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Bayesian non‐parametric conditional copula estimation of twin data

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  • Luciana Dalla Valle
  • Fabrizio Leisen
  • Luca Rossini

Abstract

Several studies on heritability in twins aim at understanding the different contribution of environmental and genetic factors to specific traits. Considering the national merit twin study, our purpose is to analyse correctly the influence of socio‐economic status on the relationship between twins’ cognitive abilities. Our methodology is based on conditional copulas, which enable us to model the effect of a covariate driving the strength of dependence between the main variables. We propose a flexible Bayesian non‐parametric approach for the estimation of conditional copulas, which can model any conditional copula density. Our methodology extends the work of Wu, Wang and Walker in 2015 by introducing dependence from a covariate in an infinite mixture model. Our results suggest that environmental factors are more influential in families with lower socio‐economic position.

Suggested Citation

  • Luciana Dalla Valle & Fabrizio Leisen & Luca Rossini, 2018. "Bayesian non‐parametric conditional copula estimation of twin data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(3), pages 523-548, April.
    • Handle: RePEc:bla:jorssc:v:67:y:2018:i:3:p:523-548
    DOI: 10.1111/rssc.12237
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    References listed on IDEAS

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    1. Emura, Takeshi & Wang, Weijing, 2012. "Nonparametric maximum likelihood estimation for dependent truncation data based on copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 171-188.
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    5. Craiu, V. Radu & Sabeti, Avideh, 2012. "In mixed company: Bayesian inference for bivariate conditional copula models with discrete and continuous outcomes," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 106-120.
    6. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
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    8. Abegaz, Fentaw & Gijbels, Irène & Veraverbeke, Noël, 2012. "Semiparametric estimation of conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 43-73.
    9. Xuelin Huang & Nan Zhang, 2008. "Regression Survival Analysis with an Assumed Copula for Dependent Censoring: A Sensitivity Analysis Approach," Biometrics, The International Biometric Society, vol. 64(4), pages 1090-1099, December.
    10. Xueqin Wang & Xiaobo Guo & Mingguang He & Heping Zhang, 2011. "Statistical Inference in Mixed Models and Analysis of Twin and Family Data," Biometrics, The International Biometric Society, vol. 67(3), pages 987-995, September.
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    Cited by:

    1. Arbel, Julyan & Crispino, Marta & Girard, Stéphane, 2019. "Dependence properties and Bayesian inference for asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 174(C).
    2. Lu Lu & Sujit Ghosh, 2024. "Nonparametric Estimation of Conditional Copula Using Smoothed Checkerboard Bernstein Sieves," Mathematics, MDPI, vol. 12(8), pages 1-17, April.
    3. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    4. Huihui Lin & N. Rao Chaganty, 2021. "Multivariate distributions of correlated binary variables generated by pair-copulas," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-14, December.
    5. Maximilian Coblenz & Simon Holz & Hans‐Jörg Bauer & Oliver Grothe & Rainer Koch, 2020. "Modelling fuel injector spray characteristics in jet engines by using vine copulas," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 863-886, August.
    6. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.

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    More about this item

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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