sibTest {difR} | R Documentation |

## SIBTEST DIF statistic

### Description

Calculates the SIBTEST statistics for DIF detection.

### Usage

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

### Arguments

`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 |

`anchor` |
a vector of integer values specifying which items (all by default) are currently considered as anchor (DIF free) items. See |

`type` |
a character string specifying which DIF effects must be tested. Possible values are |

### 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.

### Value

A list with six components:

`Beta` |
the values of the Beta SIBTEST statistics. |

`SE` |
the standard errors of |

`X2` |
the values of X^2 statistics for SIBTEST method. |

`df` |
the degrees of freedom for each |

`p.value` |
the p-values of the SIBTEST statistics. |

`type` |
the value of the |

### Author(s)

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/

### References

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

### See Also

### Examples

```
## 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)
```

*difR*version 5.1 Index]