Description

The anchor function provides a variety of anchor methods for the detection of uniform differential item functioning (DIF) in the Rasch model between two pre-specified groups. These methods can be divided in an anchor class that determines characteristics of the anchor method and an anchor selection that determines the ranking order of candidate anchor items. The aim of the anchor function is to provide anchor items for DIF testing, e.g. with anchortest.

Usage

Arguments

Details

The anchor methods provided consist of an anchor class that determines characteristics of the anchor and an anchor selection that determines the ranking order of candidate anchor items.

In the constant anchor class, the anchor length is pre-defined by the user within the argument length. The current default is four anchor items. The iterative forward class starts with a single anchor item and includes items in the anchor as long as the anchor length is shorter than a certain percentage of the number of items that do not display statistically significant DIF (default: 0.8). Furthermore, a percentage of first anchor candidates is excluded from consideration (default: 0.1) and the user is allowed to set a maximum number of anchor items using the argument length. A detailed description of the anchor classes can be found in Kopf et al. (2014a).

In more recent work Strobl et al. (2020) suggest a simpler yet powerful anchor method based on inequality criteria like the Gini coefficient or the component loss function (CLF). This can be shown to attain its optimium for a single-anchor, thus correponding to a constant class of length 1. This will likely become the default method in future versions.

Both anchor classes require an explicit anchor selection strategy (as opposed to the all-other anchor class which is therefore not included in the function anchor). The anchor selection strategy determines the ranking order of candidate anchor items. In case of two groups, each item j, j = 1, …, k (where k denotes the number of items in the test) obtains a criterion value c_j that is defined by the anchor selection strategy. The ranking order is determined by the rank of the criterion value rank(c_j).

The criterion values are defined by the respective anchor selection strategy as in the following equations, where 1 denotes the indicator function, t_j denotes the test statistic for item j, followed by the underlying anchor items in parenthesis, p_j the corresponding p-values (also with anchor items in parenthesis), <0.5k> denotes the empirical 50% quantile and A_{purified} the anchor after purification steps (a detailed description of the anchor selection strategies implemented in this function is provided in Kopf et al., 2014b).

All-other selection by Woods (2009), here abbreviated AO:

c_j^{AO} = | t_j ({1,…,k}\j) |

All-other purified selection by Wang et al. (2012), here abbreviated AOP:

c_j^{AOP} = | t_j ( A_{purified} ) |

Number of significant threshold selection based on Wang et al. (2004), here abbreviated NST:

c_j^{NST} = ∑_{l in {1,…,k} \ j} 1 { p_j ({l}) ≤ α }) |

Mean test statistic selection by Shih et al. (2009), here abbreviated MT:

c_j^{MT} = 1/(k-1) ∑_{l in {1,…,k} \ j} | t_j ({l}) |

Mean p-value selection by Kopf et al. (2014b), here abbreviated MP:

c_j^{MP} = - 1/(k-1) ∑_{l in {1,…,k} \ j} p_j ({l})

Mean test statistic threshold selection by Kopf et al. (2014b), here abbreviated MTT:

c_j^{MTT} = ∑_{l in {1,…,k} \ j} 1 { | t_j ({l}) | > ( | 1/(k-1) ∑_{l \in { 1,…, k } \ j} t_j ({l}) | )_{<0.5k>}}

Mean p-value threshold selection by Kopf et al. (2014b), here abbreviated MPT:

c_j^{MPT} = - ∑_{l in {1,…,k} \ j} 1 { p_j ({l}) > ( 1/(k-1) ∑_{l in { 1, …, k } \ j} p_j ({l}))_{<0.5k>} }

Kopf et al. (2015b) recommend to combine the class = "constant" with select = "MPT" and the class = "forward" with select = "MTT", respectively.

The all-other anchor class (that assumes that DIF is balanced i.e. no group has an advantage in the test) is here not considered as explicit anchor selection and, thus, not included in the anchor function (but in the anchortest function). Note that the all-other anchor class requires strong prior knowledge that DIF is balanced.

Value

An object of class anchor, i.e. a list including

References

Kopf J, Zeileis A, Strobl C (2015a). A Framework for Anchor Methods and an Iterative Forward Approach for DIF Detection. Applied Psychological Measurement, 39(2), 83–103. doi: 10.1177/0146621614544195

Kopf J, Zeileis A, Strobl C (2015b). Anchor Selection Strategies for DIF Analysis: Review, Assessment, and New Approaches. Educational and Psychological Measurement, 75(1), 22–56. doi: 10.1177/0013164414529792

Shih CL, Wang WC (2009). Differential Item Functioning Detection Using the Multiple Indicators, Multiple Causes Method with a Pure Short Anchor. Applied Psychological Measurement, 33(3), 184–199.

Strobl C, Kopf J, Kohler L, von Oertzen T, Zeileis A (2020). Anchor Point Selection – Scale Alignment Based on an Inequality Criterion. Applied Psychological Measurement, Forthcoming. https://EconPapers.repec.org/RePEc:inn:wpaper:2018-03

Wang WC (2004). Effects of Anchor Item Methods on the Detection of Differential Item Functioning within the Family of Rasch Models. Journal of Experimental Education, 72(3), 221–261.

Wang WC, Shih CL, Sun GW (2012). The DIF-Free-then-DIF Strategy for the Assessment of Differential Item Functioning. Educational and Psychological Measurement, 72(4), 687–708.

Woods C (2009). Empirical Selection of Anchors for Tests of Differential Item Functioning. Applied Psychological Measurement, 33(1), 42–57.

See Also

anchortest

Examples