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Revista Colombiana de Estadística

Print version ISSN 0120-1751

Rev.Colomb.Estad. vol.41 no.1 Bogotá Jan./June 2018 

Artículos originales de investigación

Finite Mixture of Compositional Regression With Gaussian Errors

Mixtura finita de una regresión composicional con errores Gaussianos

Taciana Shimizu1  a  , Francisco Louzada1  b  , Adriano Suzuki1  c 

1 Department of Applied Mathematics & Statistics, University of Sao Paulo, Sao Paulo, Brazil.


In this paper, we consider to evaluate the efficiency of volleyball players according to your performance of attack, block and serve, considering the compositional structure of the data related to the fundaments of this sport. In this way, we consider a nite mixture of regression model to compositional data. The maximum likelihood estimation of this model was obtained via an EM algorithm. A simulation study reveals that the parameters are correctly recovery. In addition, the estimators are asymptotically unbiased. By considering real dataset of Brazilian volleyball competition, we show that the model proposed presents best fit than the usual regression model.

Key words: Compositional Data; Finite Mixture Regression; EM Algorithm


En este estudio evaluamos la eficiencia de los jugadores de voleibol de acuerdo con su desempeño de ataque, bloqueo y servicio, teniendo en cuenta la estructura composicional de los datos relacionados con los fundamentos de este deporte. Así, consideramos un modelo de regresión de mixtura finita para datos composicionales. La estimación de máxima verosimilitud fue obtenida via un Algoritmo EM. Un estudio de simulación revela que los parámetros son correctamente recuperados. Adicionalmente, los estimadores son asintóticamente insesgados. Considerando dados reales del campeonato de voleyball brasileño nosotros mostramos que el modelo propuesto presenta mejor ajuste que el modelo de regresión usual.

Palabras-clave: algoritmo EM; Datos Composicionales; mixtura finita

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Aitchison, J. (1986), The statistical analysis of compositional data, Chapman & Hall. [ Links ]

Aitchison, J. & Egozcue, J. (2005), 'Compositional data analysis: Where are we and where should we be heading?', Mathematical Geology 37(7), 829-850. [ Links ]

Aitchison, J. & Shen, S. M. (1980), 'Logistic-normal distributions: Some properties and uses', Biometrika 67(2), 261-272. [ Links ]

Bozhkova, A. (2013), 'Playing efficiency of the best volleyball players in the world', Research in Kinesiology 41(1), 92-95. [ Links ]

Brazilian Volleyball Confederation (CBV) (2016), Brazilian Volleyball Confederation (CBV) (2016), . Accessed: 2016-01-20. [ Links ]

Dempster, A., Laird, N. & Rubin, D. (1977), 'Maximum likelihood from incomplete data via the em algorithm', Journal of the Royal Statistical Society. Series B (Methodological) 39(1), 1-38. [ Links ]

Egozcue, J. J., Daunis-I-Estadella, J., Pawlowsky-Glahn, V., Hron, K. & Filzmoser, P. (2011), 'Simplicial regression. the normal model', Journal of Applied Probability and Statistics 6(1), 87-108. [ Links ]

Egozcue, J. J. & Pawlowsky-Glahn (2005), 'Groups of parts and their balances in compositional data analysis', Mathematical Geology 37(4), 795-828. [ Links ]

Egozcue, J. J., Pawlowsky-Glahn, V., Mateu-Figueras, G. & Barceló-Vidal, C. (2003), 'Isometric logratio transformations for compositional data analysis', Mathematical Geology 35, 279-300. [ Links ]

Faria, S. & Soromenho, G. (2010), 'Fitting mixtures of linear regressions', Journal of Statistical Computation and Simulation 80(2), 201-225. [ Links ]

Hron, K., Filzmoser, P. & Thompson, K. (2012), 'Linear regression with compositional explanatory variables', Journal of Applied Statistics 39(5), 1115-1128. [ Links ]

McLachlan, G. J. & Peel, D. (2000), Finite Mixture Models, Wiley series in probability and statistics, Wiley & Sons, New York. [ Links ]

Migon, H. S., Gamerman, D. & Louzada, F. (2014), Statistical Inference: An Integrated Approach, Chapman & Hall/CRC, London. [ Links ]

Miljkovic, T., Shaik, S. & Miljkovic, D. (2016), 'Redefining standards for body mass index of the us population based on BRFSS data using mixtures', Journal of Applied Statistics pp. 1-15. * [ Links ]

Pawlowsky Glahn, V., Egozcue, J. J. & Tolosana-Delgado, R. (2015), Modeling and analysis of compositional data, John Wiley & Sons. [ Links ]

Pena, J., Guerra, J. R., Busca, B. & Serra, N. (2013), 'Which skills and factors better predict winning and losing in high-level men's volleyball?', Journal of Strength and Conditioning Research 27(9), 2487-2493. [ Links ]

Quandt, R. & Ramsey, J. (1978), 'Estimating mixtures of normal distributions and switching regression', Journal of American Statistical Association 73, 730-738. [ Links ]

R Development Core Team (2013), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria. *http://www.R-project.orgLinks ]

Van Den Boogaart, K. G. & Tolosana-Delgado, R. (2013), Analyzing compositional data with R, Springer. [ Links ]

Received: February 2017; Accepted: September 2017

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