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Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$ L 1 Regularization

Author

Listed:
  • Jianan Sun

    (Beijing Forestry University)

  • Yunxiao Chen

    (Emory University)

  • Jingchen Liu

    (Columbia University)

  • Zhiliang Ying

    (Columbia University)

  • Tao Xin

    (Beijing Normal University)

Abstract

We develop a latent variable selection method for multidimensional item response theory models. The proposed method identifies latent traits probed by items of a multidimensional test. Its basic strategy is to impose an $$L_{1}$$ L 1 penalty term to the log-likelihood. The computation is carried out by the expectation–maximization algorithm combined with the coordinate descent algorithm. Simulation studies show that the resulting estimator provides an effective way in correctly identifying the latent structures. The method is applied to a real dataset involving the Eysenck Personality Questionnaire.

Suggested Citation

  • Jianan Sun & Yunxiao Chen & Jingchen Liu & Zhiliang Ying & Tao Xin, 2016. "Latent Variable Selection for Multidimensional Item Response Theory Models via $$L_{1}$$ L 1 Regularization," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 921-939, December.
    • Handle: RePEc:spr:psycho:v:81:y:2016:i:4:d:10.1007_s11336-016-9529-6
    DOI: 10.1007/s11336-016-9529-6
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    References listed on IDEAS

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    1. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
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    3. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    4. Li Cai, 2010. "High-dimensional Exploratory Item Factor Analysis by A Metropolis–Hastings Robbins–Monro Algorithm," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 33-57, March.
    5. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
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    Citations

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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. Yunxiao Chen & Xiaoou Li & Siliang Zhang, 2019. "Joint Maximum Likelihood Estimation for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 84(1), pages 124-146, March.
    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. 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.
    5. Christopher J. Urban & Daniel J. Bauer, 2021. "A Deep Learning Algorithm for High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 1-29, March.
    6. 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.
    7. Yoav Bergner & Peter Halpin & Jill-Jênn Vie, 2022. "Multidimensional Item Response Theory in the Style of Collaborative Filtering," Psychometrika, Springer;The Psychometric Society, vol. 87(1), pages 266-288, March.
    8. Yunxiao Chen & Xiaoou Li & Jingchen Liu & Zhiliang Ying, 2018. "Robust Measurement via A Fused Latent and Graphical Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 83(3), pages 538-562, September.
    9. Battauz, Michela & Vidoni, Paolo, 2022. "A likelihood-based boosting algorithm for factor analysis models with binary data," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).

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