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Local Statistical Modeling via Cluster-Weighted Approach with Elliptical Distributions

Author

Listed:
  • Salvatore Ingrassia

    () (Dipartimento di Impresa, Cultura e Società, Università degli Studi di Catania)

  • Simona Caterina Minotti

    () (Dipartimento di Statistica, Università degli Studi di Milano-Bicocca)

  • Giorgio Vittadini

    () (Dipartimento di Metodi Quantitativi per l'Economia e le Scienze Aziendali, Università degli Studi di Milano-Bicocca)

Abstract

Cluster Weighted Modeling (CWM) is a mixture approach regarding the modelisation of the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both the theoretical and numerical point of view; in particular, we show that CWM includes as special cases mixtures of distributions and mixtures of regressions. Further, we introduce CWM based on Student-t distributions providing more robust fitting for groups of observations with longer than normal tails or atypical observations. Theoretical results are illustrated using some empirical studies, considering both real and simulated data.

Suggested Citation

  • Salvatore Ingrassia & Simona Caterina Minotti & Giorgio Vittadini, 2011. "Local Statistical Modeling via Cluster-Weighted Approach with Elliptical Distributions," Working Papers 20111001, Università degli Studi di Milano-Bicocca, Dipartimento di Statistica.
  • Handle: RePEc:mis:wpaper:20111001
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    File URL: http://www.statistica.unimib.it/utenti/WorkingPapers/WorkingPapers/20111001.pdf
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    References listed on IDEAS

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    1. Roman Liesenfeld & Robert C. Jung, 2000. "Stochastic volatility models: conditional normality versus heavy-tailed distributions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 15(2), pages 137-160.
    2. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466.
    3. Leisch, Friedrich, 2004. "FlexMix: A General Framework for Finite Mixture Models and Latent Class Regression in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i08).
    4. Wayne DeSarbo & William Cron, 1988. "A maximum likelihood methodology for clusterwise linear regression," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 249-282, September.
    5. Michel Wedel & Wayne DeSarbo, 1995. "A mixture likelihood approach for generalized linear models," Journal of Classification, Springer;The Classification Society, vol. 12(1), pages 21-55, March.
    6. Francesca Greselin & Salvatore Ingrassia & Antonio Punzo, 2011. "Assessing the pattern of covariance matrices via an augmentation multiple testing procedure," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(2), pages 141-170, June.
    7. Ingrassia, Salvatore & Rocci, Roberto, 2007. "Constrained monotone EM algorithms for finite mixture of multivariate Gaussians," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5339-5351, July.
    8. Cerioli, Andrea, 2010. "Multivariate Outlier Detection With High-Breakdown Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 105(489), pages 147-156.
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    Citations

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    Cited by:

    1. repec:spr:jclass:v:34:y:2017:i:2:d:10.1007_s00357-017-9234-x is not listed on IDEAS
    2. Leonardo Grilli & Maria Iannario & Domenico Piccolo & Carla Rampichini, 2014. "Latent class CUB models," 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. 8(1), pages 105-119, March.
    3. Paul D. McNicholas, 2016. "Model-Based Clustering," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 331-373, October.
    4. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    5. repec:eee:jmvana:v:163:y:2018:i:c:p:1-14 is not listed on IDEAS
    6. 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.
    7. Antonio Punzo & Salvatore Ingrassia, 2016. "Clustering bivariate mixed-type data via the cluster-weighted model," Computational Statistics, Springer, vol. 31(3), pages 989-1013, September.
    8. Paolo Berta & Salvatore Ingrassia & Antonio Punzo & Giorgio Vittadini, 2016. "Multilevel cluster-weighted models for the evaluation of hospitals," METRON, Springer;Sapienza Università di Roma, vol. 74(3), pages 275-292, December.
    9. Faicel Chamroukhi, 2016. "Piecewise Regression Mixture for Simultaneous Functional Data Clustering and Optimal Segmentation," Journal of Classification, Springer;The Classification Society, vol. 33(3), pages 374-411, October.
    10. 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.
    11. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    12. Sanjeena Subedi & Antonio Punzo & Salvatore Ingrassia & Paul McNicholas, 2015. "Cluster-weighted $$t$$ t -factor analyzers for robust model-based clustering and dimension reduction," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 623-649, November.
    13. Hien Nguyen & Geoffrey McLachlan, 2015. "Maximum likelihood estimation of Gaussian mixture models without matrix operations," 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. 9(4), pages 371-394, December.
    14. Gabriella Schoier & Adriana Monte, 2014. "On the use of cluster analysis for individuating variable influence on spread variation in large datasets," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 68(1), pages 223-229, January-M.
    15. 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.

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    Keywords

    Cluster-Weighted Modeling; Mixture Models; Model-Based Clustering;

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