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Structured latent factor analysis for large-scale data: identifiability, estimability, and their implications

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  • Chen, Yunxiao
  • Li, Xiaoou
  • Zhang, Siliang

Abstract

Latent factor models are widely used to measure unobserved latent traits in so- cial and behavioral sciences, including psychology, education, and marketing. When used in a conrmatory manner, design information is incorporated as zero constraints on corresponding parameters, yielding structured (conrmatory) latent factor models. In this paper, we study how such design information aects the identiability and the estimation of a structured latent factor model. Insights are gained through both asymptotic and non-asymptotic analyses. Our asymptotic results are established under a regime where both the number of manifest variables and the sample size diverge, mo- tivated by applications to large-scale data. Under this regime, we dene the structural identiability of the latent factors and establish necessary and sucient conditions that ensure structural identiability. In addition, we propose an estimator which is shown to be consistent and rate optimal when structural identiability holds. Finally, a non-asymptotic error bound is derived for this estimator, through which the eect of design information is further quantied. Our results shed lights on the design of 1 large-scale measurement in education and psychology and have important implications on measurement validity and reliability.

Suggested Citation

  • Chen, Yunxiao & Li, Xiaoou & Zhang, Siliang, 2019. "Structured latent factor analysis for large-scale data: identifiability, estimability, and their implications," LSE Research Online Documents on Economics 101122, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:101122
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    References listed on IDEAS

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    Cited by:

    1. Zhenghao Zeng & Yuqi Gu & Gongjun Xu, 2023. "A Tensor-EM Method for Large-Scale Latent Class Analysis with Binary Responses," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 580-612, June.
    2. Yunxiao Chen, 2020. "A Continuous-Time Dynamic Choice Measurement Model for Problem-Solving Process Data," Psychometrika, Springer;The Psychometric Society, vol. 85(4), pages 1052-1075, December.
    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. 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.
    5. Yang Liu, 2020. "A Riemannian Optimization Algorithm for Joint Maximum Likelihood Estimation of High-Dimensional Exploratory Item Factor Analysis," Psychometrika, Springer;The Psychometric Society, vol. 85(2), pages 439-468, June.

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    More about this item

    Keywords

    High-dimensional latent factor model; conrmatory factor analysis; identifiability of latent factors; structured low-rank matrix; large-scale psychological measurement;
    All these keywords.

    JEL classification:

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

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