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Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles

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  • De la Cruz, Rolando

Abstract

Typically, the fundamental assumption in non-linear regression models is the normality of the errors. Even though this model offers great flexibility for modeling these effects, it suffers from the same lack of robustness against departures from distributional assumptions as other statistical models based on the Gaussian distribution. It is of practical interest, therefore, to study non-linear models which are less sensitive to departures from normality, as well as related assumptions. Thus the current methods proposed for linear regression models need to be extended to non-linear regression models. This paper discusses non-linear regression models for longitudinal data with errors that follow a skew-elliptical distribution. Additionally, we discuss Bayesian statistical methods for the classification of observations into two or more groups based on skew-models for non-linear longitudinal profiles. Parameter estimation for a discriminant model that classifies individuals into distinct predefined groups or populations uses appropriate posterior simulation schemes. The methods are illustrated with data from a study involving 173 pregnant women. The main objective in this study is to predict normal versus abnormal pregnancy outcomes from beta human chorionic gonadotropin data available at early stages of pregnancy.

Suggested Citation

  • De la Cruz, Rolando, 2008. "Bayesian non-linear regression models with skew-elliptical errors: Applications to the classification of longitudinal profiles," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 436-449, December.
  • Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:436-449
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    1. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2007. "Model comparison of coordinate-free multivariate skewed distributions with an application to stochastic frontiers," Journal of Econometrics, Elsevier, vol. 137(2), pages 641-673, April.
    2. M. C. Jones & M. J. Faddy, 2003. "A skew extension of the t‐distribution, with applications," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(1), pages 159-174, February.
    3. Jensen, D. R., 1994. "Closure of multivariate t and related distributions," Statistics & Probability Letters, Elsevier, vol. 20(4), pages 307-312, July.
    4. 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.
    5. Fernández, Carmen & Steel, Mark F.J., 2000. "Bayesian Regression Analysis With Scale Mixtures Of Normals," Econometric Theory, Cambridge University Press, vol. 16(1), pages 80-101, February.
    6. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    7. 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.
    8. 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.
    9. Ferreira, Jose T.A.S. & Steel, Mark F.J., 2006. "A Constructive Representation of Univariate Skewed Distributions," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 823-829, June.
    10. Rolando De la Cruz‐Mesía & Fernando A. Quintana & Peter Müller, 2007. "Semiparametric Bayesian classification with longitudinal markers," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(2), pages 119-137, March.
    11. Larry J. Brant & Shan L. Sheng & Christopher H. Morrell & Geert N. Verbeke & Emmanuel Lesaffre & H. Ballentine Carter, 2003. "Screening for prostate cancer by using random‐effects models," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 166(1), pages 51-62, February.
    12. DiCiccio T.J. & Monti A.C., 2004. "Inferential Aspects of the Skew Exponential Power Distribution," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 439-450, January.
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