Reference : On the accurate selection of asymptotic detection thresholds for Infit and Outfit ind...
Scientific congresses and symposiums : Unpublished conference/Abstract
Physical, chemical, mathematical & earth Sciences : Mathematics
On the accurate selection of asymptotic detection thresholds for Infit and Outfit indexes of person fit
[fr] Sur la sélection optimale de seuils de détection asymptotiques pour les indices Infit et Outfit
Magis, David mailto [Université de Liège - ULiège > Département de mathématique > Statistique mathématique >]
Raîche, Gilles [ > > ]
Béland, Sébastien [ > > ]
International Objective Measurement Workshop
11-12 avril 2012
University of British Columbia
Vancouver (BC)
[en] Person fit ; Infit ; Outfit ; ability estimation ; asymptotic distribution
[en] It exists a bunch of person fit indexes but Lz (Drasgow, Levine, & Williams, 1985), Infit mean square W (Wright & Masters, 1982) and Outfit mean square U (Wright & Stone, 1979) are certainly the most popular. However, they have the undesirable property that their limiting distribution depends on the true ability level, which is generally unknown. In addition, the asymptotic distribution of U and W indexes was not clearly stated. Snijders (2001) proposed a generalization of the index Lz to incorporate estimated ability levels in its computation, and derived subsequent asymptotic normality of this modified Lz* index.
The purpose of this talk is threefold. First, the generalization of Lz to Lz* is briefly sketched. Second, it is shown how this generalization can be successfully applied to both U and W indexes, yielding generalized U* and W* indexes respectively. Third, the accuracy of generalized indexes in detecting person (mis)fit is assessed through a simulation study.
Three situations were investigated: (a) absence of misfit; (b) presence of cheating (yielding spuriously high scores); (c) presence of inattention (yielding spuriously low scores). Several conditions were varied, such as test length and aberrance rates when misfit was introduced. Response patterns were generated under the Rasch model and maximum likelihood estimation was performed to obtain the ability estimates. Several significance levels were selected.
It is observed, that the generalized indexes Lz*, U* and W* better recover the significance level than their standard alternatives Lz, U and W respectively, while they are more powerful in identifying the two types of person misfit. In particular, the modified index W* has the best improvement in performance with respect to its original version W.
It is concluded that Snijders' generalization of Lz index to Lz* is also accurate for U and W indexes under Rasch modelling. Possible extensions to other person fit indexes, such as ECI indexes (Tatsuoka, 1984), other ability estimators, and other IRT models are eventually briefly discussed.

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