SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

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Contributions: Abstract

When formulating traditional IRT models in a nonlinear mixed model (NLMM) framework, it turns out that these models usually include person predictors with random effects and item predictors with fixed effects. Person predictors vary between but not within persons whereas item predictors vary within but not between persons. The extension of IRT models with person-by-item predictors that vary both within and between persons is relevant for modeling different phenomena such as differential item functioning (DIF) and local item dependencies (LID). As for DIF we will indicate how standard IRT based methods for detecting DIF can be implemented in the NLMM framework. In addition, we indicate how DIF in individual items can sometimes be modeled in a more parsimonious way as differential facet functioning (DFF) and we show how individual differences in DIF/DFF within the groups under investigation can be modeled by making item-by-group or facet-by-group interactions random over persons. As for modeling LID, it is shown that the correlation between two items that goes beyond the latent trait can be modeled in an asymmetric way by including responses to one item as a predictor for modeling responses to the other item. The relation with symmetric local dependency models is discussed.