IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v180y2023ics0167947322002419.html
   My bibliography  Save this article

Robust mixture regression modeling based on the normal mean-variance mixture distributions

Author

Listed:
  • Naderi, Mehrdad
  • Mirfarah, Elham
  • Wang, Wan-Lun
  • Lin, Tsung-I

Abstract

Mixture regression models (MRMs) are widely used to capture the heterogeneity of relationships between the response variable and one or more predictors coming from several non-homogeneous groups. Since the conventional MRMs are quite sensitive to departures from normality caused by extra skewness and possible heavy tails, various extensions built on more flexible distributions have been put forward in the last decade. The class of normal mean-variance mixture (NMVM) distributions that arise from scaling both the mean and variance of a normal random variable with a common mixing distribution encompasses many prominent (symmetric or asymmetrical) distributions as special cases. A unified approach to robustifying MRMs is proposed by considering the class of NMVM distributions for component errors. An expectation conditional maximization either (ECME) algorithm, which incorporates membership indicators and the latent scaling variables as the missing data, is developed for carrying out maximum likelihood (ML) estimation of model parameters. Four simulation studies are conducted to examine the finite-sample property of ML estimators and the robustness of the proposed model against outliers for contaminated and noisy data. The usefulness and superiority of our methodology are demonstrated through applications to two real datasets.

Suggested Citation

  • Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    • Handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002419
    DOI: 10.1016/j.csda.2022.107661
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947322002419
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2022.107661?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Sylvia. Richardson & Peter J. Green, 1997. "On Bayesian Analysis of Mixtures with an Unknown Number of Components (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(4), pages 731-792.
    2. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    3. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "Erratum to: The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(2), pages 327-355, July.
    4. Naderi, Mehrdad & Hung, Wen-Liang & Lin, Tsung-I & Jamalizadeh, Ahad, 2019. "A novel mixture model using the multivariate normal mean–variance mixture of Birnbaum–Saunders distributions and its application to extrasolar planets," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 126-138.
    5. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    6. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    7. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    8. David Hunter & Derek Young, 2012. "Semiparametric mixtures of regressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 19-38.
    9. Adelchi Azzalini & Antonella Capitanio, 2003. "Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(2), pages 367-389, May.
    10. Lawrence Hubert & Phipps Arabie, 1985. "Comparing partitions," Journal of Classification, Springer;The Classification Society, vol. 2(1), pages 193-218, December.
    11. Ingrassia, Salvatore & Minotti, Simona C. & Punzo, Antonio, 2014. "Model-based clustering via linear cluster-weighted models," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 159-182.
    12. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    13. Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini & Simona Minotti, 2015. "The Generalized Linear Mixed Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 32(1), pages 85-113, April.
    14. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    15. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    16. 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.
    17. A. Capitanio & A. Azzalini & E. Stanghellini, 2003. "Graphical models for skew‐normal variates," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 30(1), pages 129-144, March.
    18. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    19. Salvatore Ingrassia & Simona Minotti & Giorgio Vittadini, 2012. "Local Statistical Modeling via a Cluster-Weighted Approach with Elliptical Distributions," Journal of Classification, Springer;The Classification Society, vol. 29(3), pages 363-401, October.
    20. Olcay Arslan, 2015. "Variance-mean mixture of the multivariate skew normal distribution," Statistical Papers, Springer, vol. 56(2), pages 353-378, May.
    21. Stanley Sclove, 1987. "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 333-343, September.
    22. Mirfarah, Elham & Naderi, Mehrdad & Chen, Ding-Geng, 2021. "Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    2. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    3. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    4. 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.
    5. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.
    6. Wan-Lun Wang, 2019. "Mixture of multivariate t nonlinear mixed models for multiple longitudinal data with heterogeneity and missing values," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(1), pages 196-222, March.
    7. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    8. Diani, Cecilia & Galimberti, Giuliano & Soffritti, Gabriele, 2022. "Multivariate cluster-weighted models based on seemingly unrelated linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    9. Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2021. "Matrix Normal Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 556-575, October.
    10. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    11. Xiaoqiong Fang & Andy W. Chen & Derek S. Young, 2023. "Predictors with measurement error in mixtures of polynomial regressions," Computational Statistics, Springer, vol. 38(1), pages 373-401, March.
    12. Chun Yu & Weixin Yao & Guangren Yang, 2020. "A Selective Overview and Comparison of Robust Mixture Regression Estimators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 176-202, April.
    13. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    14. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
    15. Salvatore Ingrassia & Antonio Punzo, 2020. "Cluster Validation for Mixtures of Regressions via the Total Sum of Squares Decomposition," Journal of Classification, Springer;The Classification Society, vol. 37(2), pages 526-547, July.
    16. Počuča, Nikola & Jevtić, Petar & McNicholas, Paul D. & Miljkovic, Tatjana, 2020. "Modeling frequency and severity of claims with the zero-inflated generalized cluster-weighted models," Insurance: Mathematics and Economics, Elsevier, vol. 94(C), pages 79-93.
    17. Gabriele Soffritti, 2021. "Estimating the Covariance Matrix of the Maximum Likelihood Estimator Under Linear Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 38(3), pages 594-625, October.
    18. Michael P. B. Gallaugher & Salvatore D. Tomarchio & Paul D. McNicholas & Antonio Punzo, 2022. "Multivariate cluster weighted models using skewed distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(1), pages 93-124, March.
    19. Michael P. B. Gallaugher & Paul D. McNicholas, 2019. "On Fractionally-Supervised Classification: Weight Selection and Extension to the Multivariate t-Distribution," Journal of Classification, Springer;The Classification Society, vol. 36(2), pages 232-265, July.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:180:y:2023:i:c:s0167947322002419. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.