Academic journal article Psychological Test and Assessment Modeling

Determinants of Artificial DIF - a Study Based on Simulated Polytomous Data

Academic journal article Psychological Test and Assessment Modeling

Determinants of Artificial DIF - a Study Based on Simulated Polytomous Data

Article excerpt

(ProQuest: ... denotes formulae omitted.)

Introduction

Independent work on requirements of invariance of comparisons for measurement by the Danish mathematician Georg Rasch (1961) incorporated ideas of Thurstone (1928) and Guttman (1950) into a probabilistic response model in which invariance is an integral property. Rasch's requirements implied that any partition of the data should provide invariant comparisons:

The comparison between two stimuli should be independent of which particular individuals were instrumental for the comparison; and it should also be independent of which other stimuli within the considered class were or might also have been compared.

Symmetrically, a comparison between two individuals should be independent of which particular stimuli within the class considered were instrumental for comparison; and it should also be independent of which other individuals were also compared, on the same or on some other occasion (p.322; Rasch, 1961).

It follows that in order to provide meaningful comparisons of different groups, the comparisons of the stimuli of a measuring instrument have to be invariant, not only along the variable of assessment, but also across the groups to be compared. In this paper instruments refer to tests or questionnaires and therefore the stimuli are referred to as items. Because the variable of assessment is inferred from the assessment by the items, it is generally referred to as a latent variable. Further references to a variable in this paper are understood to refer to such a variable.

Lack of invariance of the comparisons of item parameters across sample groups is commonly called differential item functioning (DIF). However, DIF may also be used as a generic term to include the lack of the same kind of invariance along the variable. Analysis of DIF in terms of parameter estimates across sample groups has long been used in Rasch model analyses (Andrich & Kline, 1981; Andrich, 1988), although the terminology has changed and new procedures for detecting DIF have been developed.

Among the new procedures for detecting DIF with both Rasch measurement theory and item response theory models, which do not estimate and compare item parameters from different groups, the expected value curve (EVC) of the responses of groups to an item is used. DIF across different groups implies that for the same values of the variable, the EVC of the response to an item for members of the groups are different. If the differences along the variable are homogeneous, then the DIF is referred to as uniform; otherwise it is referred to as non-uniform. Although DIF can be referenced and studied to multiple groups (e.g. DIF across countries), it has generally been focused on two groups (e.g. DIF across genders). In addition, in some cases one of the groups is considered the standard and dominant group, and the other a focal or minority group. In this paper we focus on two groups of equal standing. Although the data are simulated, to simplify the presentation of the results of the study, we refer to one group as Boys, and the other as Girls.

For items consisting of only two ordered categories, the expected value is the same as the probability of a positive response. In that case the expected value curve (EVC) is known as the item characteristic curve (ICC). In the context of an analysis of multiple items of a test or questionnaire, and as elaborated further in the ICCs of an item for different groups can be estimated by resolving the item so that an item is created in which persons from only one group respond (Andrich and Hagquist, 2012). For consistency with the literature, we continue to use the term ICC for the expected value curve in the case of dichotomous items. However, in the context of polytomous items, and because of its specific relevance to the particular DIF investigated, the more general term EVC will be used.

In the dichotomous Rasch model, which has only an item location parameter, the ICCs of all items are parallel. …

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