Determinants of Artificial DIF : a study based on simulated polytomous data
Curt Hagquist, David Andrich · UWA Profiles and Research Repository (University of Western Australia) · 2014
AbstractA general problem in DIF analyses is that some items favouring one group can induce the appearance of DIF in others favouring the other group. Artificial DIF is used as a concept for describing and explaining that kind of DIF which is an artefact of the procedure for identifying DIF, contrasting it to real DIF which is inherent to an item.The purpose of this paper is to elucidate how real both uniform and non-uniform DIF, referenced to the expected value curve, induce artificial DIF, how this DIF impacts on the person parameter estimates and how different factors affect real and artificial DIF, in particular the alignment of person and item locations.The results show that the same basic principles apply to non-uniform DIF as to uniform DIF, but that the effects on person measurement are less pronounced in non-uniform DIF. Similar to artificial DIF induced by real uniform DIF, the size of artificial DIF is determined by the magnitude of the real non-uniform DIF. In addition, in both uniform and non-uniform DIF, the magnitude of artificial DIF depends on the location of the items relative to the distribution of the persons. In contrast to uniform DIF, the direction of non-uniform real DIF (e.g. favouring one group or the other) is affected by the location of the items relative to the distribution of the persons. The results of the simulation study also confirm that regardless of type of DIF, in the person estimates, artificial DIF never balances out real DIF.Keywords: differential item functioning, uniform, non-uniform, artificial, Rasch models(ProQuest: ... denotes formulae omitted.)IntroductionIndependent 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. …