Abstract
Item response theory (IRT) is one of the most widely utilized tools for item response analysis; however, local item and person independence, which is a critical assumption for IRT, is often violated in real testing situations. In this article, we propose a new type of analytical approach for item response data that does not require standard local independence assumptions. By adapting a latent space joint modeling approach, our proposed model can estimate pairwise distances to represent the item and person dependence structures, from which item and person clusters in latent spaces can be identified. We provide an empirical data analysis to illustrate an application of the proposed method. A simulation study is provided to evaluate the performance of the proposed method in comparison with existing methods.
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Notes
An adjacency matrix is a square matrix to represent a network, whose elements indicate whether or not pairs of nodes are connected (creating edges) in the network.
The black ellipse is completely overlapped with the green ellipse, indicating that there is a strong dependence between items 1 and 3.
Note that the ‘dimensions’ of a latent space are different from ‘dimensions’ in multidimensional IRT. The dimensions of a latent space are arbitrary coordinates to define a Euclidean space for pairwise distance among items as well as among persons. Clusters of items in the latent space, which will be detected as the result of the DLSJM estimation, may be seen as the dimensions (or factors) of items.
None of the existing methods in psychometrics can identify both item and person clusters simultaneously; hence, a full scope comparison with an existing method may be infeasible.
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We appreciate the Editor, the Associate Editor, and three anonymous reviewers for their careful reading and detailed comments on the previous versions of our manuscript.
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Both Ick Hoon ** and Minjeong Jeon are first authors.
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**, I.H., Jeon, M. A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data. Psychometrika 84, 236–260 (2019). https://doi.org/10.1007/s11336-018-9630-0
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DOI: https://doi.org/10.1007/s11336-018-9630-0