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A multivariate linear regression analysis using finite mixtures of t distributions

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  • Galimberti, Giuliano
  • Soffritti, Gabriele

Abstract

Recently, finite mixture models have been used to model the distribution of the error terms in multivariate linear regression analysis. In particular, Gaussian mixture models have been employed. A novel approach that assumes that the error terms follow a finite mixture of t distributions is introduced. This assumption allows for an extension of multivariate linear regression models, making these models more versatile and robust against the presence of outliers in the error term distribution. The issues of model identifiability and maximum likelihood estimation are addressed. In particular, identifiability conditions are provided and an Expectation–Maximisation algorithm for estimating the model parameters is developed. Properties of the estimators of the regression coefficients are evaluated through Monte Carlo experiments and compared to the estimators from the Gaussian mixture models. Results from the analysis of two real datasets are presented.

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  • Galimberti, Giuliano & Soffritti, Gabriele, 2014. "A multivariate linear regression analysis using finite mixtures of t distributions," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 138-150.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:138-150
    DOI: 10.1016/j.csda.2013.01.017
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    3. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Linear mixed models with marginally symmetric nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 151-169.
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    5. Víctor H. Lachos & Celso R. B. Cabral & Marcos O. Prates & Dipak K. Dey, 2019. "Flexible regression modeling for censored data based on mixtures of student-t distributions," Computational Statistics, Springer, vol. 34(1), pages 123-152, March.
    6. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    7. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
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    9. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    10. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    11. Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    12. Antonello Maruotti & Pierfrancesco Alaimo Di Loro, 2023. "CO2 emissions and growth: A bivariate bidimensional mean‐variance random effects model," Environmetrics, John Wiley & Sons, Ltd., vol. 34(5), August.
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    14. Murray, Paula M. & Browne, Ryan P. & McNicholas, Paul D., 2017. "Hidden truncation hyperbolic distributions, finite mixtures thereof, and their application for clustering," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 141-156.

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