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

Performs DDF detection procedure based on Multinomial Log-linear Regression model and likelihood ratio test of submodel.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 | ```
ddfMLR(Data, group, focal.name, key, type = "both", match = "zscore", anchor = NULL,
purify = FALSE, nrIter = 10, alpha = 0.05, p.adjust.method = "none")
## S3 method for class 'ddfMLR'
print(x, ...)
## S3 method for class 'ddfMLR'
plot(x, item = "all", title, ...)
## S3 method for class 'ddfMLR'
coef(object, ...)
## S3 method for class 'ddfMLR'
logLik(object, item = "all", ...)
## S3 method for class 'ddfMLR'
AIC(object, item = "all", ...)
## S3 method for class 'ddfMLR'
BIC(object, item = "all", ...)
``` |

`Data` |
character: either the unscored data matrix only, or the unscored data
matrix plus the vector of group. See |

`group` |
numeric or character: either the binary vector of group membership or
the column indicator of group membership. See |

`focal.name` |
numeric or character: indicates the level of |

`key` |
character: the answer key. See |

`type` |
character: type of DDF to be tested (either "both" (default), "udif", or "nudif").
See |

`match` |
specifies matching criterion. Can be either |

`anchor` |
Either |

`purify` |
logical: should the item purification be applied? (default is |

`nrIter` |
numeric: the maximal number of iterations in the item purification (default is 10). |

`alpha` |
numeric: significance level (default is 0.05). |

`p.adjust.method` |
character: method for multiple comparison correction.
See |

`x` |
an object of 'ddfMLR' class |

`...` |
other generic parameters for |

`item` |
either character ("all"), or numeric vector, or single number
corresponding to column indicators. See |

`title` |
string: title of plot. |

`object` |
an object of 'ddfMLR' class |

DDF detection procedure based on Multinomial Log-linear model.

The `Data`

is a matrix whose rows represents examinee unscored answers and
columns correspond to the items. The `group`

must be either a vector of the same
length as `nrow(data)`

or column indicator of `Data`

. The `key`

must be
a vector of correct answers corresponding to columns of `Data`

.

The `type`

corresponds to type of DDF to be tested. Possible values are `"both"`

to detect any DDF (uniform and/or non-uniform), `"udif"`

to detect only uniform DDF or
`"nudif"`

to detect only non-uniform DDF.

Argument `match`

represents the matching criterion. It can be either the standardized test score (default, `"zscore"`

),
total test score (`"score"`

), or any other continuous or discrete variable of the same length as number of observations
in `Data`

. Matching criterion is used in `MLR()`

function as a covariate in multinomial model.

A set of anchor items (DIF free) can be specified through the `anchor`

argument. It need to be a vector of either
item names (as specified in column names of `Data`

) or item identifiers (integers specifying the column number).
In case anchor items are provided, only these items are used to compute matching criterion `match`

. If the `match`

argument is not either `"zscore"`

or `"score"`

, `anchor`

argument is ignored. When anchor items are
provided, purification is not applied.

The `p.adjust.method`

is a character for `p.adjust`

function from the
`stats`

package. Possible values are `"holm"`

, `"hochberg"`

,
`"hommel"`

, `"bonferroni"`

, `"BH"`

, `"BY"`

, `"fdr"`

, `"none"`

.

The output of the ddfMLR is displayed by the `print.ddfMLR`

function.

The characteristic curve for item specified in `item`

option can be plotted. For default
option `"all"`

of item, characteristic curves of all converged items are plotted.
The drawn curves represent best model.

Missing values are allowed but discarded for item estimation. They must be coded as `NA`

for both, `data`

and `group`

parameters.

A list of class 'ddfMLR' with the following arguments:

`Sval`

the values of likelihood ratio test statistics.

`mlrPAR`

the estimates of final model.

`mlrSE`

standard errors of the estimates of final model.

`parM0`

the estimates of null model.

`parM1`

the estimates of alternative model.

`alpha`

numeric: significance level.

`DDFitems`

either the column indicators of the items which were detected as DDF, or

`"No DDF item detected"`

.`type`

character: type of DIF that was tested.

`purification`

`purify`

value.`nrPur`

number of iterations in item purification process. Returned only if

`purify`

is`TRUE`

.`difPur`

a binary matrix with one row per iteration of item purification and one column per item. "1" in i-th row and j-th column means that j-th item was identified as DIF in i-1-th iteration. Returned only if

`purify`

is`TRUE`

.`conv.puri`

logical indicating whether item purification process converged before the maximal number

`nrIter`

of iterations. Returned only if`purify`

is`TRUE`

.`p.adjust.method`

character: method for multiple comparison correction which was applied.

`pval`

the p-values by likelihood ratio test.

`adj.pval`

the adjusted p-values by likelihood ratio test using

`p.adjust.method`

.`df`

the degress of freedom of likelihood ratio test.

`group`

the vector of group membership.

`Data`

the data matrix.

`match`

matching criterion.

`llM0`

log-likelihood of null model.

`llM1`

log-likelihood of alternative model.

`AICM0`

AIC of null model.

`AICM1`

AIC of alternative model.

`BICM0`

BIC of null model.

`BICM1`

BIC of alternative model.

Adela Drabinova

Institute of Computer Science, The Czech Academy of Sciences

Faculty of Mathematics and Physics, Charles University

[email protected]

Patricia Martinkova

Institute of Computer Science, The Czech Academy of Sciences

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | ```
## Not run:
# loading data based on GMAT
data(GMATtest, GMATkey)
Data <- GMATtest[, 1:20]
group <- GMATtest[, "group"]
key <- GMATkey
# Testing both DDF effects
(x <- ddfMLR(Data, group, focal.name = 1, key))
# Testing both DDF effects with Benjamini-Hochberg adjustment method
ddfMLR(Data, group, focal.name = 1, key, p.adjust.method = "BH")
# Testing both DDF effects with item purification
ddfMLR(Data, group, focal.name = 1, key, purify = T)
# Testing uniform DDF effects
ddfMLR(Data, group, focal.name = 1, key, type = "udif")
# Testing non-uniform DDF effects
ddfMLR(Data, group, focal.name = 1, key, type = "nudif")
# Testing both DDF effects with total score as matching criterion
ddfMLR(Data, group, focal.name = 1, key, match = "score")
# Graphical devices
plot(x, item = 1)
plot(x, item = x$DDFitems)
plot(x, item = "all")
# AIC, BIC, logLik
AIC(x)
BIC(x)
logLik(x)
## End(Not run)
``` |

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