Abstract
Most item response theory models are not robust to violations of conditional independence. However, several modeling approaches (e.g., conditioning on other responses, additional random effects) exist that try to incorporate local item dependencies, but they have some drawbacks such as the nonreproducibility of marginal probabilities and resulting interpretation problems. In this paper, a new class of models making use of copulas to deal with local item dependencies is introduced. These models belong to the bigger class of marginal models in which margins and association structure are modeled separately. It is shown how this approach overcomes some of the problems associated with other local item dependency models.
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The authors wish to thank Yuri Goegebeur and Taoufik Bouezmarni for their helpful suggestions and comments. We are also indebted to the reviewers of this paper, their generous comments and remarks greatly improved the setup and clarity of the presented material. Preparation of this manuscript was supported in part by the Fund for Scientific Research Flanders (FWO) Grant G.0148.04 and by the K.U. Leuven Research Council Grant GOA/2005/04.
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Braeken, J., Tuerlinckx, F. & De Boeck, P. Copula Functions for Residual Dependency. Psychometrika 72, 393–411 (2007). https://doi.org/10.1007/s11336-007-9005-4
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DOI: https://doi.org/10.1007/s11336-007-9005-4