Molecular Breeding

, 35:99 | Cite as

Integrated nested Laplace approximation inference and cross-validation to tune variance components in estimation of breeding value

  • Boby Mathew
  • Jens Léon
  • Mikko J. Sillanpää


The main aim of this study was to compare a number of recently proposed Bayesian and frequentist statistical methods for the estimation of genetic parameters and to apply the cross-validation (CV) approach in order to tune the variance components in simulated and field plant breeding datasets. We were especially interested in whether the CV approach was capable of improving the prediction accuracy of breeding values which have been obtained using the residual (or restricted/reduced) maximum likelihood and Markov chain Monte Carlo estimation tools. We showed that the nonsampling-based Bayesian inference method of integrated nested Laplace approximation (INLA) can be used for rapid and accurate estimation of genetic parameters in linear mixed models with multiple random effects such as additive, dominance, and genotype-by-environment interaction effects. Moreover, we also compared the INLA estimates with results obtained using Markov chain Monte Carlo and restricted maximum likelihood methods. In other studies, K-fold CV is primarily used for comparing method performance; however, here we showed that the K-fold CV method can be used to tune genetic parameters and minimize the prediction error in the estimation of breeding value . We also compared the K-fold CV results with different generalized cross-validation methods which are much faster to compute. Analysis results obtained from field and simulated datasets are presented.


Cross-validation Generalized cross-validation INLA Bayesian analysis Estimation of genetic parameters 



We thank Håvard Rue and Anna Marie Holand for their help with the implementation of our model using the R-INLA package. We also thank Jarrod D. Hadfield for helping us with the use of the MCMCglmm package.

Supplementary material

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Boby Mathew
    • 1
  • Jens Léon
    • 1
  • Mikko J. Sillanpää
    • 2
    • 3
  1. 1.Institute of Crop Science and Resource ConservationUniversity of BonnBonnGermany
  2. 2.Department of Mathematical SciencesUniversity of OuluOuluFinland
  3. 3.Department of Biology and Biocenter OuluUniversity of OuluOuluFinland

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