27. REML Estimation of Genetic Variances
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since 17 October 1995 
Updated notes
Shayle Searle has just published some excellent notes (around 250 pages) that are a mathematical supplement to Henderson's classic book Applications of linear models in animal breeding. These are rather detailed and are quite informative.
Dr. L. R. Schaeffer (Department of Animal & Poultry Science, University of Guelph, Ontario) has an outstanding set on notes on advanced topics in
Animal Models , which has much on variance component estimation.
Dr. Schaeffer also has an excellent set of notes on
historical
approaches to variance component estimation. We did not discuss many of these (Henderson's Methods 14, MIVQUE, Method R )
as they are not longer widely used, but are still occasionally seen in the literature.
Notes from
Jim Fry on using
SAS software to perform
Restricted Maximum Likelihood (REML) Analysis of QuantitativeGenetic Data.
 Programs for REML Analysis of Nested HalfSib Designs
Programs
 List of Pedigree Drawing Programs

DFREML is a suite of programs by
Karin Meyer (University of New England, Armidale, NSW, Australia) to estimate (co)variance components and genetic parameters for normally distributed traits by Restricted Maximum Likelihood, using a derivativefree algorithm. Analysis is carried out fitting a mixed linear model with a random effect for the additive genetic merit of each animal (the socalled "animal model"),
allowing for some additional random effects.

VCE 4 a suite program distributed by Eildert Groeneveld (
Institut fuer Tierzucht und Tierverhalten Forschungsanstalt fuer Landwirtschaft
 Institute of Animal Husbandry and Animal Ethology Federal Agricultural Research Centre) for Multivariate Variance Component Estimation in general pedigrees, using REML, MonteCarlo EM and Gibbs sampling.

Quercus is a suite of programs by
Ruth G.
Shaw and Frank H. Shaw (University of Minnesota) for the analysis of quantitative genetic data
by maximum likelihood. The programs
perform ML or REML on a two generation pedigree with multivariate
phenotypic observations and fixed effects. Up to six variance
components including additive genetic, dominance, maternal, paternal,
and residual (and their covariances in the multivariate case) can be
calculated. The MLE can be constrained to satisfy feasibility
requirements or for hypothesis testing. A program is also
included which will maximize the likelihood while constraining
the additive covariance component matrices of two unrelated populations
to be the same.

MTGSAM,
Multiple Trait Gibbs Sampler for Animal Models, is a set of Fortran programs for Gibbs sampling in animal models. The programs support a flexible set of multiple trait models; the programs support the same model options as the MTDFREML programs. The programs generate the Gibbs sampling information and the posterior mean estimates for a variety
of parameters including (co)variance components, heritabilities, and
correlations. The programs were developed by Curt Van Tassell at the USDA Meat Animal Research Center and the University of Nebraska.

MTDFREML,
Multiple Trait Derivative Free REstricted Maximum Likelihood, is a flexible set of FORTRAN programs which can be used to
estimate variance components using a derivative free restricted maximum
likelihood algorithm. The programs were developed by Keith Boldman, Lisa
Kriese, Dale Van Vleck, Curt Van Tassell, and Steve Kachman at the USDA
Meat Animal Research Center and the University of Nebraska. The programs
are designed to be used with animal breeding data where an animal genetic
effect is used for each trait, however it is often straightforward to apply
the programs to nonanimal breeding data. The programs can handle an arbitrary number of fixed effects, uncorrelated random effects and covariates for a number of traits. The program also generates BLUP solutions to the mixed model equations, contrasts of solutions, prediction error variances of solutions and contrasts, and calculates expected values of solutions.
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Created 25 February 1995, last updated 8 March 2000
Bruce Walsh. jbwalsh@u.arizona.edu .
Comments welcome.