A Doubly Latent Space Joint Model for Local Item and Person Dependence in the Analysis of Item Response Data

TL;DR

This paper introduces a novel latent space joint model for item response data that captures local dependence among items and persons, overcoming the limitations of traditional IRT models that assume independence.

Contribution

It develops a new approach that estimates pairwise distances in latent spaces to model dependence structures without relying on local independence assumptions.

Findings

Successfully identified item and person clusters in latent spaces.

Demonstrated improved performance over existing methods in simulations.

Applied the model to real data illustrating its practical utility.

Abstract

Item response theory (IRT) models explain an observed item response as a function of a respondent's latent trait and the item's property. 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 was also provided to evaluate the performance of the proposed method in comparison to an existing method.