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

Description Usage Arguments Details Value Author(s) References See Also Examples

Calculates the SIBTEST statistics for DIF detection.

1 2	sibTest(data, member, anchor = 1:ncol(data), type = "udif")

`data`	numeric: the data matrix (one row per subject, one column per item).
`member`	numeric or factor: the vector of group membership. Can either take two distinct values (zero for the reference group and one for the focal group) or be a continuous vector. See Details.
`anchor`	a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See Details.
`type`	a character string specifying which DIF effects must be tested. Possible values are `"udif"` (default) and `"nudif"`. See Details.

This command computes the SIBTEST Beta coefficients and relatif DIF statistics, both for uniform (Shealy and Stout, 1993) and nonuniform (or crossing-SIBTEST; Chalmers, 2018) DIF effects. It forms the basic command of difSIBTEST function and is specifically designed for this call. This function provides a wrapper to the SIBTEST function from the mirt package (Chalmers, 2012) to fit within the difR framework (Magis et al., 2010). Therefore, if you are using this function for publication purposes please cite Chalmers (2018; 2012).

The data are passed through the data argument, with one row per subject and one column per item.

The vector of group membership, specified with 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.

Option anchor sets the items which are considered as anchor items for computing the test scores and related SIBTEST DIF statistics. anchor must hold integer values specifying the column numbers of the corresponding anchor items. If all columns of data are specified as anchor items, then all items are tested for DIF with the all-other-items-as-anchor strategy. If a smaller set of items is defined as the anchor set, then only items outside the anchor set will be tested for DIF; items belonging to this anchor set are not tested and corresponding NA values are returned instead. It is mainly designed to perform item purification.

The output contains: the SIBTEST Beta statistics and related standard errors; the X2 statistics that follow an asymptotic chi-square distribution; the degrees of freedom and the corresponding p-values. The default type value is also returned.

A list with six components:

`Beta`	the values of the Beta SIBTEST statistics.
`SE`	the standard errors of `Beta` values.
`X2`	the values of X^2 statistics for SIBTEST method.
`df`	the degrees of freedom for each `X2` statistic.
`p.value`	the p-values of the SIBTEST statistics.
`type`	the value of the `type` argument.

David Magis
Department of Psychology, University of Liege
Research Group of Quantitative Psychology and Individual Differences, KU Leuven
David.Magis@uliege.be, http://ppw.kuleuven.be/okp/home/

Chalmers, R. P. (2012). mirt: A Multidimensional item response theory package for the R environment. Journal of Statistical Software, 48(6), 1-29. doi: 10.18637/jss.v048.i06

Chalmers, R. P. (2018). Improving the Crossing-SIBTEST statistic for detecting non-uniform DIF. Psychometrika, 83(2), 376–386. doi: 10.1007/s11336-017-9583-8

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

Shealy, R. and Stout, W. (1993). A model-based standardization approach that separates true bias/DIF from group ability differences and detect test bias/DTF as well as item bias/DIF. Psychometrika, 58, 159-194. doi: 10.1007/BF02294572

difSIBTEST, dichoDif

## Not run: 

 # Loading of the verbal data
 data(verbal)

 # Testing uniform DIF with all items
 sibTest(verbal[,1:24], verbal[,26])

 # Testing nonuniform DIF with all items
 sibTest(verbal[,1:24], verbal[,26], type = "nudif")

 # Removing item 6 from the set of anchor items
 sibTest(verbal[,1:24], verbal[,26], anchor = c(1:5, 7:24))

 # Considering items 3 to 9 as the set of anchor items
 sibTest(verbal[,1:24], verbal[,26], anchor = 3:9)

 
## End(Not run)