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I Misztal - One of the best experts on this subject based on the ideXlab platform.
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bias in heritability estimates from genomic Restricted Maximum Likelihood methods under different genotyping strategies
Journal of Animal Breeding and Genetics, 2019Co-Authors: Alberto Cesarani, Ivan Pocrnic, Nicolo Pietro Paolo Macciotta, B O Fragomeni, I Misztal, Daniela LourencoAbstract:We investigated the effects of different strategies for genotyping populations on variance components and heritabilities estimated with an animal model under Restricted Maximum Likelihood (REML), genomic REML (GREML), and single-step GREML (ssGREML). A population with 10 generations was simulated. Animals from the last one, two or three generations were genotyped with 45,116 SNP evenly distributed on 27 chromosomes. Animals to be genotyped were chosen randomly or based on EBV. Each scenario was replicated five times. A single trait was simulated with three heritability levels (low, moderate, high). Phenotypes were simulated for only females to mimic dairy sheep and also for both sexes to mimic meat sheep. Variance component estimates from genomic data and phenotypes for one or two generations were more biased than from three generations. Estimates in the scenario without selection were the most accurate across heritability levels and methods. When selection was present in the simulations, the best option was to use genotypes of randomly selected animals. For selective genotyping, heritabilities from GREML were more biased compared to those estimated by ssGREML, because ssGREML was less affected by selective or limited genotyping.
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the empirical bias of estimates by Restricted Maximum Likelihood bayesian method and method r under selection for additive maternal and dominance models
Journal of Animal Science, 2001Co-Authors: M Duangjinda, I Misztal, J K Bertrand, S TsurutaAbstract:Bayesian analysis via Gibbs sampling, Restricted Maximum Likelihood (REML), and Method R were used to estimate variance components for several models of simulated data. Four simulated data sets that included direct genetic effects and different combinations of maternal, permanent environmental, and dominance effects were used. Parents were selected randomly, on phenotype across or within contemporary groups, or on BLUP of genetic value. Estimates by Bayesian analysis and REML were always empirically unbiased in large data sets. Estimates by Method R were biased only with phenotypic selection across contemporary groups; estimates of the additive variance were biased upward, and all the other estimates were biased downward. No empirical bias was observed for Method R under selection within contemporary groups or in data without contemporary group effects. The bias of Method R estimates in small data sets was evaluated using a simple direct additive model. Method R gave biased estimates in small data sets in all types of selection except BLUP. In populations where the selection is based on BLUP of genetic value or where phenotypic selection is practiced mostly within contemporary groups, estimates by Method R are likely to be unbiased. In this case, Method R is an alternative to single-trait REML and Bayesian analysis for analyses of large data sets when the other methods are too expensive to apply.
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estimation of co variance function coefficients for test day yield with a expectation maximization Restricted Maximum Likelihood algorithm
Journal of Dairy Science, 1999Co-Authors: Nicolas Gengler, A Tijani, G R Wiggans, I MisztalAbstract:Abstract Coefficients for (co)variance functions were obtained via random regression models using the expectation-maximization REML algorithm. Data included milk, fat, and protein yields from 176,495 test days of 22,943 first lactation Holstein cows that calved in Pennsylvania and Wisconsin from 1990 through 1996. Three approximately equal-sized data sets were created: one for Pennsylvania and two for Wisconsin. Random regressions were on third order Legendre polynomials. Genetic and permanent environmental (co)variances each were described by three coefficients. The model contained a fixed effect for age, season, and lactation stage rather than a fixed regression on days in milk. Fixed contemporary groups were based on herd, test day, and milking frequency. The coefficient matrices were dense and included around 70,000 equations. Estimated (co)variance function coefficients, as well as the heritabilities and correlations computed from them, were quite variable across data sets. Heritabilities were at a minimum (0.14 for milk and fat and 0.13 for protein) around peak yield, increased to a Maximum (0.24 for milk and protein and 0.21 for fat) around the eighth month in milk, and declined slightly afterwards. Genetic correlations between early and late lactation were low (values of
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approximation of estimates of co variance components with multiple trait Restricted Maximum Likelihood by multiple diagonalization for more than one random effect
Journal of Dairy Science, 1995Co-Authors: I Misztal, K Weigel, T J LawlorAbstract:Abstract Canonical transformation for REML can be applied to models with several random effects by simultaneously diagonalizing (co)variance matrices for all random effects. This procedure is an approximation when matrices cannot be diagonalized completely. The level of the approximation was studied with simulated data by comparing multiple diagonalization and exact REML estimates. For a range of diagonalization levels, the error of the estimates was 2 to 10 times lower than the fraction of non-diagonalizable (co)variances because 57 to 91% of these variances were recovered after the backtransformation step. To determine whether REML by multiple diagonalization is successful with real data, a study used 98,113 records of 44,765 Holstein cows for 14 conformation traits. Effects included in the model were herd classification, animal with unknown parent groups, and permanent environmental effects. Estimates of (co)variance components were on average 5% higher for type compared with estimates from an earlier analysis using only first records, but the estimate for udder cleft increased 2.4 times. Correlations for the permanent environmental effect were within .1 of genetic correlations. Multitrait REML by multiple diagonalization provides accurate multiple-trait estimates for repeatability models more efficiently than general model REML.
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sparse matrix inversion for Restricted Maximum Likelihood estimation of variance components by expectation maximization
Journal of Dairy Science, 1993Co-Authors: I Misztal, Miguel PerezencisoAbstract:Abstract Expectation-maximization algorithms for REML estimation of variance components are regarded as expensive because they involve computation of the inverse of the coefficient matrix of the mixed model equations. The derivative-free algorithms are viewed as a less expensive alternative because they require computation of the determinant of the same matrix but not the inverse. Unfortunately, these algorithms have poorer numerical properties. We show that computing the sparse matrix inverse, used for any round of an expectation-maximization algorithm, is only about three times as expensive as computation of the determinant, used for each step of a derivative-free algorithm. Thus, the total computational costs of the expectation-maximization and derivative-free algorithms are comparable, and the difference in cost will depend mainly on the number of iterations needed to attain convergence.
K Meyer - One of the best experts on this subject based on the ideXlab platform.
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parameter expansion for estimation of reduced rank covariance matrices open access publication
Genetics Selection Evolution, 2008Co-Authors: K MeyerAbstract:Parameter expanded and standard expectation maximisation algorithms are described for reduced rank estimation of covariance matrices by Restricted Maximum Likelihood, fitting the leading principal components only. Convergence behaviour of these algorithms is examined for several examples and contrasted to that of the average information algorithm, and implications for practical analyses are discussed. It is shown that expectation maximisation type algorithms are readily adapted to reduced rank estimation and converge reliably. However, as is well known for the full rank case, the convergence is linear and thus slow. Hence, these algorithms are most useful in combination with the quadratically convergent average information algorithm, in particular in the initial stages of an iterative solution scheme.
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genetic principal components for live ultrasound scan traits of angus cattle
Animal Science, 2005Co-Authors: K MeyerAbstract:Multivariate Restricted Maximum Likelihood analyses were carried out for a large data set comprising records for eye-muscle area, fat depth at the 12/13th rib and the rump P8 site, and percentage intramuscular fat, recorded via live ultrasound scanning of Australian Angus cattle. Records on heifers or steers were treated as separate traits from those on bulls. Reduced rank estimates of the genetic covariance matrix were obtained by Restricted Maximum Likelihood, estimating the leading three, four, five, six, seven and all eight principal components and these were contrasted with estimates from pooled bivariate analyses. Results from analyses fitting five or six genetic principal components agreed closely with estimates from bivariate and eight-variate analyses and literature results. Heritabilities and variances for ‘fatness’ traits measured on heifers or steers were higher than those recorded for bulls, and genetic correlations were less than unity for the same trait measured in different sexes. Eye-muscle area showed little association with the other traits. Reduced rank estimation decreased computational requirements of multivariate analyses dramatically, in essence corresponding to those of an m-variate analysis for m principal components considered. Five or six principal components appeared to be necessary to model genetic covariances adequately. The first three of these components then explained about 97% of the genetic variation among the eight traits. A simulation study showed that errors in reduced rank estimates of the genetic covariance matrix were small, once three or more principal components from analyses fitting five or more components were used in constructing the estimates. Similarly, accuracy of genetic evaluation for the eight traits using the first four components was only slightly less than that using all principal components. Results suggest that reduced rank estimation and prediction is applicable for the eight scan traits considered. The leading three to four principal components sufficed to describe the bulk of genetic variation between animals. However, five or more principal components needed to be considered in estimating covariance matrices and the ‘loadings’ of the original traits to the principal components.
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direct estimation of genetic principal components simplified analysis of complex phenotypes
Genetics, 2004Co-Authors: Mark Kirkpatrick, K MeyerAbstract:Estimating the genetic and environmental variances for multivariate and function-valued phenotypes poses problems for estimation and interpretation. Even when the phenotype of interest has a large number of dimensions, most variation is typically associated with a small number of principal components (eigen-vectors or eigenfunctions). We propose an approach that directly estimates these leading principal components; these then give estimates for the covariance matrices (or functions). Direct estimation of the principal components reduces the number of parameters to be estimated, uses the data efficiently, and provides the basis for new estimation algorithms. We develop these concepts for both multivariate and function-valued phenotypes and illustrate their application in the Restricted Maximum-Likelihood framework.
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estimates of genetic correlations between live ultrasound scan traits and days to calving in hereford cattle
50 years of DNA: Proceedings of the Fifteenth Conference Association for the Advancement of Animal Breeding and Genetics Melbourne Australia 7-11 July, 2003Co-Authors: K Meyer, D J JohnstonAbstract:Restricted Maximum Likelihood estimates of genetic correlations between between live ultrasound scan measurements and days to calving were obtained from bivariate analyses. Scan traits considered were fat depth at the 12/13−th rib, P8 fat depth, percentage intramuscular fat and eye muscle area, treating records for heifers or steers and bulls as separate traits. Analyses were carried out including all days to calving records, and considering the subset of cows only which had a ’complete sequence’ of records, beginning with a first mating record. Heritability estimates for days to calving were low, about 3% with a repeatability of 18%. Estimates of genetic correlations were low to moderate, and consistently negative for fat depth measurements, i.e. animals with a higher genetic potential for fat deposition tended to have better reproductive performance.
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rrgibbs a program for simple random regression analyses via gibbs sampling
Proceedings of the 7th World Congress on Genetics Applied to Livestock Production Montpellier France August 2002. Session 28., 2002Co-Authors: K MeyerAbstract:INTRODUCTION Random regression (RR) models are a popular choice for the analysis of longitudinal data or ’repeated’ records. Programs for estimation of the corresponding covariance functions via Restricted Maximum Likelihood (REML) are available (e.g. Gilmour et al., 1999; Meyer, 1998), but high computational demands of REML analyses severely limit their feasibility. Bayesian analysis using Gibbs sampling provides an alternative which is markedly simpler to implement and requires considerably less memory than REML, thus facilitating large scale analyses.
Karin Meyer - One of the best experts on this subject based on the ideXlab platform.
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WOMBAT A tool for mixed model analyses in quantitative genetics by Restricted Maximum Likelihood （REML）
Journal of Zhejiang University. Science. B, 2007Co-Authors: Karin MeyerAbstract:WOMBAT is a software package for quantitative genetic analyses of continuous traits, fitting a linear, mixed model; estimates of covariance components and the resulting genetic parameters are obtained by Restricted Maximum Likelihood. A wide range of models, comprising numerous traits, multiple fixed and random effects, selected genetic covariance structures, random regression models and reduced rank estimation are accommodated. WOMBAT employs up-to-date numerical and computational methods. Together with the use of efficient compilers, this generates fast executable programs, suitable for large scale analyses. Use of WOMBAT is illustrated for a bivariate analysis. The package consists of the executable program, available for LINUX and WINDOWS environments, manual and a set of worked example, and can be downloaded free of charge from http://agbu.une.edu.au/~kmeyer/wombat.html
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Restricted Maximum Likelihood estimation of genetic principal components and smoothed covariance matrices
Genetics Selection Evolution, 2005Co-Authors: Karin Meyer, Mark KirkpatrickAbstract:Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from $k(k+1)/2$ to $m(2k-m+1)/2$ for $k$ effects and $m$ principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via Restricted Maximum Likelihood using derivatives of the Likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
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Estimating genetic covariance functions assuming a parametric correlation structure for environmental effects
Genetics Selection Evolution, 2001Co-Authors: Karin MeyerAbstract:A random regression model for the analysis of "repeated" records in animal breeding is described which combines a random regression approach for additive genetic and other random effects with the assumption of a parametric correlation structure for within animal covariances. Both stationary and non-stationary correlation models involving a small number of parameters are considered. Heterogeneity in within animal variances is modelled through polynomial variance functions. Estimation of parameters describing the dispersion structure of such model by Restricted Maximum Likelihood via an "average information" algorithm is outlined. An application to mature weight records of beef cow is given, and results are contrasted to those from analyses fitting sets of random regression coefficients for permanent environmental effects.
R Thompson - One of the best experts on this subject based on the ideXlab platform.
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employing a monte carlo algorithm in expectation maximization Restricted Maximum Likelihood estimation of the linear mixed model
Journal of Animal Breeding and Genetics, 2012Co-Authors: Kaarina Matilainen, Esa A Mantysaari, Martin Lidauer, Ismo Stranden, R ThompsonAbstract:Summary Multiple-trait and random regression models have multiplied the number of equations needed for the estimation of variance components. To avoid inversion or decomposition of a large coefficient matrix, we propose estimation of variance components by Monte Carlo expectation maximization Restricted Maximum Likelihood (MC EM REML) for multiple-trait linear mixed models. Implementation is based on full-model sampling for calculating the prediction error variances required for EM REML. Performance of the analytical and the MC EM REML algorithm was compared using a simulated and a field data set. For field data, results from both algorithms corresponded well even with one MC sample within an MC EM REML round. The magnitude of the standard errors of estimated prediction error variances depended on the formula used to calculate them and on the MC sample size within an MC EM REML round. Sampling variation in MC EM REML did not impair the convergence behaviour of the solutions compared with analytical EM REML analysis. A convergence criterion that takes into account the sampling variation was developed to monitor convergence for the MC EM REML algorithm. For the field data set, MC EM REML proved far superior to analytical EM REML both in computing time and in memory need.
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individual animal model estimates of genetic parameters for reproduction traits of landrace pigs performance tested in a commercial nucleus herd
Animal Science, 1997Co-Authors: R E Crump, R Thompson, Chris Haley, J MercerAbstract:Individual animal model Restricted Maximum Likelihood was used to estimate genetic parameters for number of piglets born, number born alive, total litter weight, average piglet weight and gestation length for a commercial Landrace population undergoing selection for performance test traits. Estimates of heritabilities and repeatabilities (around 0·1 and 0·2, respectively) for number born and number born alive are in line with other published results. Heritabilities around 0·2 and repeatabilities around 0·3 were observed for average piglet weight and gestation length, while for litter weight these values were between 0·11 and 0·15 for heritabilities and around 0·2 for repeatabilities. Estimates of common litter of birth effects and maternal genetic effects were very low across all traits analysed.
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average information reml an efficient algorithm for variance parameter estimation in linear mixed models
Biometrics, 1995Co-Authors: A R Gilmour, R Thompson, Brian R CullisAbstract:A strategy of using an average information matrix is shown to be computationally convenient and efficient for estimating variance components by Restricted Maximum Likelihood (REML) in the mixed linear model. Three applications are described. The motivation for the algorithm was the estimation of variance components in the analysis of wheat variety means from 1,071 experiments representing 10 years and 60 locations in New South Wales. We also apply the algorithm to the analysis of designed experiments by incomplete block analysis and spatial analysis of field experiments.
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Restricted Maximum Likelihood estimation of variance components for univariate animal models using sparse matrix techniques and average information
Journal of Dairy Science, 1995Co-Authors: D L Johnson, R ThompsonAbstract:An algorithm is described to estimate variance components for a univariate animal model using REML. Sparse matrix techniques are employed to calculate those elements of the inverse of the coefficient matrix required for the first derivatives of the Likelihood. Residuals and fitted values for random effects can be used to derive additional right-hand sides for which the mixed model equations can be repeatedly solved in turn to yield an average of the observed and expected second derivatives of the Likelihood function. This Newton method, using average information, generally converges in 40 iterations. Although the time required per iteration is two to three times greater than that required per Likelihood evaluation for derivative-free methods, the total time to convergence is generally much less. An example of a complex model, involving correlated direct and maternal genetic effects, and an additional uncorrelated random effect, indicates that REML, using average information, is about five times faster than a derivativefree algorithm, using the simplex method, which is about three times faster than an expectation-maximization algorithm.
Mark Kirkpatrick - One of the best experts on this subject based on the ideXlab platform.
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Restricted Maximum Likelihood estimation of genetic principal components and smoothed covariance matrices
Genetics Selection Evolution, 2005Co-Authors: Karin Meyer, Mark KirkpatrickAbstract:Principal component analysis is a widely used 'dimension reduction' technique, albeit generally at a phenotypic level. It is shown that we can estimate genetic principal components directly through a simple reparameterisation of the usual linear, mixed model. This is applicable to any analysis fitting multiple, correlated genetic effects, whether effects for individual traits or sets of random regression coefficients to model trajectories. Depending on the magnitude of genetic correlation, a subset of the principal component generally suffices to capture the bulk of genetic variation. Corresponding estimates of genetic covariance matrices are more parsimonious, have reduced rank and are smoothed, with the number of parameters required to model the dispersion structure reduced from $k(k+1)/2$ to $m(2k-m+1)/2$ for $k$ effects and $m$ principal components. Estimation of these parameters, the largest eigenvalues and pertaining eigenvectors of the genetic covariance matrix, via Restricted Maximum Likelihood using derivatives of the Likelihood, is described. It is shown that reduced rank estimation can reduce computational requirements of multivariate analyses substantially. An application to the analysis of eight traits recorded via live ultrasound scanning of beef cattle is given.
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direct estimation of genetic principal components simplified analysis of complex phenotypes
Genetics, 2004Co-Authors: Mark Kirkpatrick, K MeyerAbstract:Estimating the genetic and environmental variances for multivariate and function-valued phenotypes poses problems for estimation and interpretation. Even when the phenotype of interest has a large number of dimensions, most variation is typically associated with a small number of principal components (eigen-vectors or eigenfunctions). We propose an approach that directly estimates these leading principal components; these then give estimates for the covariance matrices (or functions). Direct estimation of the principal components reduces the number of parameters to be estimated, uses the data efficiently, and provides the basis for new estimation algorithms. We develop these concepts for both multivariate and function-valued phenotypes and illustrate their application in the Restricted Maximum-Likelihood framework.
