breslowDay {difR} | R Documentation |

## Breslow-Day DIF statistic

### 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 |

`match` |
specifies the type of matching criterion. Can be either |

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

`BDstat` |
character specifying the DIF statistic to be used. Possible values are |

### 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 |

`BDstat` |
the value of the |

`match` |
a character string, either |

### Author(s)

Sebastien Beland

Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)

Universite du Quebec a Montreal

sebastien.beland.1@hotmail.com, http://www.cdame.uqam.ca/

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/

Gilles Raiche

Collectif pour le Developpement et les Applications en Mesure et Evaluation (Cdame)

Universite du Quebec a Montreal

raiche.gilles@uqam.ca, 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

### 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)
```

*difR*version 5.1 Index]