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Mathematical Medicine and Biology 1991 8(3):171-189; doi:10.1093/imammb/8.3.171
© 1991 by Institute of Mathematics and its Applications
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Monte Carlo Estimation of Variance Component Models for Large Complex Pedigrees

SUN WEI GUO {dagger} and ELIZABETH A. THOMPSON {dagger}{dagger}

University of Washington Seattle, Washington 98195, USA

Variance component models are widely used in animal and plant breeding. In human genetics, they can be used to identify, among other traits associated with the definition of disease, those that have a significant genetic component in their aetiology. In addition, they can be used in genetic counselling. Most of the methods currently proposed for estimating variance component models often involve repeated inversion of large matrices, resulting in intensive computations, large storage requirements, and numerical instability. Consequently, these methods are restricted to data on nuclear families, to small pedigrees, or to designed pedigrees of simple form. In this paper, the authors propose a method for estimating variance component models for large complex pedigrees using jointly the EM algorithm and the Gibbs sampler. The method can handle variance component models with multiple variance components, without the need for repeated inversion of large matrices even on large complex pedigrees. The method is conceptually simple, numerically stable, and easy to implement.

Keywords: EM alogrithm; Gibbs sampler; maternal effect; Monte Carlo; variance component models


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