Variance Component Estimation

This page contains a collection of papers related to estimation of variance components. The techniques developed in this area are being used to infer both pedigree and genome-based heritabilities of complex traits.

• HO Hartley and JNK Rao. (1967). Maximum-likelihood estimation for the mixed analysis of variance model. Biometrika. 54:93-108.
  Discussion on a consistency and asymptotic efficiency of ML in the pre REML era.

• HD Patterson and R Thompson. (1971). Recovery of inter-block information when block sizes are unequal. Biometrika. 58:545-554.
  This is a seminal paper describing REML. REML accounts for loss of degrees of freedom arised in estimating fixed effects.

• DA Harville. (1977). Maximum likelihood approaches to variance component estimation and to related problems. Journal of the American Statistical Association. 72:320-338.
  A comprehensive review of ML and REML to variance component estimation.

• DL Johnson and R Thompson. (1995). Restricted Maximum Likelihood Estimation of Variance Components for Univariate Animal Models Using Sparse Matrix Techniques and Average information. J Dairy Sci. 78:449–456.
  AIREML has been proposed in this paper.

• AR Gilmour et al. (1995). Average Information REML: An Efficient Algorithm for Variance Parameter Estimation in Linear Mixed Models. Biometrics. 51:1440-1450.
  Another paper regarding AIREML.

• J Jensen et al. (1997). Residual maximum likelihood estimation of (co)variance components in multivariate mixed linear models using average information. Journal of the Indian Society of Agricultural Statistics. 49:215-236.
  Another paper regarding AIREML.

• A Hofer. (1998). Variance component estimation in animal breeding: a review. J Anim. Breed. 115:247-265.
  A review of REML in animal breeding.

• R Thompson et al. (2005). Estimation of quantitative genetic parameters. Philos Trans R Soc Lond B Biol Sci. 360:1469-1477.
  A review of variance component estimation applied to the animal breeding field.

• R Thompson. (2008). Estimation of quantitative genetic parameters. Philos Trans R Soc Lond B Biol Sci. 360:679-686.
  An updated review of R Thompson et al. (2005).