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Estimating Multivariate Latent-Structure Models

Author

Listed:
  • Stéphane Bonhomme

    (University of Chicago)

  • Koen Jochmans

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Marc Robin

    (ECON - Département d'économie (Sciences Po) - Sciences Po - Sciences Po - CNRS - Centre National de la Recherche Scientifique)

Abstract

A constructive proof of identification of multilinear decompositions of multiway arrays is presented. It can be applied to show identification in a variety of multivariate latent structures. Examples are finite-mixture models and hidden Markov models. The key step to show identification is the joint diagonalization of a set of matrices in the same non-orthogonal basis. An estimator of the latent-structure model may then be based on a sample version of this simultaneous-diagonalization problem. Simple algorithms are available for computation. Asymptotic theory is derived for this joint approximate-diagonalization estimator.

Suggested Citation

  • Stéphane Bonhomme & Koen Jochmans & Jean-Marc Robin, 2014. "Estimating Multivariate Latent-Structure Models," Working Papers hal-01097135, HAL.
    • Handle: RePEc:hal:wpaper:hal-01097135
    Note: View the original document on HAL open archive server: https://sciencespo.hal.science/hal-01097135v2
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    Cited by:

    1. Paul Schrimpf & Michio Suzuki & Hiroyuki Kasahara, 2015. "Identification and Estimation of Production Function with Unobserved Heterogeneity," 2015 Meeting Papers 924, Society for Economic Dynamics.
    2. Bonhomme, Stéphane & Jochmans, Koen & Robin, Jean-Marc, 2017. "Nonparametric estimation of non-exchangeable latent-variable models," Journal of Econometrics, Elsevier, vol. 201(2), pages 237-248.
    3. Hu, Yingyao, 2017. "The econometrics of unobservables: Applications of measurement error models in empirical industrial organization and labor economics," Journal of Econometrics, Elsevier, vol. 200(2), pages 154-168.
    4. Ying Liu & Steven Andrew Culpepper & Yuguo Chen, 2023. "Identifiability of Hidden Markov Models for Learning Trajectories in Cognitive Diagnosis," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 361-386, June.
    5. Jochmans, Koen, 2025. "Identification in Models for Matched Panel Data with Two-Sided Random Effects," TSE Working Papers 25-1649, Toulouse School of Economics (TSE), revised Oct 2025.
    6. Chen, Xiaohong & Linton, Oliver & Yi, Yanping, 2017. "Semiparametric identification of the bid–ask spread in extended Roll models," Journal of Econometrics, Elsevier, vol. 200(2), pages 312-325.
    7. Jochmans, Koen & Henry, Marc & Salanié, Bernard, 2017. "Inference On Two-Component Mixtures Under Tail Restrictions," Econometric Theory, Cambridge University Press, vol. 33(3), pages 610-635, June.
    8. Hu, Yingyao, 2017. "The Econometrics of Unobservables -- Latent Variable and Measurement Error Models and Their Applications in Empirical Industrial Organization and Labor Economics [The Econometrics of Unobservables]," Economics Working Paper Archive 64578, The Johns Hopkins University,Department of Economics, revised 2021.
    9. Schennach, Susanne M., 2020. "Mismeasured and unobserved variables," Handbook of Econometrics, in: Steven N. Durlauf & Lars Peter Hansen & James J. Heckman & Rosa L. Matzkin (ed.), Handbook of Econometrics, edition 1, volume 7, chapter 0, pages 487-565, Elsevier.
    10. Jochmans, Koen & Weidner, Martin, 2024. "Inference On A Distribution From Noisy Draws," Econometric Theory, Cambridge University Press, vol. 40(1), pages 60-97, February.
    11. Argan, Damiano & Gary-Bobo, Robert & Goussé, Marion, 2023. "Is there a devaluation of degrees ? Unobserved heterogeneity in returns to education and early experience," CEPREMAP Working Papers (Docweb) 2304, CEPREMAP.

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