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Estimation of breeding values for mean and dispersion, their variance and correlation using double hierarchical generalized linear models

  • M. FELLEKI (a1) (a2), D. LEE (a3), Y. LEE (a3), A. R. GILMOUR (a4) and L. RÖNNEGÅRD (a1) (a2)...
Summary

The possibility of breeding for uniform individuals by selecting animals expressing a small response to environment has been studied extensively in animal breeding. Bayesian methods for fitting models with genetic components in the residual variance have been developed for this purpose, but have limitations due to the computational demands. We use the hierarchical (h)-likelihood from the theory of double hierarchical generalized linear models (DHGLM) to derive an estimation algorithm that is computationally feasible for large datasets. Random effects for both the mean and residual variance parts of the model are estimated together with their variance/covariance components. An important feature of the algorithm is that it can fit a correlation between the random effects for mean and variance. An h-likelihood estimator is implemented in the R software and an iterative reweighted least square (IRWLS) approximation of the h-likelihood is implemented using ASReml. The difference in variance component estimates between the two implementations is investigated, as well as the potential bias of the methods, using simulations. IRWLS gives the same results as h-likelihood in simple cases with no severe indication of bias. For more complex cases, only IRWLS could be used, and bias did appear. The IRWLS is applied on the pig litter size data previously analysed by Sorensen & Waagepetersen (2003) using Bayesian methodology. The estimates we obtained by using IRWLS are similar to theirs, with the estimated correlation between the random genetic effects being −0·52 for IRWLS and −0·62 in Sorensen & Waagepetersen (2003).

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Corresponding author
*Corresponding author: School of Technology and Business Studies, Dalarna University, SE-79188 Falun, Sweden. Tel: +46(0)23 77 82 82. E-mail: mfl@du.se
References
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Cardoso, F. F., Rosa, G. J. M. & Tempelman, R. J. (2005). Multiple-breed genetic inference using heavy-tailed structural models for heterogeneous residual variances. Journal of Animal Science 83, 17661779.
del Castillo, J. & Lee, Y. (2008). Glm-methods for volatility models. Statistical Modelling 8, 263283.
Gilmour, A. R. (2010). ASReml 3.1 alpha version. Available at http://www.mmontap.org/downloads (accessed 8 December 2010).
Hill, W. G. (1984). On selection among groups with heterogeneous variance. Animal Production 39, 473477.
Hill, W. G. & Mulder, H. A. (2010). Genetic analysis of environmental variation. Genetics Research 92, 381395.
Hill, W. G. & Zhang, X. S. (2004). Effects on phenotypic variability of directional selection arising through genetic differences in residual variability. Genetics Research 83, 121132.
Hoaglin, D. C. & Welsch, R. E. (1978). The hat matrix in regression and anova. American Statistician 32, 1722.
Kizilkaya, K. & Tempelman, R. J. (2005). A general approach to mixed effects modeling of residual variances in generalized linear mixed models. Genetics Selection Evolution 37, 3156.
Lee, Y. & Nelder, J. A. (1996). Hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology) 58, 619678.
Lee, Y. & Nelder, J. A. (2001). Hierarchical generalised linear models: a synthesis of generalized linear models, random-effect models and structured dispersions. Biometrika 88, 9871006.
Lee, Y. & Nelder, J. A. (2006). Double hierarchical generalized linear models (with discussion). Journal of the Royal Statistical Society: Series C (Applied Statistics) 55, 139185.
Lee, Y., Nelder, J. A. & Pawitan, Y. (2006). Generalized Linear Models with Random Effects:Unified Analysis via H-likelihood. Boca Raton, FL: Chapman & Hall/CRC.
Magnus, J. R. & Neudecker, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics, rev. edn. Chichester: John Wiley & Sons.
McCullagh, P. & Nelder, J. A. (1989). Generalized Linear Models, 2nd edn. London: Chapman & Hall.
Meuwissen, T. H. E., de Jong, G. & Engel, B. (1996). Joint estimation of breeding values and heterogeneous variances of large data files. Journal of Dairy Science 79, 310316.
Molas, M. & Lesaffre, E. (2011). Hierarchical generalized linear models: The R package HGLMMM. Journal of Statistical Software 39(13), 120.
Mulder, H. A., Bijma, P. & Hill, W. G. (2007). Prediction of breeding values and selection response with genetic heterogeneity of environmental variance. Genetics 175, 18951910.
Mulder, H. A., Hill, W. G., Vereijken, A. & Veerkamp, R. F. (2009). Estimation of genetic variation in residual variance in female and male broiler chickens. Animal 3, 16731680.
Noh, M. & Lee, Y. (2007). REML estimation for binary data in GLMMs. Journal of Multivariate Analysis 98, 896915.
Rönnegård, L., Felleki, M., Fikse, F., Mulder, H. A. & Strandberg, E. (2010). Genetic heterogeneity of residual variance – estimation of variance components using double hierarchical generalized linear models. Genetics Selection Evolution 42(8), 110.
Rönnegård, L., Shen, X. & Alam, M. (2010). HGLM: a package for fitting hierarchical generalized linear models. The R Journal 2, 2028.
SanCristobal-Gaudy, M., Elsen, J. M., Bodin, L. & Chevalet, C. (1998). Prediction of the response to a selection for canalisation of a continuous trait in animal breeding. Genetics Selection Evolution 30, 423451.
Sorensen, D. & Waagepetersen, R. (2003). Normal linear models with genetically structured residual variance heterogeneity: a case study. Genetics Research 82, 207222.
Wolc, A., White, I. M. S., Avendano, S. & Hill, W. G. (2009). Genetic variability in residual variation of body weight and conformation scores in broiler chickens. Poultry Science 88, 11561161.
Yang, Y., Christensen, O. F. & Sorensen, D. (2011). Analysis of a genetically structured variance heterogeneity model using the Box–Cox transformation. Genetics Research 93, 3346.
Yang, Y., Schön, C.-C. & Sorensen, D. (2012). The genetics of environmental variation of dry matter grain yield in maize. Genetics Research 94, 113119.
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Genetics Research
  • ISSN: 0016-6723
  • EISSN: 1469-5073
  • URL: /core/journals/genetics-research
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