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Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics

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  • Cancho, Vicente G.
  • Dey, Dipak K.
  • Lachos, Victor H.
  • Andrade, Marinho G.

Abstract

The purpose of this paper is to develop a Bayesian analysis for nonlinear regression models under scale mixtures of skew-normal distributions. This novel class of models provides a useful generalization of the symmetrical nonlinear regression models since the error distributions cover both skewness and heavy-tailed distributions such as the skew-t, skew-slash and the skew-contaminated normal distributions. The main advantage of these class of distributions is that they have a nice hierarchical representation that allows the implementation of Markov chain Monte Carlo (MCMC) methods to simulate samples from the joint posterior distribution. In order to examine the robust aspects of this flexible class, against outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. Further, some discussions on the model selection criteria are given. The newly developed procedures are illustrated considering two simulations study, and a real data previously analyzed under normal and skew-normal nonlinear regression models.

Suggested Citation

  • Cancho, Vicente G. & Dey, Dipak K. & Lachos, Victor H. & Andrade, Marinho G., 2011. "Bayesian nonlinear regression models with scale mixtures of skew-normal distributions: Estimation and case influence diagnostics," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 588-602, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:588-602
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    References listed on IDEAS

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    1. Hyunsoon Cho & Joseph G. Ibrahim & Debajyoti Sinha & Hongtu Zhu, 2009. "Bayesian Case Influence Diagnostics for Survival Models," Biometrics, The International Biometric Society, vol. 65(1), pages 116-124, March.
    2. Jara, Alejandro & Quintana, Fernando & San Marti­n, Ernesto, 2008. "Linear mixed models with skew-elliptical distributions: A Bayesian approach," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 5033-5045, July.
    3. Lee, Sik-Yum & Xu, Liang, 2004. "Influence analyses of nonlinear mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 321-341, March.
    4. Adelchi Azzalini & Marc G. Genton, 2008. "Robust Likelihood Methods Based on the Skew‐t and Related Distributions," International Statistical Review, International Statistical Institute, vol. 76(1), pages 106-129, April.
    5. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    6. Xie, Feng-Chang & Lin, Jin-Guan & Wei, Bo-Cheng, 2009. "Diagnostics for skew-normal nonlinear regression models with AR(1) errors," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4403-4416, October.
    7. Vanegas, Luis Hernando & Cysneiros, Francisco José A., 2010. "Assessment of diagnostic procedures in symmetrical nonlinear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 54(4), pages 1002-1016, April.
    8. Xie, Feng-Chang & Wei, Bo-Cheng & Lin, Jin-Guan, 2009. "Homogeneity diagnostics for skew-normal nonlinear regression models," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 821-827, March.
    9. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    10. Branco, Márcia D. & Dey, Dipak K., 2001. "A General Class of Multivariate Skew-Elliptical Distributions," Journal of Multivariate Analysis, Elsevier, vol. 79(1), pages 99-113, October.
    11. Cysneiros, Francisco José A. & Vanegas, Luis Hernando, 2008. "Residuals and their statistical properties in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 78(18), pages 3269-3273, December.
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    Cited by:

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    2. Matthew Heiner & Athanasios Kottas, 2022. "Autoregressive density modeling with the Gaussian process mixture transition distribution," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(2), pages 157-177, March.
    3. Vicente G. Cancho & Gladys D. C. Barriga & Gauss M. Cordeiro & Edwin M. M. Ortega & Adriano K. Suzuki, 2021. "Bayesian survival model induced by frailty for lifetime with long‐term survivors," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(3), pages 299-323, August.
    4. Liu, Baisen & Wang, Liangliang & Nie, Yunlong & Cao, Jiguo, 2019. "Bayesian inference of mixed-effects ordinary differential equations models using heavy-tailed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 137(C), pages 233-246.
    5. Zareifard, Hamid & Jafari Khaledi, Majid, 2013. "Non-Gaussian modeling of spatial data using scale mixing of a unified skew Gaussian process," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 16-28.

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