934
[19,] 23.5307   16 0.1003
[20,]  6.8938   13 0.9075
[21,]  8.9631   10 0.5356
[22,] 11.5910   14 0.6391
[23,] 12.6692   16 0.6968
[24,] 13.6452   15 0.5526

$BDstat
[1] "BD"

$match
[1] "score"

$res
        [,1] [,2]   [,3]
 [1,] 0.5906    1 0.4422
 [2,] 2.6089    1 0.1063
 [3,] 0.8851    1 0.3468
 [4,] 0.0282    1 0.8666
 [5,] 0.6547    1 0.4184
 [6,] 3.3089    1 0.0689
 [7,] 0.7732    1 0.3792
 [8,] 0.1651    1 0.6845
 [9,] 0.3933    1 0.5306
[10,] 0.3225    1 0.5701
[11,] 2.4165    1 0.1201
[12,] 0.0467    1 0.8288
[13,] 2.7006    1 0.1003
[14,] 0.3649    1 0.5458
[15,] 0.3855    1 0.5347
[16,] 0.0700    1 0.7913
[17,] 0.5066    1 0.4766
[18,] 1.0832    1 0.2980
[19,] 0.2859    1 0.5928
[20,] 0.4443    1 0.5051
[21,] 0.4146    1 0.5197
[22,] 1.4847    1 0.2230
[23,] 0.4184    1 0.5177
[24,] 0.0282    1 0.8665

$BDstat
[1] "trend"

$match
[1] "score"

$res
         [,1] [,2]   [,3]
 [1,] 15.5122   12 0.2146
 [2,] 14.7817   15 0.4673
 [3,] 22.2659   15 0.1010
 [4,]  9.7643   11 0.5517
 [5,] 16.4130   14 0.2888
 [6,] 17.3823   16 0.3613
 [7,] 17.1332   15 0.3110
 [8,] 13.4975   13 0.4102
 [9,]  7.6864   16 0.9577
[10,] 14.3226   14 0.4260
[11,] 25.9684   15 0.0384
[12,] 12.2163   14 0.5889
[13,] 13.4863   14 0.4886
[14,] 10.5515   11 0.4816
[15,] 14.2458   15 0.5070
[16,] 17.2975   14 0.2407
[17,] 13.9141   14 0.4561
[18,] 19.4672   14 0.1479
[19,] 17.5266   14 0.2292
[20,] 18.3878   12 0.1044
[21,]  6.2345   10 0.7952
[22,] 11.3065   14 0.6618
[23,] 17.7245   14 0.2196
[24,]  7.8156   13 0.8554

$BDstat
[1] "BD"

$match
[1] "score"

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