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Robust measurement via a fused latent and graphical item response theory model

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  • Chen, Yunxiao
  • Li, Xiaoou
  • Liu, Jingchen
  • Ying, Zhiliang

Abstract

Item response theory (IRT) plays an important role in psychological and educational measurement. Unlike the classical testing theory, IRT models aggregate the item level information, yielding more accurate measurements. Most IRT models assume local independence, an assumption not likely to be satisfied in practice, especially when the number of items is large. Results in the literature and simulation studies in this paper reveal that misspecifying the local independence assumption may result in inaccurate measurements and differential item functioning. To provide more robust measurements, we propose an integrated approach by adding a graphical component to a multidimensional IRT model that can offset the effect of unknown local dependence. The new model contains a confirmatory latent variable component, which measures the targeted latent traits, and a graphical component, which captures the local dependence. An efficient proximal algorithm is proposed for the parameter estimation and structure learning of the local dependence. This approach can substantially improve the measurement, given no prior information on the local dependence structure. The model can be applied to measure both a unidimensional latent trait and multidimensional latent traits.

Suggested Citation

  • Chen, Yunxiao & Li, Xiaoou & Liu, Jingchen & Ying, Zhiliang, 2018. "Robust measurement via a fused latent and graphical item response theory model," LSE Research Online Documents on Economics 103181, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:103181
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    References listed on IDEAS

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    Cited by:

    1. Siliang Zhang & Yunxiao Chen, 2022. "Computation for Latent Variable Model Estimation: A Unified Stochastic Proximal Framework," Psychometrika, Springer;The Psychometric Society, vol. 87(4), pages 1473-1502, December.
    2. M. Marsman & H. Sigurdardóttir & M. Bolsinova & G. Maris, 2019. "Characterizing the Manifest Probability Distributions of Three Latent Trait Models for Accuracy and Response Time," Psychometrika, Springer;The Psychometric Society, vol. 84(3), pages 870-891, September.
    3. Jinsong Chen, 2020. "A Partially Confirmatory Approach to the Multidimensional Item Response Theory with the Bayesian Lasso," Psychometrika, Springer;The Psychometric Society, vol. 85(3), pages 738-774, September.
    4. Zhang, Siliang & Chen, Yunxiao, 2022. "Computation for latent variable model estimation: a unified stochastic proximal framework," LSE Research Online Documents on Economics 114489, London School of Economics and Political Science, LSE Library.
    5. Nussbaum, Frank & Giesen, Joachim, 2020. "Pairwise sparse + low-rank models for variables of mixed type," Journal of Multivariate Analysis, Elsevier, vol. 178(C).

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    More about this item

    Keywords

    item response theory; local dependence; robust measurement; differential item functioning; graphical model; Ising model; pseudo-likelihood; regularized estimator; Eysenck personality questionnaire-revised;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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