This paper considers REML (residual or restricted maximum likelihood) estimation for heteroscedastic linear models. An explicit algorithm is given for REML-scoring which yields the REML estimates together with their standard errors and likelihood values. The algorithm includes a Levenberg-Marquardt restricted step modification which ensures that the REML-likelihood increases at each iteration. ...

Abstract The objective of this work was to compare different methods estimate heritability in 30 pigeon pea families from the F3, F4, F5, and F6 generations, for nine variables. experimental design a randomized complete block with three replicates 20 plants per plot. Broad-sense estimated by analysis variance ( A N O V A) [ h 2b-E(MS)], restricted maximum likelihood/best linear unbiased predict...

Estimation of variance components by Monte Carlo (MC) expectation maximization (EM) restricted maximum likelihood (REML) is computationally efficient for large data sets and complex linear mixed effects models. However, efficiency may be lost due to the need for a large number of iterations of the EM algorithm. To decrease the computing time we explored the use of faster converging Newton-type ...

The purpose of this study is to present guidelines in selection of statistical and computing algorithms for variance components estimation when computing involves software packages. For this purpose two major methods are to be considered: residual maximal likelihood (REML) and Bayesian via Gibbs sampling. Expectation-Maximization (EM) REML is regarded as a very stable algorithm that is able to ...

This note derives the variational free energy under the Laplace approximation, with a focus on accounting for additional model complexity induced by increasing the number of model parameters. This is relevant when using the free energy as an approximation to the log-evidence in Bayesian model averaging and selection. By setting restricted maximum likelihood (ReML) in the larger context of varia...

Volumes of official data sets have been increasing rapidly in the genetic evaluation using the Japanese Black routine carcass field data. Therefore, an alternative approach with smaller memory requirement to the current one using the restricted maximum likelihood (REML) and the empirical best linear unbiased prediction (EBLUP) is desired. This study applied a Bayesian analysis using Gibbs sampl...

The research was conducted on 3 844 Polish Merino lamb dams born in 1991-2001, used in 15 flocks from the Pomerania and Kujawy region in Poland. The assessed parameters were the number of lambs born from a dam after lambing (LSB) (1, 2, 3) and the number of lambs reared (LSW) (0, 1, 2, 3). The genetic parameters LSB and LSW were estimated with the use of two methods: Average Information – REML ...

In the numerous forms of analysis of variance (ANOVA) discussed in previous chapters, variance components were estimated by equating observed mean squares to expressions describing their expected values, these being functions of the variance components. ANOVA has the nice feature that the estimators for the variance components are unbiased regardless of whether the data are normally distributed...

BACKGROUND Likelihood-based methods can work poorly when the residuals are not normally distributed and the variances across clusters are heterogeneous. METHOD The performance of two estimation methods, the non-parametric residual bootstrap (RB) and the restricted maximum likelihood (REML) for fitting multilevel models are compared through simulation studies in terms of bias, coverage, and pr...

We explore the estimation of uncertainty in evolutionary parameters using a recently devised approach for resampling entire additive genetic variance-covariance matrices (G). Large-sample theory shows that maximum-likelihood estimates (including restricted maximum likelihood, REML) asymptotically have a multivariate normal distribution, with covariance matrix derived from the inverse of the inf...