Using a Laplace approximation to estimate the genetic variance components in animal models

[1] H. Baghishani, H. Rue and M. Mohammadzadeh, On a hybrid data cloning method and its application in generalized linear mixed models, Statist. Comput. 22 (2012), no. 2, 613–597.
[2] B.M. Bolker, M.E. Brooks, C.J. Clark, S.W. Geange, J.R. Poulsen, M.H.H. Stevens and J.S.S. White, Generalized
linear mixed models: a practical guide for ecology and evolution, Trends Ecol. Evol. 24 (2009) no. 3, 127—135.
[3] N.E. Breslow and D.G. Clayton, Approximate inference in generalized linear mixed models, J. Amer. Statist.
Assoc. 88 (1993), no. 421, 9-25.
[4] E. Evangelou, Z. Zhu and R. Smith, Estimation and prediction for spatial generalized linear mixed models using
high order Laplace approximation, J. Statist. Plann. Inference 141 (2011), no. 11, 3564–3577.
[5] J. Guan, W. Wang, Y. Hu, M. Wang, T. Tian, J. Kong, Estimation of genetic parameters for growth trait of
turbot using Bayesian and REML approaches, Acta Oceanologica Sinica 36 (2017), no. 6, 47–51.
[6] F. Hosseini, J. Eidsvik and M. Mohammadzadeh, Approximate Bayesian inference in spatial GLMM with skew
normal Latent variables, Computat. Statist. Data Anal. 55 (2011), no. 4, 1791–1806.
[7] F. Hosseini and M. Mohammadzadeh, Bayesian prediction for spatial GLMM’s with closed skew normal Latent
variables, Aust. New Zealand J. Statist. 54 (2012), 43–62.
[8] F. Hosseini, A new algorithm for estimating the parameters of the spatial generalized linear mixed models, Envir.
Ecol. Statist. 23 (2016), no. 2, 205–217.
[9] F. Hosseini and O. Karimi, Approximate likelihood Inference in Spatial Generalized Linear Mixed Models with
Closed Skew Normal latent Variables, Commun. Statist. Simul. Comput. 49 (2020), no. 1, 121–134.
[10] F. Hosseini and O. Karimi, Approximate composite marginal likelihood inference in spatial generalized linear mixed
models, J. Appl. Statist. 46 (2019), no. 3, 542–558.
[11] D.L. Johnson, and R. Thompson, Restricted maximum likelihood estimation of variance components for univariate
animal models using sparse matrix techniques and average information, J. Dairy Sci. 78 (1995), no. 2, 449–456.
[12] O. Karimi and M. Mohammadzadeh, Bayesian spatial prediction for discrete closed skew Gaussian random field,
Math. Geosci. 43 (2011), no. 5, 565—582.
[13] O. Karimi and M. Mohammadzadeh, Bayesian spatial regression models with closed skew normal correlated errors
and missing observations, Statist. Papers 53 (2012), no. 1, 205—218.
[14] O. Karimi, F. Hosseini and M. Mohammadzadeh, Pairwise likelihood in spatial GLMM with skew normal latent
variables, Proc. 15th Conf. Int. Assoc. Math. Geo. Salzburg, Austria, 2011.
[15] L.E. Kruuk, T.H. Clutton-Brock, J. Slate, J.M. Pemberton, S. Brotherstone and F.E. Guinness, Heritability of
fitness in a wild mammal population, Proc. Nat. Acad. Sci. USA. 97 (2000), no. 2, 698—703.[16] L.E. Kruuk, Estimating genetic parameters in natural populations using the “animal model”, Philos. Trans. R.
Soc. B Biol. Sci. 359 (2004), no. 1446, 873—890.
[17] J.M. Milner, J.M. Pemberton, S. Brotherstone and S.D. Albon, Estimating variance components and heritabilities
in the wild: a case study using the ‘animal model’ approach, J. Evol. Bio. 13 (2000), no. 5, 804—813.
[18] P. McCulloch and J.A. Nelder, Generalized linear models, Chapman and Hall, London, 1989.
[19] F. Pakbaz, F. Hosseini and A. Nematollahi, Modeling additive genetic effects in animal models by closed skew
normal distribution, Commun. Statist. Simul. Comput. 51 (2022), no. 3, 1186–1198.
[20] E. Ruli, N. Sartori and L. Ventura, Improved Laplace approximation for marginal likelihoods, Electron. J. Stat.
10 (2016), no. 2, 3986–4009.
[21] Z. Shun and P. McCullagh,Laplace approximations of high dimensional integrals, J. Royal Statist. Soc. Ser. B 57
(1995), no. 4, 749–760.
[22] M. Torabi, Likelihood inference in generalized linear mixed measurement error models, Comput. Statist. Data
Anal. 57 (2013), no. 1, 549–557.
[23] M. Torabi, Likelihood inference for spatial generalized linear mixed models, Commun. Statist. Simul. Comput. 44
(2015), no. 7, 1692–1701.
[24] T.R. Vaez, F.W. Nicolas and H.W. Raadsma, REML estimates of variance and covariance components for production traits in Australian Merino sheep, using an animal model. 1. Body weight from birth to 22 months, Aust.
J. Agricul. Res. 47 (1996), no. 8, 1235–1249.
[25] B.J. Wilson, F.W. Nicholas, J.W. James, C.M. Wade and P.C. ThomsonEstimated breeding values for Canine
Hip Dysplasia Radiographic Traits in a cohort of Australian German Shepherd Dogs, PLoS One 8 (2013), no. 10,
e77470.
[26] A.J. Wilson, D.W. Coltman, J.M. Pemberton, A.D.J. Overall, K.A. Byrne and L.E.B. Kruuk, Maternal genetic
effects set the potential for evolution in a free-living vertebrate population, J. Evol. Bio. 18 (2005), no. 2, 405—414.
[27] A.J. Wilson, D. Reale, M.N. Clements, M.M. Morrissey, E. Postma, C.A. Walling, L.E. Kruuk and D.H. Nussey,
An ecologist’s guide to the animal model, J. Animal Eco. 79 (2010), no. 1, 13-–26.
[28] H. Zhang, On estimation and prediction for spatial generalized linear mixed models, Biometrics 58 (2002), no. 1,
129-–136.