Closed-form approximations to the REML estimator of a variance ratio (or heritability) in a mixed linear model

Brent D Burch, Ian R. Harris

Research output: Contribution to journalArticle

6 Scopus citations


In this article, we estimate heritability or intraclass correlation in a mixed linear model having two sources of variation. In most applications, the commonly used restricted maximum likelihood (REML) estimator can only be obtained via an iterative approach. In some cases, the algorithm used to compute REML estimates may be slow or may even fail to converge. We develop a set of closed-form approximations to the REML estimator, and the performance of these estimators is compared with that of the REML estimator. We provide guidelines regarding how to choose the estimator that best approximates the REML estimator. Examples presented in the article suggest that the closed-form estimators compete with and, in some cases, outperform the REML estimator.

Original languageEnglish (US)
Pages (from-to)1148-1156
Number of pages9
Issue number4
StatePublished - 2001



  • Asymptotic relative efficiency
  • Intraclass correlation coefficient
  • Variance components

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Public Health, Environmental and Occupational Health
  • Agricultural and Biological Sciences (miscellaneous)
  • Applied Mathematics
  • Statistics and Probability

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