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Least squares moment identification of binary regression mixture models

Author

Listed:
  • Benjamin Auder

    (Université Paris-Saclay)

  • Elisabeth Gassiat

    (Université Paris-Saclay)

  • Mor Absa Loum

    (Université Paris-Saclay)

Abstract

We consider finite mixtures of generalized linear models with binary output. We prove that cross moments (between the output and the regression variables) up to order three are sufficient to identify all parameters of the model. We propose a least-squares estimation method based on those moments and we prove the consistency and the Gaussian asymptotic behavior of the estimator. We provide simulation results and comparisons with likelihood methods. Numerical experiments were conducted using the R-package morpheus that we developed for our least-squares moment method and with the R-package flexmix for likelihood methods. We then give some possible extensions to finite mixtures of regressions with binary output including both continuous and categorical covariates, and possibly longitudinal data.

Suggested Citation

  • Benjamin Auder & Elisabeth Gassiat & Mor Absa Loum, 2021. "Least squares moment identification of binary regression mixture models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(4), pages 561-593, May.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:4:d:10.1007_s00184-020-00787-x
    DOI: 10.1007/s00184-020-00787-x
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    References listed on IDEAS

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    3. Utkarsh J. Dang & Antonio Punzo & Paul D. McNicholas & Salvatore Ingrassia & Ryan P. Browne, 2017. "Multivariate Response and Parsimony for Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 34(1), pages 4-34, April.
    4. Bettina Grün & Friedrich Leisch, 2008. "Identifiability of Finite Mixtures of Multinomial Logit Models with Varying and Fixed Effects," Journal of Classification, Springer;The Classification Society, vol. 25(2), pages 225-247, November.
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    7. Wang, Shaoli & Yao, Weixin & Huang, Mian, 2014. "A note on the identifiability of nonparametric and semiparametric mixtures of GLMs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 41-45.
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