Monte Carlo estimation of mixed models for large complex pedigrees

In human quantitative genetics, computational complexity restricts the current methods for estimation of mixed models that include major gene effects to data on small pedigrees. However, large complex pedigrees are not uncommon in practice. Also, large pedigrees tend to provide more information on genetic transmission and are more genetically homogeneous than a pooled sample of many nuclear families. We present a Monte Carlo method, using jointly the EM algorithm and the Gibbs sampler, for estimation of mixed models. The approach also provides a Monte Carlo estimate of the asymptotic variance-covariance matrix of the parameters. The methods are conceptually simple, easy to implement, and can handle multiple heritable/nonheritable random components. A numerical example is given to illustrate the methods.